NEWSLETTER No. 47March 2003

EMS Agenda ................................................................................................. 2

Editorial by Sir John Kingman .................................................................... 3

Executive Committee Meeting ....................................................................... 4

Introducing the Committee ............................................................................ 7

An Answer to the Growth of Mathematical Knowledge? ............................... 9

Interview with Vagn Lundsgaard Hansen .................................................. 15

Interview with D V Anosov .......................................................................... 20

Israel Mathematical Union ......................................................................... 25

Society of Mathematicians, Physicists and Astronomers in Slovenia .......... 26

Problem Corner ........................................................................................... 28

Mathematical Biography ............................................................................. 31

Forthcoming Conferences ............................................................................ 34

Recent Books ............................................................................................... 39

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Published by European Mathematical SocietyISSN 1027 - 488X

The views expressed in this Newsletter are those of the authors and do not necessarilyrepresent those of the EMS or the Editorial team.

NOTICE FOR MATHEMATICAL SOCIETIESLabels for the next issue will be prepared during the second half of May 2003.Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department ofMathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail:makelain@cc.helsinki.fi

INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTERInstitutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat,Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e-mail: (makelain@cc.helsinki.fi). Please include the name and full address (with postal code), tele-phone and fax number (with country code) and e-mail address. The annual subscription fee(including mailing) is 80 euros; an invoice will be sent with a sample copy of the Newsletter.

EDITOR-IN-CHIEFROBIN WILSONDepartment of Pure MathematicsThe Open UniversityMilton Keynes MK7 6AA, UKe-mail: r.j.wilson@open.ac.uk

ASSOCIATE EDITORSVASILE BERINDEDepartment of Mathematics,University of Baia Mare, Romania e-mail: vberinde@univer.ubm.ro KRZYSZTOF CIESIELSKIMathematics Institute Jagiellonian UniversityReymonta 4 30-059 Kraków, Polande-mail: ciesiels@im.uj.edu.plSTEEN MARKVORSENDepartment of Mathematics Technical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: s.markvorsen@mat.dtu.dk

SPECIALIST EDITORSINTERVIEWSSteen Markvorsen [address as above]

SOCIETIESKrzysztof Ciesielski [address as above]

EDUCATIONTony GardinerUniversity of BirminghamBirmingham B15 2TT, UKe-mail: a.d.gardiner@bham.ac.uk

MATHEMATICAL PROBLEMSPaul JaintaWerkvolkstr. 10D-91126 Schwabach, Germanye-mail: PaulJainta@aol.com

ANNIVERSARIESJune Barrow-Green and Jeremy GrayOpen University [address as above]e-mail: j.e.barrow-green@open.ac.ukand j.j.gray@open.ac.uk

CONFERENCESVasile Berinde [address as above]

RECENT BOOKSIvan Netuka and Vladimir Sou³ekMathematical InstituteCharles UniversitySokolovská 8318600 Prague, Czech Republice-mail: netuka@karlin.mff.cuni.czand soucek@karlin.mff.cuni.cz

ADVERTISING OFFICERVivette GiraultLaboratoire d’Analyse NumériqueBoite Courrier 187, Université Pierre et Marie Curie, 4 Place Jussieu75252 Paris Cedex 05, Francee-mail: girault@ann.jussieu.fr

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CONTENTS

EMS March 2003

EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY

EXECUTIVE COMMITTEEPRESIDENTProf. Sir JOHN KINGMAN (2003-06)Isaac Newton Institute20 Clarkson RoadCambridge CB3 0EH, UKe-mail: emspresident@newton.cam.ac.uk

VICE-PRESIDENTSProf. LUC LEMAIRE (2003-06)Department of Mathematics Université Libre de BruxellesC.P. 218 – Campus PlaineBld du TriompheB-1050 Bruxelles, Belgiume-mail: llemaire@ulb.ac.beProf. BODIL BRANNER (2001–04)Department of MathematicsTechnical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: b.branner@mat.dtu.dk

SECRETARY Prof. HELGE HOLDEN (2003-06)Department of Mathematical SciencesNorwegian University of Science andTechnologyAlfred Getz vei 1NO-7491 Trondheim, Norwaye-mail: h.holden@math.ntnu.no

TREASURERProf. OLLI MARTIO (2003-06)Department of MathematicsP.O. Box 4, FIN-00014 University of Helsinki, Finlande-mail: olli.martio@helsinki.fi

ORDINARY MEMBERSProf. VICTOR BUCHSTABER (2001–04)Steklov Mathematical InstituteRussian Academy of SciencesGubkina St. 8, Moscow 117966, Russiae-mail: buchstab@mendeleevo.ru Prof. DOINA CIORANESCU (2003–06)Laboratoire d’Analyse NumériqueUniversité Paris VI4 Place Jussieu75252 Paris Cedex 05, Francee-mail: cioran@ann.jussieu.frProf. PAVEL EXNER (2003-06)Mathematical InstituteCharles UniversitySokoloská 8318600 Prague, Czech Republice-mail: exner@ujf.cas.czProf. MARTA SANZ-SOLÉ (2001-04)Facultat de MatematiquesUniversitat de BarcelonaGran Via 585E-08007 Barcelona, Spaine-mail: sanz@cerber.mat.ub.esProf. MINA TEICHER (2001–04)Department of Mathematics and Computer ScienceBar-Ilan UniversityRamat-Gan 52900, Israele-mail: teicher@macs.biu.ac.il

EMS SECRETARIATMs. T. MÄKELÄINENDepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlandtel: (+358)-9-1912-2883fax: (+358)-9-1912-3213telex: 124690e-mail: makelain@cc.helsinki.fiwebsite: http://www.emis.de

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EMS NEWS

EMS March 2003

200315 MayDeadline for submission of material for the June issue of the EMS NewsletterContact: Robin Wilson, e-mail: r.j.wilson@open.ac.uk

18-23 MayIPAM-SIAM-EMS Conference in Los Angeles (UCLA Lake ArrowheadConference Center), USAApplied Inverse Problems: Theoretical and Computational Aspectswebpage: http://www.ipam.ucla.edu/programs/aip2003

30 June-4 July EMS Summer School at Porto (Portugal) Dynamical Systems Organiser: Maria Pires de Carvalho, e-mail:mpcarval@fc.up.ptwebpage: http://www.fc.up.pt/cmup/sds

6-13 July CIME-EMS Summer School at Bressanone/Brixen (Italy)Stochastic Methods in FinanceOrganisers: Marco Frittelli and Wolfgang J. Runggaldiere-mail: runggal@math.eunipd.itwebpage: www.math.unifi.it/~cime

15 August Deadline for submission of material for the September issue of the EMSNewsletter

12-14 SeptemberSPM-EMS Weekend Meeting at the Calouste Gulbenkian Foundation, Lisbon(Portugal)Organiser: Rui Loja Fernandes, e-mail: rfern@math.ist.utl.pt

14-15 September EMS Executive Committee meeting at Lisbon (Portugal) Contact: Helge Holden, e-mail: holden@math.ntnu.no

200425-27 June EMS Council Meeting, Stockholm (Sweden)

27 June-2 July4th European Congress of Mathematics, Stockholmwebpage: http://www.stocon.se/4ecm/

2-6 September EMS Summer School at Universidad de Cantabria, Santander (Spain) Empirical processes: theory and statistical applications

EMS AgendaEMS Committee

Cost of advertisements and inserts in the EMS Newsletter, 2003(all prices in British pounds)

AdvertisementsCommercial rates: Full page: £210; half-page: £110; quarter-page: £66 Academic rates: Full page: £110; half-page: £66; quarter-page: £40 Intermediate rates: Full page: £160; half-page: £89; quarter-page: £54

Inserts Postage cost: £13 per gram plus Insertion cost: £52

The European Mathematical Society cov-ers the whole of what is conventionallycalled pure and applied mathematics, fromthe most abstract and theoretical to appli-cations in diverse fields of science andtechnology. Attempts to define or delimitthe scope of mathematics always fail to cap-ture the richness of the subject. The best Ican offer is the circular definition: mathe-matics is what mathematicians do, andmathematicians are people who do mathe-matics.

What is often not sufficiently understoodby those outside mathematics is howimportant it is to see the subject as a whole,and we inside sometimes make the situa-tion worse by putting ourselves into com-partments. We set up departments of puremathematics, applied mathematics, statis-tics, operational research; we argue aboutthe relative merits of algebra and geome-try; we quote G. H. Hardy on the useless-ness of mathematics. In doing so, weunderplay the interconnected nature of thesubject and the extent to which, through-out history, unexpected links and novelapplications are discovered.

In thinking about the unity of mathe-matics, I find it helpful to consider ametaphor in the form of a great ocean.Isaac Newton spoke of himself as playingon a seashore, while the whole ocean oftruth lay undiscovered, but my analogytakes mathematics itself as the ocean. Theareas to which it is applied, with which itinteracts, are the continents and islandsagainst whose shores the ocean breaks.Observers see these shores and admire thefoaming breakers, and they see too the sur-face of the waters far from land, but theymiss what is going on in the depths, andthe fact that the whole ocean is one greatecosystem in which the health of the life indifferent parts depends on that of thewhole.

When mathematicians attack a problemin physics or biology or economics, theymay be able to make progress in a directand straightforward way, writing downequations and solving them analytically ornumerically, but if the problem is at allchallenging, obstacles will soon arise thatstand in the path and frustrate simple solu-tions. The mathematician will try tounderstand these obstacles, assessing howfundamental they are. Often it will berealised that they are similar to difficultiesthat have arisen in other areas, and thatmethods developed in those other areascan be fruitfully transferred. A process ofabstraction and generalisation can oftenprove extremely powerful, and may lead tomore subtle solutions, or at least to a deep-er understanding of why a solution is elu-sive.

In practice, this process of abstraction

will be repeated several times, and othermathematicians with other expertise willtransform the original problem into almostunrecognisable form. It is however impor-tant that a chain of communication shouldnot be broken, so that those concernedwith real problems know what is beingdone at a more abstract level, and can bothuse the more general theory and challengeits relevance.

This whole process is very like the waythe flora and fauna in different levels of theocean feed off those in adjacent levels. Wemay for administrative convenience givedistinct names to different levels, but theyremain interdependent. In the depthsthere are strange creatures that never seethe sunlight above, while on the surface arethose who never venture below, but they alldepend on each other, perhaps throughlong and subtle chains of mutual need.

There also great leviathans of the sub-ject, whales that descend to the deepestwater and then rise to the surface withspouts of profound new mathematicalunderstanding. We celebrate this year thecentenaries of two such, von Neumann andKolmogorov, who brought the purest ofpure mathematics to bear on a variety ofapplied fields with a power and authoritythat defied the distinctions of lesser math-ematicians. We need more such who dis-turb the ocean and shake our preconcep-tions.

The continents against which the waterslap are very different from one another.The best known is of course that of physics,which has gentle beaches and broad bays inwhich play amphibious creatures whohardly know or care whether they aremathematicians or physicists. But evenhere there are penguins, clumsy on landbut beautiful swimmers in the water. Andthere are crocodiles, which lie half sub-merged in the shallows looking like harm-

less logs until they spy a target nearby,when they spring ashore with frighteningspeed and open jaws. I leave my readers toconstruct their own examples, to describethe variety of behaviour in highly devel-oped fields like mathematical physics.

Unfortunately, there are contrastingcontinents in which the waves beat againsthigh cliffs of incomprehension, on top ofwhich the inhabitants look down on themathematicians in the sea, who in turnshout in vain to those on land. In time,some of these cliffs will crumble, but mean-while we lose opportunities because of aninability to communicate.

On the other hand, there are some areaswhere mathematics gets inextricably mixedwith difficult non-mathematical disci-plines. The science of statistics, for exam-ple, is neither a subset nor a superset ofmathematics, and resembles those land-scapes that are neither land nor sea butsome admixture of the two.

Meanwhile, far out to sea, it is possible toforget the existence of land altogether, butthe nature of the ocean is in fact influencedstrongly by the nature of the invisible con-tinents that bound it. And they in turn aresometimes radically affected by what hap-pens over the horizon. In the depths of theocean an event may show on the surface asa wave a few centimetres high. But as thewave travels towards the land it may growinto a tsunami with dramatic consequencesfor those on shore.

We live in a world that has been deci-sively shaped by the applications of mathe-matics. Mathematics will advance, fasterthan ever, in response to practical chal-lenges and its internal momentum ofmathematical curiosity. New connectionswill be discovered between apparently dif-ferent fields, and good mathematicians willcontinue to spring surprises on their col-leagues and on the world.

EDITORIAL

EMS March 2003 3

Editorial: An Ocean of MathematicsEditorial: An Ocean of MathematicsSir John Kingman (EMS President)

Our hosts, the French mathematical soci-eties SMF and SMAI, had arranged forgood food and pleasant weather, so it wasrather a shame to sit indoors and transactthe Society’s business. All members of theExecutive Committee were there, togetherwith Tuulikki Mäkeläinen, our invaluableexecutive secretary, the energetic figure ofour past president, Rolf Jeltsch, saying thathe could now sit in a quiet corner, RobinWilson, the Editor of the Newsletter (with agarish two-sided tie), Saul Abarbanel (mak-ing sure that applied mathematics was notdisregarded) and myself, listening for any-thing that could be turned into publicity.

Our new President, Sir John Kingman,presided imperturbably over the businessof what was a very amicable meeting.

Gentle reader, not even the muses couldmake all that business interesting. Theroutine ratification of appointments to thestanding committees of the society anddecisions about terms of office will bereflected in due course on EMIS.Decisions to support (or not to support)meetings and other activities may notappear here, because the applicants shouldbe informed first. So I shall try to give ageneral idea of what was discussed and,where I can, of the more important deci-sions taken, which I shall list at the end.

In a year when subscriptions have risen,it may not be politic to report that theSociety made a small surplus overall of4754 euros. However, this represented anoperating loss, principally because of theexpense of holding our Council meeting inOslo. Even the auditors agreed that costsin Oslo could be high. The apparent sur-plus arose from receiving income on pro-jects whose expenditure was incurred in adifferent financial year. Income frommembership fees had increased, reflectinga significant rise in membership.

The President, Past President, and Vice-Presidents reported on the many meetingsat which they had represented, or wouldrepresent, the Society. These included sci-entific meetings, representation on organ-isations, and meetings to do withEuropean funding. The President alsoreported on the ‘hand-over’ meeting inZürich. He thanked Rolf Jeltsch and DavidBrannan for their devotion to, and bril-liant work for, the EMS.

Under the 6th Framework arrange-ments, Luc Lemaire explained, theEuropean Union would accept applica-tions only for series of meetings: eitherlarge meetings or events such as summerschools for training young researchers. Hehad therefore issued a call for proposals:some had already been received, and theCommittee approved a number of them.He had also asked the Committee for helpin drawing up a list of mathematicians who

would give the Committee Scientific adviceabout proposed meetings, and who alsocould be nominated as a panel of expertsfor the 6th Framework programme.

Several of the Society’s committeesreported. The Committee on EasternEurope was in charge mainly of distribut-ing travel grants to young EasternEuropean mathematicians. The Commit-tee for Developing Countries was veryactive and sought working capital from theEMS. The Executive Committee was sym-pathetic, but it had limited funds at its dis-posal: however there was an unspentamount that it could allocate. TheEducation Committee was drawing upposition papers on The preparation of stu-dents for university, The supply of maths teach-ers, Technology in teaching andPopularisation. The Raising Public Aware-ness Committee reported that it hadreceived 26 articles for its competition.The Committee for Women andMathematics reported on a scheme formentoring young women mathematicians,run by European Women in Mathematics.The Special Events Committee submittedamended rules governing the DiderotMaths Forum. The Committee forDeveloping Countries has been very activewith its book distribution programme, butis also getting new facets of its activitiesunder way.

Ari Laptev joined the committee onSunday to tell us about progress on 4ecm(see page 5). That day, we moved from ananonymous hotel conference room to theimposing Maison du Séminaire on the seafront.

Rolf Jeltsch reported on his meeting atBerlingen about the project to digitise allpast mathematical literature. Althoughthis had been agreed by the IMU, neitherthe NSF in the USA nor the EuropeanUnion would fund the main costs of digiti-sation. An application could still be madeto the 6th Framework programme for

some aspects, but the main funding wouldhave to come from other sources.

Robin Wilson confirmed that, due toextra responsibilities at the OpenUniversity, the June issue of the Newsletterwould be his last as Editor-in-Chief. TheCommittee thanked Robin for his work:under his guidance, the Newsletter hadbecome a major asset to the Society.

SMAI and SMF and (particularly) DoinaCioranescu, were thanked, not only fortheir warm welcome and the smooth run-ning of the arrangements for the meeting,but also for their organisation of AMAM03,which promised to be a great success.

Some Decisions• The Society should have a booth at

ICIAM in Sydney.• The Committee approved academic

institutional membership for the CentralEuropean University (Budapest) and theFaculty of Mathematics at the Universityof Barcelona.

• The Committee agreed to support theCortona Scuola Matematica Interuniver-sitaria on the same basis as the BanachCentre. The Committee resolved that,in principle, it could provide this kind ofsupport where there was direct EMSinput and a measure of internationalisa-tion, but that each application would beconsidered on its merits.

• It was agreed to accept the bid of theNetherlands Mathematical Society tohold 5ecm in Amsterdam in 2008, sub-ject to a site visit.

• It was agreed to provide 4000 euro asworking capital for the Committee forDeveloping Countries.

• A common letterhead incorporating thelogo was agreed.

• It was agreed in principle that EMSshould become a full member of theEULER Consortium.

• It was agreed that the Committee shouldnot support individuals for prizes.

EMS NEWS

EMS March 20034

Executive Committee MeetingExecutive Committee MeetingNice (France), 8-9 February 2003

David Salinger

Preparations for 4ecm: the Fourth European Congress of Mathematics 4ecm: Stockholm, 27 June – 2 July 2004

The poster for the congress has been distributed. A letter will be sent to all participants in 3ecm (Barcelona, 2000).

A number of Nobel prizewinners have been asked to speak to the congress about the role of mathematics in their subject.So far, six expressions of interest in organising satellite conferences have been received.

Fourteen EU networks have responded to the call to hold their network meetings in Stockholm.The conference fee will be 200 euros, with a 20% discount for EMS members.

Call for Nominations of Candidates for Ten EMS PrizesFourth European Congress of Mathematics

Principal GuidelinesAny European mathematician who has not reached his/her 35th birthday on 30 June 2004, and who has not previously received theprize, is eligible for an EMS Prize at 4ecm. A total of 10 prizes will be awarded. The maximum age may be increased by up to threeyears in the case of an individual with a corresponding ‘broken career pattern’.Mathematicians are defined to be ‘European’ if they are of European nationality or their normal place of work is within Europe.‘Europe’ is defined to be the union of any country part of which is geographically within Europe or that has a corporate memberof the EMS based in that country.Prizes are to be awarded for the best work published before 31 December 2003.The Prize Committee shall interpret the word ‘best’ using its judgement: for example, it may refer to innate quality or impressive-ness, influence, etc.

Nomination for the AwardThe Prize Committee, headed by Prof. Nina Uraltseva (St Petersburg), is responsible for solicitation and evaluation of nominations.Nominations can be made by anyone, including members of the Prize Committee or by the candidates themselves. It is the respon-sibility of the nominator to provide all relevant information to the Prize Committee, including a resume and documentation.The nomination for the awards should be reported by the Prize Committee to the EMS President at least three months prior to thedate of the awards. The nomination for each award must be accompanied by a written justification and a citation of about 100 wordsthat can be read out at the award ceremony. The prizes cannot be shared.

Description of the AwardThe award comprises a certificate including the citation and a cash prize of 5000 euro.

Award PresentationThe prizes will be presented at the Fourth European Congress of Mathematics by the President of the European MathematicalSociety. The recipients will be invited to present their work at the conference.

Prize FundThe money for the Prize Fund will be raised by the organisers of the Fourth European Congress of Mathematics in Stockholm.

Deadline for SubmissionNominations for the prize must reach the office in Stockholm at the following address, no later than 1 February 2004:4ECM Organising Committee, Prof. Ari Laptev, Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm,Sweden.

e-mails: laptev@math.kth.se, uunur@nur.usr.pu.ruhttp://www.math.kth.se/4ecm/

fax: +46-8-723-17-88, phone: +46-8-790-84-86

Instructions for Organisers of 4ecm Satellite ConferencesThe Organising Committee of the 4ecm offers the following advantages to organisers of satellite activities.• A summary of information about each satellite activity will be freely distributed through the printed and electronic systems of the

4ecm.• The reduced registration fee offered to participants of the 4ecm registered before April 2004 will be extended until the begin-

ning of the 4ecm for participants of satellite activities.• Addresses of satellite activity participants may be included in the mailing list of the 4ecm for distribution of information.The Organising Committee requires the following information in order to decide if an activity can be considered as a satellite of the 4ecm.• Title and a short presentation of the activity (periodicity, objectives, etc.).• Location and dates.• Organising Committee and Scientific Committee, if applicable.• Preliminary list of speakers, if applicable.The experience from previous EMS conferences and other international events shows that it is also convenient to request the following.• The dates of satellite activities should be close to the dates of the 4ecm (27 June – 2 July 2004).• People responsible for each satellite activity should provide their participants with information about the 4ecm. In addition, they

should assist them in organising their trip to or from Stockholm. The organisers of the 4ecm will also assist 4ecm participants who are registered in some satellite activity in arranging their travel plans.

Contact details for organisers:Mikael Passare, e-mail: passare@matematik.se

website: http://www.math.kth.se/4ecm/Instructions.htmThe deadline for proposals for satellite activities is 1 February 2004.

We regret that activities communicated after this date cannot be acknowledged by the Organising Committee.

EMS NEWS

EMS March 2003 5

AustraliaMatthew Brown

AustriaHerbert FleischnerAli ÜnlüFranz Winkler

BelgiumJan AdriaenssensPierre CapraceStefaan De WinterCindy De WolderSandy FerretNicholas HamiltonGeorges HansoulNatalia KatilovaThierry LucasPierre MathonetCedric RivièreKoen ThasJan van Geel

BulgariaIvailo Mladenov

CanadaNicolas Juge

ChinaHuafei Sun

Czech RepublicPavel Exner

FinlandSeppo HeikkiläIlkka HolopainenMatti HonkapohjaTimo KarviMika KoskenojaPetri OlaMatti RantanenLeo SaloMari SavelaSamuli SiltanenEero Tamminen

FranceDenis AubryPierre BalvayMohammed-NajibBenbourhimSylvie Benzoni-GavageNicole BerlineValérie BerthéStéfanella BoattoFrédéric J. BonnansNicole BoppAlain BrettoPierre CartierDenise ChenaisGuillaume DouardJean Charles GilbertVivette GiraultMarc GrandottoFabien GrangerGeorges GrisoJean-Claude GuillotFrancois HamelPaul-Louis Hennequin

Jacques IstasChristian LecotBernard MarchandVictor Filipe Martins da RochaGuy MetivierRégis MonneauDumitry MotreanuJean-Philippe NicolasAshkan NikeghbaliPierre OrengaAnnie RaoultBruno ReyJoel RivatBenoit RottembourgRaphael RouquierLéon SaltielLionel SchwartzNgoc Nam TramJacques Levy VehelCharles Walter

GermanyPeter EichelsbacherUlrich PinkallNikolai SapunarowNorbert SchappacherRalf SchumacherOnnen SiemsLuise Unger

GreeceChryssa Ganatsiou S. Molho N. Papoulas

HungaryAndras Batkai

IrelandEimear ByrneMichael McGettrickJames T. WardDavid Wilkins

IsraelFlavian Abramovici Buma AbramovitzZvi ArtsteinGill Barequet Eugene Barsky David Blanc Achi Brandt Daoud Bshouty Gideon Ehrlich Elsa FismanMaria Gorelik Vladimir HinichYoram Hirschfeld Alexander IoffeShmuel KantorovitzYael Karshon Meir KatchalskiDavid KatsVictor KhatskevichJuri KiferVladimir KormanEran London Iakov LutskyShahar MozesBernard PinchukAllan Pinkus

Nizar RadwanAmitai RegevAndre ReznikovJoseph Roseman Mozes Shahar Yehuda Shalom Vladimir Shevelev Eduard Yakubov Zvi Ziegler

ItalyElisabetta Alvoni Maria Artale Luca Barzanti Rita Capodaglio Gaetano Cavallaro Alfredo Ciano Paolo Custodi Franca Degani Cattelani Gerardo De Maio Luigi D’Onofrio Margherita Fasano Petroni Eva Ferrara Dentice Marianna Fornasiero Donato Fortunato Lorenzo Fucci Federica Galluzzi Alessandro Giacomini Ugo Gianazza Gian Mario Gianella Gennaro Infante Giovanni Landi Marta Macri Antonio Manna Cristina Marcelli Emanuela Maresi Francesco Marino Antonino Maugeri Alessandra Micheletti Michele Mininni Luciana Misso Marco Modugno Gioconda Moscariello Loianno Franco Nardini Paolo A. Oliverio Carlo Domenico Pagani Rita Pardini Fulvio Ricci Pietro Rigo Carla Rossi Rodolfo Salvi Claudia Scarani in Tampieri Alessandro Scarselli Antonino Surdo Sandra Tucci Mariacristina Uberti Antonio Zitarosa

JapanTakao Matumoto

LuxembourgDenise Kass-Hengesch Gérard Lorang

NetherlandsWilfred W. J. Hulsbergen

NigeriaJ. A. Oguntuase

NorwayHarald Hanche-Olsen Arne B. Sletsjoe

PolandTeresa Lenkowska-Czerwinska

RomaniaDan Barbosu Gheorghe Micula Constantin Niculescu Nicolae Pop

RussiaVyacheslav S. Kalnitsky

SpainSonia Esteve Frigola Jorge Galindo Pastor Garcia Bellido I.E.S.A. Isabel Marrero Rodriguez Ricard Marti Miras Carlos Romero Chesa

SwedenAnders Björn Jana Björn Lars Hörmander Ulf Ottoson Gunnar Mossberg

SwitzerlandHerbert Amann Demetrios Christodoulou Norbert Hungerbühler Wesley Petersen Richard Pink Bert Reinold René SperbMichel Thiebaud

TunisiaPatrick Cabau

UkraineEugene Tokarev

United Arab EmiratesRaymond F. Tennant

United KingdomR. E. Abraham John BibbyJ. F. Bradley D. Brown Luminita Manuela Bujorianu H. J. Carvill Paul J. Flavell Greig J. Fratus Ting Guo Ho S. J. Lewis R. S. McDermott E. J. Park S. C. Roy Anthony E. Solomonides J. Trevor Stuart Ola Törnkvist Sheung Tsun Tsou Reidun Twarock John Wright Ioannis Zois

United States of AmericaFrancis Bonahon L. E. DominoSigurdur Helgason Ricardo Perez Marco Loki Quaeler

EMS NEWS

EMS March 20036

New members 2002

Sir John Kingman (President) is the Director of the Isaac Newton Institute forMathematical Sciences in Cambridge, a post he has held since 2001. Cambridge was hisfirst university, which he left in 1965 for professorships at the Universities of Sussex andOxford. He was Chair of the UK Science and Engineering Research Council from 1981-85, and then served for 16 years as Vice-Chancellor (equivalent to Rector) of theUniversity of Bristol.

Sir John works on probability theory and its applications to random processes in a vari-ety of applications, including population genetics and operational research. He becamea Fellow of the Royal Society in 1971, and has been President of both the Royal StatisticalSociety and the London Mathematical Society. He also chairs the Statistics Commission,which monitors the integrity of official statistics in the UK.

Luc Lemaire (Vice-President) received a Doctorat from the Université Libre de Bruxelles in 1975 anda Ph.D. from the University of Warwick in 1977. From 1971 to 1982 he held a research position at theBelgian F.N.R.S., and has been a professor at the Université Libre de Bruxelles since then. Hisresearch interests lie in differential geometry and the calculus of variations, with a particular interestin the theory of harmonic maps.

A former chairman of the Belgian Mathematical Society, Luc has been associated with the EuropeanMathematical Society since its creation in 1990, being a member of the Council from 1990 to 1997, amember of the group on relations with European Institutions since 1990, Liaison Officer with theEuropean Union since 1993, Vice-President 1999, and now Chair of the General meetings committee.

Bodil Branner (Vice-President) is a professor at the Technical University of Denmark, Lyngby(Copenhagen). She graduated from the University of Aarhus in 1967 in algebraic topology, but forthe last 20 years has concentrated on problems within dynamical systems, in particular in holomor-phic dynamics. She has been a visiting professor at Cornell University and the Université de Paris-Sud, and a visitor at the Max-Planck-Institut für Mathematik in Bonn and the Mathematical SciencesResearch Institute (MSRI) in Berkeley.

Bodil has been involved in establishing the network of European Women in Mathematics from itsbeginning in 1986. Since 1992 she has been a delegate of the EMS Council, representing individualmembers, and has been a member of the Executive Committee since 1997. She was recentlyPresident of the Danish Mathematical Society and a member of the Danish Natural Science ResearchCouncil. She is currently a member of the EURESCO committee under the European ScienceFoundation, representing the EMS.

Helge Holden (Secretary) was born in Oslo, Norway in 1956. He received his Ph.D. from theUniversity of Oslo in 1985. After a year as a postdoc at the Courant Institute in New York, he accept-ed a position in Trondheim at the Norwegian University of Science and Technology, where he was pro-moted to full professor in 1991.

Helge’s area of research is partial differential equations. His first work was in the mathematical the-ory of Schrödinger operators, and he then moved on to stochastic partial differential equations, flowin porous media, hyperbolic conservation laws, and completely integrable systems.

He is currently Vice-President of ECMI, the European Consortium for Mathematics in Industry.

Olli Martio (Treasurer) received his Ph.D. at the University of Helsinki in 1967. He becamean Associate Professor at the University of Helsinki in 1972, a professor at the University ofJyväskylä in 1980, and from 1993 he has been a professor and Head of Department ofMathematics in Helsinki. He has been a visiting professor in the University of Michigan,Norwegian Institute of Technology and Universidad Autonoma de Madrid. He has been aneditor of Mathematica Scandinavica and Acta Mathematica. he is a member of several editorialboards and currently edits the Finnish journal Ann. Acad. Sci. Fenn. Math.

His research interests include function theory (quasiconformal maps), non-linear poten-tial theory and associated partial differential equations. He has organised several confer-ences and edited nine international conference proceedings, starting with the NordicSummer School in quasiconformal mappings in Helsinki in 1971.

Olli has held various positions in the Finnish Mathematical Society. He has been thePresident of the Finnish Academy of Sciences and Letters and a member of the Committeefor Natural Sciences in the Academy of Finland, as well as a member of several EuropeanUnion Scientific Panels for Mathematics. He is a honorary doctor of the Linköping Instituteof Technology, the University of Volgograd and the University of Jyväskylä, as well as a hon-orary professor of the University of Brasov.

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IntrIntroducing the Committeeoducing the Committee(part 1)

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In March 1885, the Société Mathématique deFrance (SMF) conceived the project of a bib-liographical catalogue of nineteenth-centurymathematical sciences. Facing the constantincrease of mathematical journals and theexponential growth of mathematical knowl-edge, the SMF members felt the lack of abibliographical tool for advanced studentsand mathematicians. The RépertoireBibliographique des Sciences Mathématiques wasto be the SMF’s answer to the expansion ofmathematics.

This long-term bibliographicalenterprise – which was directed by HenriPoincaré – rapidly became an internationalendeavour: for almost 27 years, about 50mathematicians from 16 different countrieswent through more than 300 mathematicaljournals. Between 1885 and 1912, morethan 20,000 bibliographical references tomathematical works (articles, books, treatises,etc.) were identified, collected, and pub-lished, using a methodical and systematicclassification.

This repertoire constitutes an importantstage for the history of nineteenth-centuryscience. The reconstitution of its historyrepresents an interpretative key for thestudy of the internationalisation of science.Moreover, it may be an essential source forinvestigations concerning the organisationof disciplinary frontiers within mathematicalsciences.

The aim of this article is to set out the firstelements of an investigation devoted to thehistory and operation of the RépertoireBibliographique des Sciences Mathématiques. Wefirst describe the scientific and intellectualcontext of its emergence. Next, we relatethe history of its creation. Finally, using afew elements extracted from our computerdatabase, we try to give a general survey ofthe contribution of this bibliography to thehistory of mathematics.

Nineteenth-century science: a growing con-cern for bibliographyDuring the second half of the nineteenthcentury, a large number of disruptionsaffected European science: an unprecedent-ed increase of research and a growing spe-cialisation in every domain; the organisationof institutions in networks; an institutionali-sation of research in most European coun-tries via the creation of academies, learnedsocieties and universities; an increase in thenumber of university students, notably inFrance after the 1880 and 1890 reforms;and the considerable acceleration of theinternationalisation of science (for instance,the organisation of the first internationalcongresses).

Besides these disruptions, one should addan important phenomenon: the exponentialgrowth of the number of scientific journals.At the end of the nineteenth century many

scholars perceived the constant increase ofprinted matter as a serious problem. Twosimple figures can give some idea of this sit-uation: in 1890, international statistics ofprinted matters estimated that 100,000items a year were published. In 1900, oneestimated the annual production at 20,000books, 76,000 journals and approximately600,000 articles (see [Goldstein 2001],[Rasmussen 1995], and [Otlet 1900]).

The first scientific journals appeared dur-ing the seventeenth century. At that time,these journals were usually published byacademies and learned societies, and theydidn’t exclusively contain mathematicalpublications (one could find, for instance,articles devoted to botanical or zoologicalissues): the Journal des scavants (1665) or thePhilosophical Transactions of the Royal Society ofLondon (1665) are two good examples ofsuch publications.

The first issue of Gergonne’s Annales demathématiques pures et appliquées was pub-lished in 1810, and this was probably thefirst significant mathematical journal exclu-sively devoted to mathematics. It ceased in1831, but several other journals took over:the Journal für die reine und angewandteMathematik (1826), the Journal de mathéma-tiques pures et appliqués (1836) and the Annalidi scienze mathematiche e fisiche (1850). Oneshould add that, during the second half ofthe nineteenth century, the appearance ofvarious learned societies was followed by thecreation of several specialised journals; forinstance, the SMF was created in 1872 andthe first issue of its journal, the Bulletin de laSociété Mathématique de France, was publishedin 1873.

According to Neuenschwander [1994, pp.1534-5], only 15 journals contained mathe-

matical articles in 1700; in 1900, probablymore than 600 journals published mathe-matical works (see [Gispert 2000]). Facingsuch an increase, many mathematicianswere strongly in favour of the creation ofbibliographical catalogues, and bibliographyrapidly became a major part of scientificresearch.

Many bibliographical indices were pro-duced during the nineteenth century. Themost important national libraries in Europestarted to publish their exhaustive cata-logues, and many scholars or members oflearned societies tried to set up various bib-liographic catalogues for specific fields ofknowledge: bibliographical catalogues onindex cards; monthly, quarterly or annualbibliographical reviews; chronological,alphabetical and methodical bibliographies;bibliographies centred on a particular disci-pline such as mathematics or covering alarger field (such as the InternationalCatalogue of Scientific Literature, with sectionsdevoted to mathematics, zoology, etc.), oreven universal repertoires, such as PaulOtlet’s Répertoire Bibliographique Universel(see [Rasmussen 1995], [Otlet 1906, 1908,1918] and [Rayward 1990]).

There were also such bibliographicalendeavours before the nineteenth century:for mathematics, at least two bibliographiesare significant: J.E. Scheibel’s Einleitung zurmathematischen Bücherkenntnis (Breslau)1769-98, and F.W.A. Murhard’s Literatur dermathematischen Wissenschaften (Leipzig),1797-1805, each recording about 10,000mathematical works.

The following table gives an indication ofthe most important catalogues for mathe-matics in the second half of the nineteenthcentury:

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An Answer to the GrAn Answer to the Growth of Mathematical Knowledge? owth of Mathematical Knowledge? The Répertoire Bibliographique des Sciences Mathématiques

Laurent Rollet & Philippe Nabonnand

The most important mathematical bibliographies (1850-1900)

For further information concerning thebibliographical repertoires devoted to var-ious fields, see [Besterman 1949]. Thistable should be complemented by the dif-ferent editions of Poggendorf’sBiographisch-literarisches Handwörterbuch derexakten Naturwissenschaften and by theRépertoire Bibliographique des SciencesMathématiques. Houzeau’s and Lancaster’sbibliographies for astronomy ([Houzeau1878], [Houzeau /Lancaster 1882, 1887])had a strong influence on the mathemati-cal repertoire

All these bibliographical attempts consti-tute a sign for a general consensus on sci-entific research around 1900. Many math-ematicians agreed that it was almostimpossible to be certain that other scholarshad not yet studied their ideas. Moreover,they were increasingly upset by the timelag between the publication of an articleand its registration in a mathematical bib-liography (up to three years in the Jahrbuchüber die Fortschritte der Mathematik (see[Neuenschwander 1994, p. 1836]) or in theCatalogue of Scientific Papers). Consequent-ly, many mathematical journals paid greatattention to bibliographical issues in the1880s and the 1890s: what is the best bib-liographical system for mathematical sci-ences? what kind of classification shouldbe adopted? who should do the biblio-graphical work? should mathematiciansadopt an alphabetical classification, orshould they elaborate a systematic andconsensual classification at an internation-al level? (For echoes of these discussions,see [Eneström 1890].)

The first years: 1885-94The SMF formulated the idea of a biblio-graphical repertoire for mathematics in1885, and the Society rapidly diffused apreliminary project within the internation-al mathematical community. A first men-tion of the project appears in a lettre circu-laire of March 1885 entitled Projet de réper-toire bibliographique. This letter began withan acknowledgement of the incapacity ofmathematicians regarding the increase ofmathematical publications, and continuedwith a presentation of the different steps ofthe project: compilation of bibliographicalreferences on individual index cards;ordering of the cards with the help of asuitable classification; and publication.According to Eneström [1890], this propo-sition was warmly welcomed; consequently,a month later, the SMF sent another circu-lar that gave more precise instructions.

Nevertheless, the project was notdefined and accepted until four years later,in 1889, and the first set of a hundredprinted index cards was not to be pub-lished until 1894. Such a time lag finds itsmain source in the complexity and thesophistication of the classification adopt-ed.

The intention of the SMF was to differ-entiate its project from other bibliographi-cal endeavours by proposing a logical clas-sification of items based on a thematicindex. This index probably started to cir-culate in an informal way in 1887: the let-ters of Poincaré, Perott, Mathieu, Schlegel,

Brioschi, Eneström and Mittag-Lefflercontain numerous discussions about thelogical organisation of mathematicaldomains in the index. A 67-page Projet declassification détaillée pour le RépertoireBibliographique des Sciences Mathématiqueswas published by Gauthier-Villars in June1888. The first edition of the index wasfinally published in 1893, and several latereditions were printed (see [Commission per-manente du Répertoire Bibliographique desSciences Mathématiques [1893], [1898],[1908], [1916]).

Noting the occasion of the 1889 WorldFair, the commission of the repertoire,chaired by Henri Poincaré, decided toorganise the first Congrès International deBibliographie des Sciences Mathématiques.The purpose of the organisers (PaulAppell, Gaston Darboux, Charles Rouché,Jules Tannery and Georges Humbert) wasto gather in Paris all those involved inmathematical research and eager to con-tribute to the project at an internationallevel.

During this congress, which was support-ed by the Ministry of Trade, Industry andColonies, several decisions were taken:• The bibliography should consist of an

inventory of the titles of memoirs inpure and applied mathematics pub-lished from 1800 to 1889, as well asworks concerning the history and thephilosophy of mathematics from 1600 to1889: the purpose was to establish a sys-tematic list of all articles and memoirspublished in the most important mathe-matical journals.

• The titles of memoirs should be classi-fied, not by the authors’ names, butaccording to the logical order of sub-jects.

• Publications on astronomy already men-tioned in the astronomical bibliographyof Houzeau and Lancaster in the 1880sshould be excluded.

• The titles of works written in languagesother than French, Italian, German,Spanish or Latin should be translatedinto French.

The commission appealed to a generaladoption of the classification index bymathematicians and mathematical jour-nals.

Finally, it was decided to establish a per-manent commission, based in Paris: itscomposition was Henri Poincaré, DésiréAndré, Georges Humbert, Mauriced’Ocagne, Henry (France), E. Catalan(Belgium), D. Bierens de Haan (Holland),Glaisher (Great Britain), G. Gomes-Texeira (Portugal), Holst (Norway), GeorgValentin (Germany), E. Weyr (Austria),Guccia (Italy), G. Eneström (Sweden), J.P.Gram (Denmark), Liguine (Russia) and C.Stephanos (Greece).

However, despite this strong interna-tional participation, one should not expectthat every country worked at the samelevel: it is likely that several countriesnever sent any bibliographical reference tothe Paris office. This was certainly the casefor Great Britain and United States, partlybecause they were involved in other biblio-graphical projects. Moreover, the interna-

tional dimension of the project was coun-terbalanced by the fact that the bibliogra-phy was created in Paris, directed fromParis, subsidised by French authorities andpublished in France. It is very difficult toknow whether it met with success or wasdistributed outside of France.

At the beginning, the SMF had plannedto publish the bibliography as a book – butthis would have implied a very slow publi-cation process, since it would have beennecessary to wait for the end of the perusalprocess before printing anything.Consequently Maurice d’Ocagne andRoland Bonaparte proposed to publish themathematical bibliography as a collectionof printed index cards. This optionenabled the publication to start as soon asa sufficient number of bibliographicalitems had been collected. Despite thisarrangement, the publication lasted foralmost 20 years: the first set of cards waspublished in 1894 and the last one (the20th) in 1912.

The perusal of mathematical periodicalsprobably began in 1888, but acquired itscruising speed after the 1889 congress.The following procedure was adopted forthe preparation and the publication of theseries: • All the memoirs and periodicals of a

given country were placed under theresponsibility of a member of the per-manent commission living and workingin the country.

• This representative directed the perusaland redaction of individual bibliograph-ical index cards for each memoir andarticle that had been identified; for eachmemoir or article one index card con-taining its bibliographical references wasmade.

• Each individual index card containedthe common bibliographical informa-tion (title, name of review, date, etc.), aswell as a classification code correspond-ing to a specific domain of research (thiscode was furnished by the Index duRépertoire Bibliographique des SciencesMathématiques).

• Individual index cards were then regu-larly sent to Paris, and were centralisedand prepared for publication.

• The Paris secretariat directed theprocess of publication, which was veryslow: they had to gather together indi-vidual cards according to their classifica-tion, but the index cards concerning aspecific division were not published untilthey contained a sufficient number ofbibliographical references: for instance,if there weren’t enough references forthe code A1, no card was published andthey had to wait for the sending of otherbibliographical references concerningthis classification code.

Each printed card contained approximate-ly ten references. Each set of 100 indexcards contained about 1000 bibliographicitems. The illustration on page 11 is areproduction of a standard index card: thefigure in the upper right corner indicatesthe number of the card and the framedcode indicates the classification codeaccording to the index.

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Reproduction of a printed index card

Three main mathematical domains weredistinguished in the classification of theindex: mathematical analysis, geometryand applied mathematics. Within thesedomains, several classes were identifiedand designated by a capital letter (see thetable below). For instance, class A con-tained works devoted to elementary alge-bra, theory of algebraic and transcendentequations, Galois groups, rational fractionsand interpolation. Each class (A to X) wasgenerally divided into subclasses, divisions,sections and subsections: for instance, thecode L14cá was used to designate the classof conics and surfaces of second degree(L), the subclass of conics (1), the divisioncorresponding to tangents (4), the sectiondealing with tangents satisfying specificconditions (c) and the subsection corre-sponding to the case of right angles (á).

Mathematical domain ClassesMathematical analysis A-J Geometry K-Q Applied mathematics R-X

Repartition of the classes in each mathematical domain

The repertoire was published from 1894until 1912, during which 20 series of 100index cards were published. Each seriescontained about 1000 bibliographical ref-erences, and thus these series represent alist of 20,000 mathematical works. Moreprecisely, we can distinguish threemoments in the publication of the series;they correspond to the three attempts tocover the whole classification, as shown inthe following table:

Period Number of Coveredseries published classes

1894-1895 3 A1-X71896-1905 12 A1-V91906-1912 5 B12-X8

The three periods of publication

Is the mathematical repertoire a new toolfor historians of mathematics?The intention of the SMF was to create abibliographical tool for scholars in math-ematics. Some journals adopted the clas-sification of the index (for instance, theBulletin de la Société Mathématique deFrance), but it is quite difficult to deter-mine whether the mathematical commu-nity really used it. We are in possessionof various documents concerning the cre-ation and the publication of this bibliog-raphy, but there remain many pointsabout which our information is still frag-mentary. How many copies did the com-mission permanente print and sell? Was thebibliography largely distributed outsideFrance? Why is it so difficult to findcopies of the index cards in French orforeign libraries? (As far as we know, it isimpossible to find a complete set of the20 series of the repertoire in any libraryin France, even in the BibliothèqueNationale de France: we had the opportu-nity to work on a complete set thanks toJean-Luc Verley.)

There are some further questions con-cerning the general context of its cre-ation: it would be useful to determine therelationships between this project and theuniversalistic and internationalist trendsat the turn of the nineteenth century.The mathematical repertoire constitutesa modest project, compared to similarattempts in Germany, Belgium and GreatBritain: there were three major chal-lengers:• The mathematical bibliography compiled by

Hermann Georg Valentin. Valentin was achief librarian at the Berlin Library andhe started the compilation of a mathe-matical bibliography in 1885, at thesame time as the SMF. His aim was tocollect all mathematical publications sincethe invention of typography. After severalyears of strained relations with the rep-resentatives of the French bibliogra-phy, Valentin finally became a memberof the permanent commission (see[Eneström 1911], [Valentin 1885, 1900,1910]). His bibliography was probablynever published, partly because of theFirst World War.

• The Universal Bibliographical Repertoire.The Belgians Paul Otlet and HenriLafontaine created this repertoirearound 1895. It was conceived as a uni-versal bibliography of human thought,and had some success for some years,but French mathematicians had someserious reservations.

• The International Catalogue of ScientificLiterature. The London Royal Societycreated this project in the 1890s. Itsaim was to publish, at an internationallevel, regular bibliographies on everyfield of scientific research. Althoughthe French scientific community wasinvolved in this project, professionalmathematicians (especially in France)also expressed strong reservations (see[Rasmussen 1995]).

From a scientific point of view, the math-ematical repertoire raises the problem ofthe internal structure of nineteenth-cen-

tury mathematics. At first glance, thisbibliography can constitute an interestingtool for the study of mathematical pro-duction over a large period: its 20,000bibliographical references constitute avaluable source of investigation for histo-rians of mathematics. However, this isprobably not the main point. Indeed,with its specific and complex classifica-tion, the mathematical repertoire givesan outline of a specific conception ofmathematics. It gives access to mathe-matics, and also to the conception ofmathematics constructed by the mathe-matical community at that time. Does itgive an adequate description of nine-teenth-century mathematics? In the lightof recent works in history of science,should its classification be considered asconservative or modern? Did the classifi-cation really take into account all theexisting mathematical domains of nine-teenth-century mathematics? Did theclassification contain gaps, and if so, whatwere they?

The creators of the project didn’t onlypropose a thematic ordering of mathe-matical fields; they also elaborated a per-sonal definition of the mathematical cor-pus that the repertoire should take intoaccount. They were, for instance, con-vinced that most of the works concerningpure and applied mathematics publishedsince 1800 would be of interest for schol-ars. On the other hand, they excludedclassical works that didn’t contain gener-al results, notably those intended for stu-dents and for the preparation of exami-nations. In a similar way, they decidedthat works in applied mathematics wouldbe mentioned only when they impliedprogress in pure mathematics. The intro-duction of such a separation betweenpure and applied mathematics is quiteastonishing, particularly in the context ofthe development of engineer training inall European countries.

What can historians of mathematicslearn from such a bibliographical endeav-our? In order to study precisely the struc-ture of the catalogue, we created a com-puter database. Although we are a longway from the end of the data entryprocess, we can give an overview of theinformation that may be extracted fromsuch a database. Our database currentlycontains 3692 bibliographical items, cor-responding to the first four series of therepertoire (400 index files out of 2000).It is accessible on-line, thanks to LaurentGuillopé at the Cellule MathDoc:http://math-sahel. ujf-grenoble.fr/RBSM/.

A general investigation covering 1700index files (17 series) provides informa-tion concerning the repartition of biblio-graphical references within the threemain mathematical domains: mathemati-cal analysis (A to J) represents 50% of thereferences, applied mathematics (R to X)33%, and geometry (K to Q) 17%. Formathematical analysis, the most impor-tant classes are those devoted to algebra(A), theory of functions (D), differentialequations (H) and arithmetic (I). Forapplied mathematics, one can distinguish

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three significant classes: mathematicalphysics (T), general mechanics (R) andfluid mechanics (S). Finally, the mainclasses in geometry are those devoted toelementary trigonometry (K), algebraiccurves and surfaces (M) and conics (L).

Apart from these general figures, wecan give some precise descriptive infor-mation concerning the first 300 indexfiles (3 series) of the repertoire. Thesefigures concern only 2723 bibliographicalreferences, and it would be hazardous toclaim that they provide an adequateaccount of the whole repertoire.Nevertheless, these items correspond tothe first attempt to cover the whole classi-fication (from A to X), and may be inter-esting, for two reasons: they furnish someindications about the complexity of thisbibliography, and they give some idea ofthe richness of the classification and ofthe extent of the work that had been donein 1895. Very significantly, the figures ofthe repartition of items among the threemathematical fields is similar to the pre-vious ones, which concerned 17 series:mathematical analysis represented 53%,geometry 13%, and applied mathematics34%.

There are 850 mathematicians listed inthe first three series of the repertoire.Although impressive, this figure requiresfurther analysis: in fact, most of theseauthors have between 1 and 5 biblio-graphical references, and there are only120 mathematicians with more than 5 ref-erences. The prominent authors of thethree series (with 20 items or more) are:A. Cauchy (101), N.H. Abel (55), L.Gegenbauer (49), C.-G.-J. Jacobi (42), M.Chasles (37), A.L. Crelle (31), Sophus Lie(29), F.-J. Studnicka (23), C. Duhamel(23), J. Liouville (22), P. Tannery (21),Th. Clausen (21), A. Cayley (21), E. Heine(20) and S.D. Poisson (20).

The 2723 listed items come from 83mathematical journals: this figure shouldbe compared with the list of 227 journalsof the Index du repertoire. Moreover, 62 ofthese journals contain less than 20 biblio-graphical references. Only 8 periodicalscontain more than 50 references and rep-resent 71% of the total number of items:Journal für die reine und angewandteMathematik (712), Comptes Rendus desSéances de l’Académie des Sciences (500),Sitzungsberichte der Königliche Akademie derWissenschaften in Wien (299), Journal de l’É-cole Polytechnique (134), Bulletin de laSociété Mathématique de France (117),Casopis pro pèstovàni mathematiky a fysiky (ajournal published in Prague, then part ofthe Austrian territory) (80), AnnalesScientifique de l’École Normale Supérieure(78), Journal de mathématiques pures etappliqués (58). The repertoire also tookmathematical monographs (books, trea-tises, etc.) into account; the first threeseries contain around 50 items of thistype.

These eight journals were published inGermany, Austria or France, a phenome-non explained by the strong mathemati-cal domination of France and Germanyduring the nineteenth century. As we will

see, the presence of Austria probablyfinds its origin in the strong activity ofEmil Weyr’s crew at the beginning of theperusal work. As an illustration, when foreach class of the index we take intoaccount the most important journals list-

ed (more than 20 references for eachperiodical), the only remaining ones arethose edited in France, Germany andAustria. We can then give an overview ofthe repartition of these countries accord-ing to the three mathematical fields (seethe graph below). Of course, these dataare still fragmentary and must be con-firmed by a more precise investigation ofthe whole set of 20 series.

The perusal of memoirs and periodi-cals of a given country was placed underthe responsibility of one or several math-ematicians living and working in thecountry. Nevertheless, it is quite clearthat, at the beginning of the project, veryfew countries put a lot of effort into theconstitution of the bibliography. Apartfrom France, Germany and Austria, onlyfour countries sent more than 15 biblio-graphical references to the Paris office:Portugal (100 items, 3 journals perused),

Russia (95 items, 4 journals), Italy (59items, 1 journal) and Norway (52 items, 1journal): in contrast, 920 bibliographicalreferences concerned French mathemati-cal journals, 783 were published inGerman journals and 539 in Austrian

periodicals. (Of course, these figuresdon’t furnish any information about theauthors’ nationality!)

In a 1900 report concerning theprogress of the repertoire, CharlesLaisant gave some information about thenumber of bibliographical referencessubmitted by each country. At that time,only the half of the bibliography (tenseries) had been printed and the mostimportant suppliers were still France(10,682 items, 6 journals: 7200 referencescome from the Comptes rendus del’Académie des Sciences), Germany (3593items, 7 journals) and Austria (1843items, 8 journals). The graph below pro-vides an overview of the participation ofeach country: Russia, Italy, Holland,Portugal, Belgium and Spain are themost significant suppliers: these figurescome from Charles Laisant’s report[Laisant 1900].

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Repartition of the mathematical domains according to the place of edition of the mostimportant journals

Number of bibliographical references submitted by each country in 1900

The absence of Great Britain andUnited States is not surprising, since thetwo countries were engaged in a compet-ing project, the International Catalogueof Scientific Literature. The case ofSweden is also quite paradoxical:Eneström was the representative of thecountry within the Commission Permanenteand he had written several articles infavour of the constitution of a mathemat-ical bibliography during the 1880s.Nevertheless, he rapidly showed someserious reservations about the Frenchproject, partly because of its system ofclassification. His growing inertiatowards the French repertoire is a plausi-ble explanation for the absence ofSweden.

To a great extent, the references sentby Holland, Russia and Spain correspondto the heading Mémoires ou ouvragesséparés. These nations were taking part inthe broadening of mathematical produc-tion, and it is likely that they used therepertoire in order to gain some recogni-tion at an international level. Moreover,one can assume that the mathematiciansof these countries judged that theirnational periodicals were not importantenough, and that monographs and booksconstituted the best illustration of theirnational production.

Only 157 classification codes were usedfor the ordering of the first three series,although the Index du RépertoireBibliographique des Sciences Mathématiquesproposed around 2000 possible codes.(Moreover, in his report, Charles Laisant[1900] confirmed that the first ten seriesthat had been printed at that time didn’tuse more than 300 classification codes ofthe index.) Concerning these 300 indexfiles, it is important to notice that 113 ofthe 157 codes refer to bibliographicalitems that were equally published before1840 as after 1870. We can thereforeconclude that most of the mathematicaldomains designated by these codes wereactive over a large period of the nine-teenth century. Furthermore, 11 classifi-cation codes are exclusively devoted tomathematical works published after1860; 8 of these concern mathematicaldomains that emerged in the second halfof the nineteenth century: determinants(2 codes), Dedekind and Kronecker’sarithmetical theory of algebraic functions(2 codes), properties of ϕ (n), Lie’s theoryof continuous groups, Gyldén’s theoryand nomography. The presence of twoother domains – the properties of gener-al involutions according to Chasles, andone devoted to axonometric or isometricperspective – reveals the active role ofEmil Weyr at the beginning of the perusalwork, since most of these bibliographicalreferences come from the Sitzungsberichteder Königliche Akademie der Wissenschaftenin Wien. The last domain (descriptivegeometry on curves and surfaces) gives anillustration of the vitality of this old theo-ry: this can be explained by the impor-tance of descriptive geometry training inEngineer Schools and Faculties ofScience.

Who was in charge of the perusalprocess and how was it done? Most of theGerman and Austrian contributions arisesfrom perusal of the Journal für die reineund angewandte Mathematik and theSitzungsberichte der Königliche Akademie derWissenschaften in Wien. Emil Weyr essen-tially did this work. He was the Austrianrepresentative in the Commission perma-nente and the leader of a small crew. Hewas certainly the most dynamic foreigncontributor and his work ensured theinternational representation of the reper-toire for the first three series. In a letterto Henri Poincaré (25/04/1892), Weyrwrote: “J’ai l’honneur de vous signalerqu’il nous sera possible de remplir votredemande au moins quant aux principauxrecueils allemands. M. Le baron deLichtenfels, professeur de mathématiquesà l’École Polytechnique de Graz s’estchargé de dépouiller avec moi le Journalde Crelle. […] Cette collection de fichesdéjà finie, concernant les Sitzungsbericht etles Denksschriften de Vienne et de Prague,les publications polonaises et quelquesautres publications, vous parviendra enquelques jours par la poste”. On theother hand, it seems that his work was notat all exhaustive. For instance, accordingto his collected works, Jacobi published104 articles in the Journal für die reine undangewandte Mathematik, but one can onlyfind 36 references to Jacobi’s works in thefirst three series of the repertoire.Judging from this example (and fromseveral others), it appears that considera-tions concerning the mathematicaldomains, the length, or the theoreticalimportance of publications were not auto-matically seen as relevant criteria.

Most of the French contribution arisesfrom perusal of the Comptes rendus del’Académie des sciences. This was made byHenri Brocard, who was the director ofthe Alger Meteorology Institute and oneof the French representatives of the com-mission. His work concerned only publi-cations in applied mathematics (classes R,S, T, U, V, X) – this would require furtheranalysis since the situation is similar forother French journals – but it was exhaus-tive: in his report, Laisant [1900] noticedthat the Comptes rendus had been com-pletely perused: “Il n’y a cependant peut-être que les Comptes rendus de l’Académiedes Sciences de Paris qui soient tout à faitau courant, grâce au dévouement de M. leCommandant Brocard ; c’est lui qui a priscette si lourde tâche, et il s’en est acquit-té avec une exactitude et une régularitévéritablement admirable”.

To conclude, we note that two majormathematical journals seem to be absentfrom the whole repertoire: theMathematische Annalen and the Nouvellesannales de mathématiques. The former isastonishing, since Weyr announced thebeginning of the perusal of this journal toPoincaré in 1892: “Mr le Dr Krohn,Privatdozent dans notre université, s’oc-cupera avec les Mathematische Annalen…”.The case of the Nouvelles annales is quitedifferent, and probably reveals the(intentional?) choice made by French

mathematicians for a specific style ofmathematical (that is, ‘official’) academicand professional mathematics, to thedetriment of mathematics for education,a domain that was not much recognised.

We believe that this mathematical bibli-ography can constitute a valuable sourcefor historians of mathematics. In partic-ular, it gives access to the conception ofmathematics that was constructed by thenineteenth-century mathematical com-munity. Our analyses will be completedat the end of the data entry process.Moreover, a possible development of thisresearch could consist in a comparisonbetween this bibliography and someother repertoires, such as the BelgianRépertoire Bibliographique Universel or theJahrbuch über die Fortschritte derMathematik. Finally, an understanding ofthe expectations, difficulties, illusions,etc. raised by this first attempt to organ-ise mathematical activity at an interna-tional level might be helpful for contem-porary mathematicians, at a time whenmany international projects are devotedto the numerisation of past or presentmathematical works.

BibliographyTheodore Besterman [1949]: A World

Bibliography of Bibliographies and ofBibliographical Catalogues, Calendars, Abstracts,Digests, Indexes, and the Like, Genève,Societas Bibliographica, 3rd ed.

Commission permanente du Répertoire bibli-ographique des sciences mathématiques:[1888]: Projet de classification détaillée pourle Répertoire bibliographique des sciencesmathématiques (Gauthier-Villars), 67 pages.[1893]: Index du Répertoire bibli-ographique des sciences mathématiques(Gauthier-Villars). [1894]: Index duRépertoire bibliographique des sciences mathéma-tiques – Errata, additions et modifications(Octobre 1894) à joindre à l’édition (1893) del’index (Gauthier-Villars). [1898]: Index duRépertoire bibliographique des sciences mathéma-tiques, 2nd ed. (Gauthier-Villars). [1908]:Index du Répertoire bibliographique des sciencesmathématiques, new ed. (Gauthier-Villars /H.C. Delsman). [1916]: Index duRépertoire bibliographique des sciences mathéma-tiques, 3rd ed. (Gauthier-Villars /H.C.Delsman).

Gustaf Eneström [1890]: Sur lesBibliographies des sciences mathématiques,Bibliotheca math. (2) 4, 37-42. [1895]:Répertoire Bibliographique des SciencesMathématiques, Bibliotheca math. (2) 9, 29.[1898]: Über die neuesten mathematisch-bibliographischen Unternehmungen,Verhandlungen der ersten internationalenMathematiker-Kongresses, Leipzig, 280-288.[1911]: Wie soll die Herausgabe derValentinschen mathematischenBibliographie gesichert werden?, Bibliothecamath. (3) 11, 227-232.

Hélène Gispert [2000]: Les journaux scien-tifiques en Europe, L’Europe des sciences: con-stitution d’un espace scientifique (ed. M. Blayand E. Nicolaïdis), Seuil, Paris, 191-211.

Catherine Goldstein [2001]: Sur quelques pra-tiques de l’information mathématique,Philosophia Scientiæ 5, 125-160.

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J.C. Houzeau [1878]: Catalogue des ouvragesd’Astronomie et de météorologie qui se trouventdans les principales bibliothèques de la Belgique,préparé et mis en ordre à l’Observatoire Royal deBruxelles; suivi d’un appendice qui comprendtous les autres ouvrages de la bibliothèque de cetétablissement, Bruxelles, Hayez, imprimeurde l’Académie Royale.

J.C. Houzeau and A. Lancaster: [1882]:Bibliographie générale de l’astronomie ou cata-logue méthodique des Ouvrages, des Mémoires oudes observations astronomiques publiés depuis l’o-rigine de l’imprimerie jusqu’en 1880, mémoires etnotices, Bruxelles, Imprimerie XavierHavermans. [1887]: Bibliographiegénérale de l’astronomie, Ouvrages imprimés etmanuscrits, Bruxelles, Hayez, imprimeur del’Académie Royale de Belgique.

Charles Laisant [1900]: Sur l’état d’avance-ment des travaux du Répertoire bibli-ographique des sciences mathématiques,Bibliotheca mathematica (3) 1, 246-249.

Charles Laisant and Georges Humbert[1894]: Sur l’état d’avancement des travauxdu Répertoire bibliographique des sciencesmathématiques, 32° Congrès des Sociétéssavantes, extrait du Journal Officiel du 31 mars1894, Paris, Imprimerie des Journaux offi-ciels.

Armand Mattelart [2000]: Histoire de laSociété de l’Information, Paris, Éditions de laDécouverte.

Philippe Nabonnand and Laurent Rollet[2002]: Une bibliographie mathématiqueidéale? Le Répertoire Bibliographique desSciences Mathématiques, Gazette des mathé-maticiens 92, 11-25.

E. Neuenschwander [1994]: Les Journauxmathématiques, Companion Encyclopedia of theHistory and Philosophy of the MathematicalSciences (ed. I. Grattan-Guinness),Routledge, London-New York, 1533-1539.

Paul Otlet: [1900]: La statistique interna-tionale des imprimés, Revue de l’InstitutInternational de Bibliographie 5, 109-121.[1906]: L’office International deBibliographie, Le mouvement scientifique enBelgique. [1908]: La sociologie bibli-ologique, Le mouvement sociologique interna-tional. [1918]: Transformations opéréesdans l’appareil bibliographique des sciences,Revue scientifique 58, 236-241.

Anne Rasmussen [1995]: L’Internationale scien-tifique: 1890-1914, Paris, EHESS.

W.B. Rayward (ed.) [1990]: InternationalOrganization and Dissemination ofKnowledge. Selected Essays of Paul Otlet,Amsterdam, Elsevier.

Georg Hermann Valentin: [1885]: VorläufigeNotiz über eine allgemeine mathematischeBibliographie, Bibliotheca Mathematica (1) 2,90-92. [1900]: Die Vorarbeiten für dieallgemeine mathematische Bibliographie,Bibliotheca Mathematica (3) 1, 237-245.[1910]: Über den gegenwärtigen Stand derVorarbeiten für die allgemeine mathematis-che Bibliographie”, Bibliotheca Mathematica(3) 11, 153-157.

Laboratoire de Philosophie et d’Histoire desSciences – Archives Henri-Poincaré, UMR7117 du CNRS, Université Nancy 2, 23Boulevard Albert Ier, 54015 Nancy Cedex.e-mail: philippe.nabonnand@univ-nancy2.fr, laurent.rollet@univ-nancy2.fr

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EMS CommitteesA list of the EMS committees, together with their Chairs, is as follows.

Applied Mathematics Committee [Saul Abarbanel]Developing Countries [Herbert Fleischner]Eastern and Central Europe [Andrzej Pelczar]Electronic Publishing [Bernd Wegner]Group of Relations with European Institutions [Sir John Kingman (EMS President,

ex officio]European Research Centres of Mathematics (ERCOM) [Manuel Castellet]Education [Tony Gardiner]Raising Public Awareness [Vagn Lundsgaard Hansen]General Meetings [Luc Lemaire]Women and Mathematics [Emilia Mezzetti]Special Events [Jochen Bruening]Publications [Rolf Jeltsch]

Two MathematicsDigitisation

ProjectsWhile the mathematics community gearsup to digitise the whole of the mathe-matics literature, it’s a good idea to lookat two projects already up and running.These are the Jahrbuch Project atGöttingen and the Cellule MathDoc groupbased at Grenoble.

The Jahrbuch über die Fortschritte derMathematik was the first comprehensivejournal of reviews of the mathematicalliterature. It was founded in 1868 andappeared until 1942. The project has asits centrepiece the goal of making theentire Jahrbuch electronically available.

Much has already been done. If yougo to the EMIS homepage (www.emis.de)and click on the Jahrbuch project, you canuse the search facility, for instance, byauthor. I typed in ‘Hardy, G.H.’ and gota list of 314 titles, starting in 1899. Fromthere, it’s not hard to access the Jahrbuchreview for the titles selected.

For some publications, includingMathematische Annalen, MathematischeZeitschrift and Journal de MathématiquesPures et Appliqués, the project providesdirect access to facsimiles of the articlesthemselves. This is a fascinating site, awindow into both the past and the futureof mathematics.

Cellule MathDoc has recently opened awebsite, www.numdam.org. From thispage you can search by author, title orkeyword summaries of the articles in theAnnales de l’Institut Fourier and theJournées équations aux dérivées partielles.Again, you can summon the articlesthemselves to your computer screen.This service is entirely free if your insti-tution subscribes to the journals and, inany case, free for the Annales for articlesup to 1996.

Cellule MathDoc intends, in time andsubject to publishers’ permission, tomake all French mathematical journalsavailable in this way.

David SalingerEMS Publicity Officer

NSF, SCIENCEJOURNAL

ANNOUNCE SCIENCE

VISUALIZATIONCONTEST

The National Science Foundation andthe journal Science are now acceptingentries for the inaugural 2003 Scienceand Engineering VisualizationChallenge.

Winning selections will be featured ina special section of Science’s 12September issue and winners willreceive an expenses-paid trip to thefoundation for its Art of Science Projectexhibit and accompanying lecture.

This new international contest willrecognise outstanding achievement byscientists, engineers and visual informa-tion practitioners in the use of visualmedia to promote understanding ofresearch results.

The contest is open to individual sci-entists, engineers, visual informationpractitioners, and scientific teams –including technicians and support teammembers – who produce or commissionphotographs, illustrations, animations,interactive media, video sequences orcomputer graphics for research.

Entries must have been producedafter 1 January 2000. The contest dead-line for postmarked entries is 31 May2003. The contest rules and entry sub-mission instructions are available on theweb at

http://www.nsf.gov/od/lpa/events/sevc/Prospective entrants are encouraged toreview the contest rules before submit-ting an entry. Entry forms are availableat that web address as well.

Science is published by the AmericanAssociation for the Advancement ofScience.

Vagn, please tell us a little about your child-hood and background.I was born in 1940 in the beautiful town ofVejle, lying at the end of one of the Danishfjords along the east coast of Jylland.Close to forests and the fjord, it was anideal place for children to grow up.

With a working class background, it wasunusual at the time to attend secondaryschool beyond grade 7, and later the gym-nasium, but with the full support of myparents, I broke the social barrier, and fin-ished gymnasium in 1960 with excellentresults.

It was not always easy – and often ratherlonely – to step outside your social class,but altogether, I had a very happy child-hood with much love. Outside school, Iwas an eager soccer player – almostmandatory in my native town, which hasfostered several famous soccer players.Many happy hours were also spent as aScout, where I ended up as group leader.

A musician and music teacher living inthe same house as us persuaded my par-ents to buy a piano. At the time, I wasmore interested in football and other phe-nomena exhibiting curvature, but Ilearned the notes and music becameimportant to me – in particular, jazz.Today I prefer improvisation, and have aspecial weakness for Fats Waller.

After gymnasium you went to Aarhus tostudy. Why did you choose mathematics asyour main subject?In September 1960, I matriculated at theUniversity of Aarhus to study mathematicsand physics. There was never any realdoubt in my mind that these subjects weremy favourite subjects and my teachers atschool had several times pushed me in thisdirection.

The 1960s was a tremendous time formathematics and the natural sciences. Inthe opening paragraph of the handbookfor these studies, it said something like:‘For everyone completing these studies,the future is bright with a multitude of verydiverse possible appointments ...’. Withsuch words, you could fully submit yourselfto the study of the sciences without anyworries for the future. As a matter of fact, Ithink one could say the same today!

Originally, I thought that I would end upwith physics as my main subject. But at theMathematical Institute reigned ProfessorSvend Bundgaard, an energetic and all-time-consuming enthusiast for mathemat-ics. After less than three weeks of intensivebombardment with lovely mathematicalconcepts, mathematics became dominant.Svend Bundgaard has placed his mark on

a whole generation of mathematicians inDenmark.

In 1960, Aarhus was still a young univer-sity and the Mathematical Institute wasonly a few years old. There was a pioneer-ing spirit and Svend Bundgaard made thebest out of the positive economical situa-tion for the sciences. He made sure that aconstant flow of eminent mathematiciansvisited Aarhus, some of them for long peri-ods. Naturally, this created a very stimu-lating atmosphere, and also the social lifeof the institute was legendary.

For my final studies of mathematics, Ispecialised in topology with Professor LeifKristensen as adviser. The subject for mymasters thesis in 1966 was Morse theory andSmale’s proof of the generalised Poincaré con-jecture. This subject was along a differentline from the main emphasis in topology inAarhus, namely algebraic topology, whereLeif Kristensen himself was a leadingexpert on the Steenrod algebra. Leif wasnot very much older than his students andwe had a very friendly relationship withhim.

Immediately after obtaining my degree,I was appointed to a temporary position inAarhus. In the fall of 1967, I was appoint-ed assistant professor with the special taskof developping a contemporary and newcourse in differential geometry for theupper undergraduate level. I wrote a com-prehensive set of lecture notes for thecourse, laying the foundations of smoothmanifolds and developing the calculus ofdifferential forms and integration on man-ifolds, culminating in a complete proof ofthe generalised Stokes’ theorem. It was arather ambitious course for the given level,but it was a great success and several very

good students emerged from the course.Karsten Grove, now professor at theUniversity of Maryland, was one of the verybest and went on to make a brilliant careeras a research mathematician. In connec-tion with my teaching, Professor EbbeThue Poulsen followed the full course. Heclaimed that it was out of pure interest.Whether this was the full truth or not, Ifound this caring from an experienced andexcellent teacher very comforting.

From time to time, I discussed my planswith Svend Bundgaard and he encouragedme to go abroad to do a PhD. I wasextremely well motivated for this: myteaching had gone very well and I had writ-ten a complete set of lecture notes offeringan original introduction to a relativelyadvanced subject. I really felt eager to dooriginal research in order to qualify myselfproperly for a permanent university posi-tion.

How did England become your choice?In the summer of 1968, Professor Zeeman(now Sir Christopher) was one of the mainlecturers at a Summer School in Aarhus. Ithardly comes as a surprise to anyone who

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Interview with Interview with VVagn Lagn Lundsgaarundsgaard Hansend Hansen

Interviewers: Bodil Branner and Steen Markvorsen (Lyngby)

Vagn Lundsgaard Hansen.

Vagn Lundsgaard Hansen in the Study for House 4, Mathematics Research Centre, Universityof Warwick. The family lived in this marvellous house during the first year of their stay atWarwick, 1969-72.

knows him that Professor Zeeman made astrong impression on me, and I discussedmy interests in mathematics with him toseek his advice. I got, as it turned out,tremendously good advice.

Professor Zeeman was the founder of theInstitute of Mathematics at the Universityof Warwick in Coventry, established in1964, and was for many years a charismat-ic leader of the institute. Combining inone person an eminent researcher, a bril-liant teacher and a visionary and cleveradministrator and organiser, the Instituteof Mathematics at the University ofWarwick under his direction quicklygained a reputation as a very strongresearch school for mathematics with alarge visitors’ programme.

From Professor Zeeman, I learned thatthey were about to hire the Americanmathematician James Eells as a professorof mathematics at the University ofWarwick to develop the then relatively newfield of global analysis. Combining strongelements of analysis, geometry and topolo-gy, this clearly matched my interests inmathematics, and I eagerly went toWarwick in September 1969 to study withProfessor Eells.

This was the best decision in my life, onlyexceeded by my marriage to Birthe in1964. Together with our eldest daughterHanne, we spent three extremely happyand unforgettable years in Warwick. In thesecond year of our stay, Birthe wasappointed mathematics teacher at a gram-mar school, so we got altogether a magnif-icent insight into the British school systemat the time.

Studying with Jim Eells was an enjoy-ment. His good spirit and sense ofhumour were a perfect match for me. Hehad a way of encouraging you so that youreally felt that you could do it. Most often,I found the problems to work on myself,but Jim was there putting it all in perspec-tive and due to his scholarly knowledge ofthe literature, you felt sure that you werenot just reinventing old things.

In Warwick, I found everywhere the bub-bling enjoyment of mathematics that I hadfelt inside myself for years, but somehowhad suppressed in Denmark. I came toknow many excellent mathematicians andseveral of them became my very goodfriends, including many of the young staffmembers at the institute and some of theforeign visitors.

I defended my thesis in the summer of1972: it contained work on the topology ofmapping spaces. As one of my results, Ihad succeeded in giving a complete divi-sion into homotopy types of the (countablymany) components in the space of contin-uous mappings of the n-sphere for all n.The result is rather surprising, and a paperabout it was published in the QuarterlyJournal of Mathematics, Oxford, 1974.

Then you went back to Denmark?Yes, but I must first mention that anothermajor result obtained during our stay inWarwick was our second daughter Helle.And then I felt ready for a permanent job.In 1972, the job market in mathematicswas tightening up. I got some offers fortemporary positions from different coun-tries, but I was relieved when an applica-tion for a position as associate professor atthe University of Copenhagen was success-ful. In August 1972 we moved toCopenhagen and a new period in our lifebegan.

The University of Copenhagen is theoldest, and was for hundreds of years theonly, university in Denmark. The eminentDanish mathematicians from the pasttherefore all had relations with this univer-sity. Such strong historical traditions add aflavour to a university and gave me valu-able experiences, in addition to the expe-riences I had enjoyed at the younger uni-versities in Aarhus and Warwick.

The senior professors at the Universityof Copenhagen counted among othersThøger Bang, Werner Fenchel, BentFuglede and Børge Jessen, all first-classmathematicians. In addition there were

several newly appointed young staff mem-bers of high quality. I was very kindlyreceived and quickly accepted.

In addition to research and teaching, Inow also became involved in administra-tion and ended up as Chair of the commit-tee of study affairs in the science faculty.At the time, the universities in Denmarkwere run very democratically, implyingthat students had 50% of the seats in thisinfluential committee. Obviously, thiscaused many discussions, but being fond ofdiscussions leading to democratic deci-sions, I found this stimulating and inspir-ing.

In connection with a graduate course onsingularity theory in 1976, I was inspiredto define the notion of polynomial cover-ing maps. In addition to my continuedinterest and work on the topology of map-ping spaces, I now began a study of thesespecial covering maps, defined by project-ing the zero sets for parametrised familiesof complex polynomials onto the parame-ter space. An account of my work in thisfield was given in the book Braids andCoverings, published by CambridgeUniversity Press in 1989. This book isbased on a set of lectures delivered while Iwas a visiting professor at the University ofMaryland, College Park, in the fall of 1986.

Finally you came to Lyngby.In 1978, I was contacted by mathemati-cians from the Technical University ofDenmark about whether I would apply fora position as professor at this university. Isaw some challenges and promising possi-bilities at the Technical University ofDenmark, situated in Lyngby in the out-skirts of Copenhagen, so I applied for theposition. At that time, a professor wasappointed as a civil servant by the Queen,and the whole process with selection com-mittee, approval by the democraticallycomposed senate of the university, etc.,took some time. In 1979, our son Martinhad been born. And then, on 1 February1980 I was appointed professor of mathe-matics at the Technical University ofDenmark.

During the late 1970s the DTU Departmentof Mathematics went through a somewhatturbulent period of reorganisation. At thesame time, it was fighting for survivalagainst the old idea that the staff teachingand doing research in mathematics ought tobe distributed into the other departments inorder to serve the applied disciplines best.How did you see these challenges and yourown possibilities at DTU at that time?I knew about these difficulties, but Ifocussed on the fact that the senate of theUniversity, after thorough considerations,had decided that the Department ofMathematics should survive as an indepen-dent department. I also had the impres-sion that influential members of the senateduring the process had recognised thatmathematicians need to be members of amathematical community in order tomaintain a level of mathematical expertise,whereas it was useful for our colleagues inthe engineering sciences to consult their

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Vagn Lundsgaard Hansen presents a lecture on catastrophe theory in connection with an openhouse arrangement for the public at the Faculty of Sciences, University of Copenhagen, in 1977

mathematicians with mathematical prob-lems. I think they also recognised thatmathematical research is necessary toensure that the teaching of mathematicsshould not stagnate.

I felt that I had something to offer afterthe experiences I had gained at other uni-versities, and I appreciated very much theexpectations and the great confidence inme shown by my new colleagues. I knew afew of them very well from earlier, and Iwas sure that the large majority of the staffmembers would do their utmost to helpcreating a good department.

As I have said earlier, the universitieswere run very democratically at the time,and you had to argue your points of view.I went for open discussions of strategiesand attitudes, since I am convinced thatthis kind of leadership is the only one giv-ing lasting results in research institutionswith qualified staff members. I tried to bethe first in the morning and the last in theevening at work, keeping up positive dis-cussions about mathematics and ourduties. I think maybe I functioned as agood catalyser in these discussions, andover the years the department has reacheda high degree of consensus about our roleas mathematicians at a university with itsmain emphasis on the engineering sci-ences. I am very fond and proud of mycolleagues: many of them have developedas research mathematicians in a way thatcould not have been foreseen in 1980.Trust and confidence in people are strongand indispensable tools for keeping upgood spirits.

Lately there have been many changes inthe university structure in Denmark, mov-ing very far away from a democratic elec-tion of leaders. The current mantraappears to be strong leaders of the univer-sities, appointed by small boards dominat-ed by outside members, and the ability forquick decision-making seems to be morevalued than the ability to make wise deci-sions based on arguments presented in

public. This may be a good approach inprivate firms, but is not necessarily good inuniversities. I am not in favour of thisdevelopment, but I am still confident inmathematics.

Is it fair to say that the idea behind yourconstruction of the Department’s logo wasto iconise that mathematics is strongestwhen considered a unity across the disci-plines?Yes, I think that this is a fair description. Icertainly wanted to iconise the majorresearch fields in our department – geom-etry, analysis and discrete mathematics – asappear together in the logo. At the sametime, it gave me the opportunity to con-nect with some of the major Danish math-ematicians who have been associated withDTU – namely, Jakob Nielsen and JuliusPetersen. Our department has much to beproud of in the past. This is a good levelto strive for.

Problems from applications do not comedivided into mathematical specialitiesfrom the beginning. So, maybe instinctive-ly, I also wanted to signal that in order tobe valuable mathematical members of anengineering community, it is important tobe broadly educated in mathematics and tokeep an open mind for mathematics on abroader scope than isolation into narrowspecialities will admit.

A very special enjoyment has been themany excellent students I have met atDTU. Around 1985, I planned anddesigned a new course on Fundamental con-cepts in modern analysis; the course materialdeveloped eventually into a book with thesame title, published by World Scientific in1999. I have been fortunate to be theadviser at Masters and PhD levels for someof the very best and able students, and invery diverse areas of mathematics. I amhappy that they all developped indepen-dence and an inner drive to follow their

own tracks, some of them with extremelygood results. I was deeply touched whenfor two days in November 2000, many ofthem delivered excellent and inspired lec-tures at a symposium organised by mydepartment in collaboration with the asso-ciation of secondary school teachers ofmathematics, in celebration of my sixtiethbirthday.

I have had a wonderful time at DTU. Ihave come to know many first-rate peoplefrom other departments. In the period1988-93, I was Dean of the Faculty of BasicSciences. In the period 1992-98, I was amember of the Science Research Councilof Denmark, four of these years as vice-chair. Also, in this connection, I met somevery interesting researchers from otherfields. This is also true for the DanishAcademy of Natural Sciences, of which Ihave been president since 1984.

And your own scientific work flourishes aswell! Could you tell us about some of thehighlights?In a paper published 1983 in the Bulletin ofthe London Mathematical Society, I succeededin determining the complete homotopytype of the space of homotopy equiva-lences of the 2-sphere – that is, the space ofmaps of degree 1 on the 2-sphere. Earlierin 1926, Kneser had proved that the corre-sponding space of homeomorphisms hasthe homotopy type of the orthogonalgroup SO(3), and in 1959 Smale provedthat the same holds true for the smallerspace of diffeomorphisms. I think that it isfair to say that topologists had expectedthat the same would also be true for thelarger space of homotopy eguivalences.But, as it turned out, I proved in my paperthat the space of homotopy equivalences ofthe 2-sphere is the product of SO(3) andthe double loop space of the 2-sphere,which is a highly non-trivial space. Veryrecently my work on mapping spaces has

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The logo of the DTU Department ofMathematics shows a geodesic immersion of thePetersen graph into the Poincaré disc of con-stant negative curvature, emphasising the sym-biosis between global analysis and discretemathematics. Julius Petersen was Reader atDTU from 1871-86 and Jakob Nielsen wasone of the founding fathers of global analysis;he was Professor at DTU from 1925-51.

Nordic Summer School on Differential Geometry, Technical University of Denmark, Summer1985. In the front row from left to right are Jerry Kazdan, Karsten Grove, Flemming DamhusPedersen, Lone Aagesen (secretary), Vagn Lundsgaard Hansen, Jean-Pierre Bourguignon andCliff Taubes. In the second row is Jim Eells (third from the left).

attracted some interest, in connection withtopological aspects of the calculus of varia-tions. This is the type of application I havealways hoped for.

Around 1980, the Danish MathematicalSociety decided to investigate the possibil-ity of publishing the collected mathemati-cal works of the Danish mathematicianJakob Nielsen, renowned for his pioneer-ing work in combinatorial group theoryand for his investigations of the fixed-pointstructure of homeomorphisms of surfacesof genus = 2. Such surfaces are covered bythe hyperbolic plane, and you can transferthe investigations to an investigation ofhomeomorphisms in the hyperbolic plane.This opens possibilities for exploitingmethods from non-Euclidean geometry,which Nielsen mastered to perfection. Iwas happy when the Society asked me to bethe editor of the collected works. Myresearch on mapping spaces and coveringspaces were not directly related toNielsen’s work, but it did contain some ofthe same basic ingredients, and JakobNielsen had been professor at theTechnical University of Denmark foralmost 25 years during his career.

The publication of Nielsen’s collectedworks entailed, among other things, thetranslation of Nielsen’s major papers, sev-eral of which had monograph size, fromGerman to English. For the actual transla-tion we had highly competent and expedi-ent help by the Australian mathematicianJohn Stillwell. He even translated a fewpapers from Danish.

The collected works were finally pub-lished in a two-volume set by Birkhäuser in

1986. Throughout the whole process, Ihad an intensive and very close collabora-tion with Werner Fenchel, who for manyyears had been a close co-worker of JakobNielsen. On many Saturdays, Werner cameto our house where we proof-read thetranslations and had lunch and dinnertogether. It was very rewarding for me tocome to know this noble and modest schol-ar so well.

You have written several books – bestsellers,like those listed in the references below. Doyou find it easy choosing what to write andhow to write it?Writing essays on a narrow and uninspiredtopic was not my strongest side in school,and spelling was something I had to workhard at: but now and then, when I foundthe topic engaging, I surprised my teach-ers. Nevertheless, I never thought aboutmyself as a good writer. Writing is some-thing I had to work at, but over the years ithas become an enjoyment and great stimu-lus to me.

As a child I often went to the locallibrary, sometimes several times a week, tolisten to librarians reading aloud novels,etc. I became fascinated by story telling,and I loved short elegant openings whereyou immediately felt in the middle ofevents. Like many children and adults allover the world, I was deeply fascinated bythe short novels of Hans ChristianAndersen: few authors can paint a picturein words so well. Along a different line, theBritish author W. Somerset Maughammastered the importance of good open-ings and the ability to stimulate your imag-

ination in short stories. Without reallythinking clearly about it at the time, some-how such writings became an ideal for me.

When I started university, mathematicswas not a topic you really thought about inconnection with pleasure reading or withhigh-class stylistic exposition: there was nostory telling spirit. However, I came toadmire the short and precise language ofmathematics, and I was often amazed bythe amount of information you can put ina few well-selected sentences. Being atopologist, I was particularly keen on thewritings of John Milnor: I have read manyof his books from cover to cover, enjoyingboth the mathematics and the elegantexposition.

I suppose I have always been thinkingabout how to get an element of good story-telling into the precise conceptual world ofmathematics, both when lecturing andwriting. Good story-telling involves leav-ing something to the imagination, andgood mathematics requires that you giveenough precise details in your arguments.

Over the years I have become more andmore daring in my attempts to combinestory-telling with mathematics. I try tocommit myself never to write about mathe-matics without presenting a concrete math-ematical result and elements of a mathe-matical argument. This is difficult to do,especially when addressing the public. Afruitful way is to combine the abstractstructures of mathematics with concretemanifestations of mathematics from theworld around us. The symbiosis betweenthe abstract and the concrete is the essenceof mathematics for me: I see it like yin andyang in Chinese philosophy – both abstrac-tion and concreteness are necessary ingre-dients for the health of mathematics andfor its vitality.

You have certainly applied this principlewith success, not least during WorldMathematical Year 2000. How did you getinvolved?In 1995, Jean-Pierre Bourguignon, thenpresident of the European MathematicalSociety, asked me whether I would be will-ing to chair the World Mathematical Yearcommittee that the society was about toestablish. I agreed to this, and in October

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Vagn Lundsgaard Hansen with one of his fourgrandchildren during holidays 2000.

A mathematical family photo taken during the symposium ‘Facets of Mathematics’, held inNovember 2000 to celebrate the 60th birthday of Vagn Lundsgaard Hansen. Here he is sur-rounded by several of his students and Jim Eells.

1995 the committee was formally estab-lished by the Executive Committee.Among the excellent and energetic mem-bers of the committee, I am sure thateverybody will allow me to single outMireille Chaleyat-Maurel as a quite excep-tional and dynamical person in this con-nection. Working with Mireille is a plea-sure, and we all owe a lot to her for herpositive and highly creative work in con-nection with the WMY. Quite early in thelife of the committee, my old friendRonnie Brown became a member of thecommittee, and his extensive experienceswith the popularisation of mathematicsalso became vital to the committee. A spe-cial personal benefit for me was that,through Ronnie, I became familiar withthe fascinating symbolic sculptures of theAustralian-British artist John Robinson.

During my work with the WMY, I cameto know many wonderful persons with adeep dedication to mathematics, and thework has given me many inspiring experi-ences.

Last year you were an invited speaker at theInternational Congress of Mathematiciansin Beijing, where your talk, PopularisingMathematics: From Eight to Infinity, wasextremely well received. You demonstratedonce again, that mathematics contains anabundance of concrete topics and resultsthat lend themselves directly to mathemati-cal conversations. [This article will appearin the June issue of the EMS Newsletter.]Could you tell us some of your impressionsfrom the Congress?It came as a great and unexpected surprisefor me when I was invited to lecture at theInternational Congress of Mathematiciansin Beijing on the popularisation of mathe-

matics. Many people from all over theworld have made valuable and inspiredcontributions to the presentation of math-ematics for the public, so I felt greatly hon-oured by this invitation. For the lecture Ichose subjects that I find suitable for con-versation on mathematics among people,with my starting point as concrete manifes-tations of mathematics in nature or civili-sation: I think that such conversations mayprove a good way of raising the publicawareness of mathematics. After my lec-ture I was interviewed by journalists fromthe leading Chinese press agency, whowanted to use some of my ideas in futurearticles about mathematics. I was certainlyconfirmed in my hopes that the idea of‘mathematical conversations’ will catch on.

I was thoroughly impressed by the con-gress. It was amazing to see the ChinesePresident, the Vice-Premier of China andthe Mayor of Beijing attending the fullopening ceremony. I think all participantsfelt really welcome in China, and ourChinese hosts did everything they could to

make it a very special event. It was clear toeverybody that mathematics is held in highesteem in China. This gives renewedmomentum and hopes for a world-wideand bright future for our subject.

A selection of works by V. LundsgaardHansen related to this interviewGeometry in Nature, A. K. Peters, Ltd., 1993.Shadows of the Circle – Conic Sections, Optimal

Figures and Non-Euclidean Geometry, WorldScientific, 1998.

Braids and Coverings – Selected Topics,Cambridge University Press, 1989.

Fundamental Concepts in Modern Analysis, WorldScientific, 1999.

(ed.) Collected Mathematical Papers of JakobNielsen, Birkhäuser Verlag, 1986.

‘Jakob Nielsen and his contributions to topolo-gy’, Chapter 37 in History of Topology (ed. I.M. James), Elsevier Science B.V. (1999).

‘I am the Greatest’, Mathematics in School 25 (4)(1996), 10-11.

‘The Story of a Shopping Bag’, MathematicalIntelligencer 19 (2) (1997), 50-52.

INTERVIEW

EMS March 2003 19

Carlo Pucci, one of the most distinguished Italian mathematicians of his generation,died in Firenze on 10 January 2003, at the age of 77.

Carlo Pucci was the Honorary President of the Italian Mathematical Union (UMI).He was born in Firenze in 1925 and, after graduating under the direction ofGiovanni Sansone, he worked in Rome under the direction of Mauro Picone. From1962 until his retirement in 2000 he was full professor in mathematical analysis inCatania, Genova and Firenze. He also worked also in the United States: for two yearshe was assistant professor in the Institute for Fluid Dynamics, University of Maryland,and was subsequently visiting professor at Rice University, the University ofLouisiana at Baton Rouge, and the University of California at Berkeley.

Pucci was a mathematician of remarkable presence and immense energy. Hebelieved that mathematicians’ jobs could be wholly fulfilling if world-wide connec-tions could be made as soon as they began their research. So he worked tirelessly tosee this goal realised. As President of the National Mathematical Committee of theItalian Research Council he promoted an impressive programme of fellowships foryoung students in mathematics and for visiting professors, in order to establishstrong connections between Italian and foreign mathematics researchers.

Among the most striking aspects of his personality was his long-term vision: he wasable to see and pursue ideas that would come to maturity only some years later. So,as President of the UMI and President of the National Institute for HigherMathematics he later had considerable influence on mathematicians and mathemat-ical institutions and achieved his aims to a very large extent.

The mathematical work of Carlo Pucci was mainly concerned with partial differen-tial equations. He obtained a celebrated maximum principle (simultaneously andindependently discovered by A. D. Alexandrov), where sharp analytic and geometricarguments concur to bring about an appealing result. Together with F. John, M. M.Lavrentiev and A. N. Tikhonov, he was also a pioneer in investigating the so-calledill-posed problems in the sense of Hadamard. His work in this field contributed toestablishing the basics of the current theory of these problems.

Carlo Pucci was, in many respects, an exceptional person. Generous, open andaccessible, particularly with his young students, he had many good ideas and initia-tives and the talent (and the physical strength) to understand the people who wouldimplement them. All his students were delighted and amazed at his availability todiscuss their mathematical drafts, together and with each of them separately. Manyof his students have themselves become well-established mathematicians.

He grew up very close to his uncle Ernesto Rossi, one of the strongest opponentsof the fascist dictatorship in Italy, and this legacy was strongly impressed on CarloPucci. During World War II he was active in the Resistance, and subsequently had astrong sense of civil commitment. In his last years he devoted himself to the ErnestoRossi - Gaetano Salvemini Foundation as a historical and cultural heritage of thesetwo major Italian personalities from the last century.

Carlo Pucci will be very much missed by his friends and colleagues.

Obituary: Carlo PucciGiuseppe Anichini

At a meeting in connection with the WorldMathematical Year held during the ThirdEuropean Congress of Mathematics inBarcelona, Vagn Lundsgaard Hansen presentsa Danish poster picturing the bridge over theGreat Belt in Denmark, entitled ‘Mathematicsbridges gaps in culture, science and technology’.(The poster appeared on the back cover of EMSNewsletter 38 (December 2000). The otherperson in the picture is Kim Ernest Andersen,who designed and implemented the EMS-gallery containing the posters submitted for theposter competition organised by the EMS inconnection with the WMY.

This interview is in two parts: the secondpart will appear in the June issue.

Dmitry Anosov was born in 1936 in Moscow.He graduated from the Department ofMechanics and Mathematics of Moscow StateUniversity in 1958, and took postgraduatecourses at the Steklov Mathematical Institute inMoscow in 1961. Since then he has worked inthat institute, in various positions: he is cur-rently head of the Department of DifferentialEquations. From time to time he has alsoworked at the Moscow State University (wherehe is Honorary Professor and head of thedepartment of Dynamical Systems) and atMoscow Independent University.

He is an expert on dynamical systems andrelated areas of the theory of differential equa-tions and geometry. His best-known achieve-ment was the active role he played in creatingthe ‘hyperbolic’ direction of dynamical systemstheory. This was officially recognised by theState Prize of the USSR in 1976 and unoffi-cially by the appearance of his name in Anosovsystems, flows, diffeomorphisms and foliations,and quasi-Anosov homeomorphisms. He was aninvited section speaker at the InternationalMathematical Congresses in 1966 and 1974.

What are your most important childhoodmemories?I have almost no recollection of the timebefore Hitler’s Germany attacked theUSSR in June 1941 – only a few blurryepisodes: I cannot say when they tookplace. During the war my family sufferedmuch less than most other people, but theprofound changes in our lives at the begin-ning of the war and during evacuation inKazan left such a strong imprint that Iremember a lot. I was four-and-a-half atthe beginning of the war: later, as I grew, Iremembered more.

Tell me about your parents.My parents were scientists – chemists whoreached professorial level. They were fromSaratov, and from the 1920s they lived inLeningrad where they worked mainly atthe Academy of Sciences (created when thecapital of the Russian Empire was StPetersburg). Later they moved with themain body of the Academy to Moscow.During this transition, many Academyemployees received rather spacious quar-ters (even by present-day standards) – forus, it was a three-room apartment for threepersons (the third was my grandmother).After that, the fresh Muscovites merrily‘became fruitful and multiplied’ (thoughstill not with biblical intensity).

This generosity in accommodating theAcademy employees during the move to

Moscow was rather exceptional, since theattention of the powers-that-be to sciencewas generally more verbal than real. Thesalary was not the same as during the post-war period. However, even before the warmany talented young people chose a scien-tific career. For many, science was inter-esting in itself, but there were at least twoother factors. First, in many other profes-sions the salaries were also low. Second,for many young people other choices wereclosed for administrative reasons, or wereunattractive because of ideological or otherpressures.

At that time there were not enough com-petent college instructors (the scale ofengineering education expanded dramati-cally after the beginning of industrialisa-tion), so my father, besides working at theAS, taught simultaneously at three othercolleges. This was not due to his desire toshare knowledge (which he satisfied afterthe war by lecturing on more advancedsubjects to graduate students of the ASinstitute), but for extra income. So thefamily was relatively wealthy, both beforethe war and during the early war years.

After this, the leadership learned thatscience was capable of producing valuablefruit, such as radar (information on atomicenergy became available at that time, butphysically appeared later), and the salaryand rations of scientists were increasedconsiderably (the consequences of this,though gradually eaten by inflation, sur-vived until the arrival of so-called ‘democ-racy’). Because of this, we were lucky tolive through the war without misery: weevacuated to Kazan where we lived in oneroom in a former university dormitory.

Since my parents no longer spent asmuch time at home and my grandmotherwas constantly busy with housekeeping, Iwas urgently taught to read so that I hadan occupation. Maybe because of that self-study period I acquired a taste for theoret-ical science.

Do you remember Moscow life in the late-1930s?I don’t remember anything, and could notknow much: I know only from the stories ofolder people. The initial ignorance of theimportance of science had a positive sideto it – the repression at the end of the1930s affected others. This was clear inour apartment building, where some sec-tions were occupied by AS employees andsome by the employees of the FederalBank, mainly those who worked abroad.

When did your mathematical talentsbecome evident?

To a certain extent my interest in mathe-matics became apparent in the middle ofsecondary school. But at that time I wasmore attracted to physics. During theearly post-war years it undoubtedly becamethe dominant part of the natural sciences:atomic energy, rockets, radar, and alsotelevision (this had been invented earlierbut entered our life in the 1950s – evenordinary radio receivers were not wide-spread until the early post-war years). Thequality of popular scientific literature inphysics and astronomy was quite high atthat time.

In 9-10th grades I went to the physicalcircle (study group) at the University,supervised by G. D. Petrov: I was less inter-ested in the mathematical circles. I reck-oned that the next step after high-schoolmaths was higher mathematics which wastaught in colleges, and what they did in themathematical circles was not very impor-tant. I now think I was half-right and half-wrong, which agrees with R. Courant’spoint of view in his book What isMathematics? (with H. Robbins). I studiedmore on my own then. I had average suc-cess in Olympiads, no brilliance: I under-stand that I am not alone in this respect –success in such competitions is not neces-sary to reach the level of an RAS member.Of course, there were competition winnerswho later became famous mathematiciansat the highest level – such as V. I. Arnold,who was one year younger than me; I didnot have contact with him then.

In my later grades I gave more attentionto mathematics, since I came to under-stand that the great book of the universe ‘iswritten in mathematical language’(Galileo). Gradually I became interested inmathematics itself.

How did you enter the Moscow StateUniversity?I graduated from high school in 1953 witha gold medal (high honours) and so need-ed only to pass an interview. If it had gonebadly, I would have had another chance bytaking the entrance examinations – but itwent well. I was interviewed by L. N.Bolshev and V. G. Karmanov, who askedsomething mathematical – had I ever beeninterested in something beyond the high-school curriculum? I remember a questionwhich sounded like ‘Are there more ratio-nal numbers or irrational ones?’ Then

INTERVIEW

EMS March 200320

Interview with Interview with D.VD.V. Anosov. Anosov

interviewer: R. I. Grigorchuk

Dmitry Anosov

they proceeded to general questions. Isaid that I liked classical music. Theyasked whether I liked Prokofiev, and Ireplied honestly that I liked only theClassical Symphony. The interviewersgrinned – ‘you will have to grow up’: theywere right.

The year 1953 was very important forour country – Stalin died in March, and inthe summer his right-hand man Beria wasarrested (later he was put on trial andshot). Life became freer, though people inthe West would not have considered it free.(This is not only my opinion.) Many yearslater, A. N. Kolmogorov told Arnold thathe ‘got a glimpse of hope’ at that time andthat it partly stimulated a rush in his scien-tific activity in the mid-1950s.

The year 1953 is also memorable forMoscow University, because it acquired anew building – the famous (more than 30-storey) building that became almost asmuch a symbol of Moscow as the Kremlin.The University was fortunate that I. G.Petrovsky had become rector shortlybefore that: he was quite influential at thetime and for a few years later. Of course,the communist party group made many ofthe decisions, but from time to timePetrovsky managed to stand his ground: Ithink that the highest party leaders trustedhim and did not have much respect fortheir party servants. (Unfortunately, helater lost his influence, in the middle of theBrezhnev period, and the influence of theparty group grew.) Petrovsky could notchange the situation in social sciences orbiology, but could (and did) do things inother fields.

Tell me about your first two student years?At first I was rather disappointed: I waswell prepared and could have been taughtfaster and more intensively. On the otherhand, nobody prevented me from studyingmore intensively by myself – quite theopposite. During my freshman year I. R.Shafarevich started a study seminar inalgebra. By the spring, only Yu. I. Manin,E. A. Golod and I still attended the semi-nar: by that time we had reached the ele-ments of Galois theory.

Also, during my freshman year, E. F.Mishchenko supervised recitation sessionsin analytic geometry. He told me thatthere was a famous mathematician, L. S.Pontryagin (I had heard of him indepen-dently), who would lecture to us the follow-ing year and would hold a special seminar.That is where I went. I was grateful toShafarevich for the algebra (later I tooktopics courses from him), but I was moreattracted to analysis, and to some extent togeometry.

Many people expressed the opinion thatthe 1950s to 70s were the blossom time forthe MSU Department of Mechanics andMathematics. This prosperity had no ana-logue elsewhere in our country, or possiblyin the whole world; it was manifested in theabundance of topics courses and seminarscovering all of mathematics. I dived intothat sea during my third year, and for thefirst two years was satisfied with what Idescribed.

Which MSU professors had the most influ-ence on you?First was Pontryagin (see below) and his co-workers (not yet professors) Boltyansky,Gamkrelidze and Mishchenko. I havealready mentioned Shafarevich, one of thebest, if not the best, lecturer I have everheard. During my third year a group ofrelatively young mathematicians started alecture-and-seminar series on new areas oftopology (mainly, homotopic topology):these were Boltyansky, Gamkrelidze,Onishchik, Postnikov, Shafarevich andSchwarz. They were joined by E. B.Dynkin, who did not take part in the edu-cational aspects but studied some thingswith the others, and in particular workedon a collection of translations, ‘FibreBundles and their Applications’, whichappeared in 1958 and played an importantrole in our country. I never heard of a sim-ilar undertaking among MSU mathemati-cians or elsewhere to study a whole field.Not all of the students who took to the newwind stayed in science, and not all of thosewho remained worked in algebraic or dif-ferential topology or in the adjacent areaof algebraic geometry: this was also true ofour teachers. But, I think, nobody washurt by the acquired culture.

The announcement (by A. S. Schwarz?)of this enterprise for students said some-thing like ‘one can study simple propertiesof complex spaces or complex propertiesof simple spaces’. This phrase irritated P.S. Aleksandrov, the chair of topology andgeometry, who was generally an importantperson who had switched to general topol-ogy. He did not oppose the new areas, butneither did he support them, tryinginstead to make room for general topolo-gy. Several years later, at an all-uniontopology conference in Tashkent, he saidthat according to Kolmogorov (a scientistwith a wide range) algebraic and differen-tial topology had not attained as wide animportance in mathematics in general asgeneral topology, in spite of all theirremarkable achievements. To a certaindegree, Kolmogorov was right – continuityis encountered more often than (say) somebordisms or others. However, the additionof integers is encountered still more often.

At the beginning, smooth manifolds didnot play a special role in our education.But in 1955 (coinciding with the start of

our topological education), Pontryagin’sbook Smooth Manifolds and Their Applicationsin Homotopy Theory appeared; its first chap-ter was the first ever textbook on smoothmanifolds. (G. de Rham’s bookDifferentiable Manifolds, which came out in1953 and appeared in Russian in 1956,could not play such a role: it brought thereader too quickly to its main subject –homology theory based on differentialforms and currents – without giving thereader time to get used to manifolds.Maybe de Rham did not have this educa-tional goal in mind, while Pontryagin did.)

When Pontryagin’s book appeared, Ihesitated – was it worth buying? Bookswere cheap then in Russia, the price wasnot a problem even for a poor student, andI was not poor – my parents had a goodincome. But I knew that Pontryagin’sachievements in homotopic topology weresurpassed by the French, so how good washis book? Fortunately, Gamkrelidze cameup to me at that moment: he could notimagine that I doubted the value of thebook. He thought I had no cash and kind-ly offered to lend me some money. Thatconvinced me that the book was worthyand I bought it. Thanks to RevazValerianovich for his advice!

During my fourth student year,Gamkrelidze started a seminar with‘smooth’ orientation. Of special impor-tance to me was learning the area thatSerge Lang later called ‘the no-man’s landbetween the great three differential theo-ries’ (differential topology, differentialgeometry and ordinary differential equa-tions). Very quickly I learned to think ininvariant terms, with the correspondingunderlying notions, and to bring to gener-al position by small perturbations usingSard’s theorem. (Sard’s work appearedduring the war and was not known inMoscow for a long time; his theorem waslater rediscovered by Dubovitsky, whosename we attached to it.)

Later, at the Steklov graduate school, S.P. Novikov and I became interested in cal-culus of variations in the large, and weread the monograph on it by M. Morse.We later used our acquired knowledge dif-ferently. For me, the main thing was notthe calculus of variations in the large itself,but rather seeing how a far-reachingmixed analytical and geometrical theory isdeveloped. By that time I had not enjoyedthe supervising and directing influence ofsenior colleagues, but I had very usefulcontacts with S. I. Alber who then workedin Gorkii (Nizhnii Novgorod).

The middle of the 1950s saw the remark-able achievements of A. N. Kolmogorov inthe theory of dynamical systems.Somewhat later (in 1958-59, when I was agraduate student), these were included in atopics course that he gave (only once) andin a related seminar.

In many respects Kolmogorov had hisown ‘style’ which made him very differentfrom the rest. In particular, unlikePontryagin, Gelfand and many others,including scientists of my generation,Kolmogorov did not conduct a permanentseminar that would reflect the changes in

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Anosov as a student

his scientific interests. I think that therewas a ‘central’ seminar on probability the-ory to which Kolmogorov devoted moretime than to anything else; but afterbecoming interested in other things, hedid not change the direction of that semi-nar but rather started a new seminar whichran for only a year or two. As far as Iremember, the entropy approach inergodic theory, which he invented, was notmentioned either in the course or in theseminar, although some other aspects of‘abstract’ (purely metric) ergodic theorywere considered, such as the spectrum anddynamical systems with discrete spectrum;I think that there was some discussion ofsystems with unusual spectral properties,but I do not remember this well; in anycase, some random processes were consid-ered as dynamical systems.

However, another of Kolmogorov’sachievements – now called the KAM theo-ry – was covered. Strangely, Kolmogorovnever wrote a detailed exposition of theseresults – it was done by Arnold. Of course,KAM is difficult to present, and it wouldnot have been surprising if it had notappeared for several years. Pontryaginand P. S. Novikov (my friend’s father)spent several years writing full expositionsof their achievements in topology andgroup theory (with Novikov finishing thiswork in collaboration with his student S. I.Adian). But Kolmogorov never wrote a fulltext on his results in KAM, although he wasnot tight-lipped – he wrote several paperson different subjects in the period betweenhis first KAM announcements and Arnold’spublications.

Kolmogorov has over 500 publications,but his high reputation is based on a few‘pearls’ whose number is naturally smaller.In the middle of the 1950s he had a rushof scientific activity – I have already men-tioned dynamical systems, but he also sug-gested using entropy notion in the theoryof functional spaces. (Entropy dimensionto some extent was discussed byPontryagin and Shnirelman, but they hadno applications.) His whole entropy enter-prise was new and important. As for KAM,he may have hoped to obtain other newresults in this area and then write about it.Curiously, when preparing a full collectionof his works at the end of his life, he wasvery selective and included only a fewthings.

I was very impressed by Kolmogorov’slectures and seminars, but I did not under-stand many things. His lecturing style wasdifficult for the audience. I don’t know ifhe overestimated us or purposefully aimedexclusively at the best prepared and capa-ble in the audience. Only later did Iremember something I had heard, thoughtit through anew and began to understand.

I was also very interested in N. V.Efimov’s course on differential geometryin the large: this was mainly on the rigidi-ty of surfaces of different types. Efimov’smost famous result on the non-existence ofcomplete surfaces in R3 with negative cur-vature separated away from 0 had not yetbeen obtained, but Efimov was ‘approach-ing’ it and talked about some partial results

in that direction. I have never dealt withdirection in my work, so in this case oneshould rather talk about impressionsrather than influences.

The last topics courses in which I hadgreat interest were those run by Arnoldand Sinai on KAM and ‘abstract’ ergodictheory. I took other courses as well, butwas mostly influenced by those I havedescribed.

Tell us about your teachers.I shall talk mainly about Lev SemyonovichPontryagin. It is well known that he wasblind – he lost his sight at 13 in an acci-dent. For a blind person to get highereducation is quite a feat, and he becameone the most important mathematicians ofhis time. Of course, we reckon that ourmain work is done in the brain and paperscribbling only helps, but it is a significanthelp and anyone deprived of it must beunder considerable stress. This does notcome for free. Pontryagin was a worka-holic, and with time this took its toll.

Unfortunately, memories of his last yearsare overshadowed by several circum-stances. One talks about his anti-Semitism,but not about his trying to judge thingsthat he could not keep track of (and thosewere not his private views – he played anactive administrative role too).Undoubtedly, he was used. Several yearsafter his death Shafarevich even remarkedin print that if LSP had lived longer, hewould have moved away from rulingAreopagus. But even during that periodthere were two significant bright momentsin his life. First, he actively fought turningthe rivers. (A giant hydro-technical projectinvolving transferring water from thenorthern rivers to Middle Asia and partlyto the Volga had been suggested: the eco-nomical soundness of this project wasunconvincing, and the ecological conse-quences would have been catastrophic.)Second, as head of the commission on sec-ondary mathematical education, he helpedto correct the consequences of the carelessreforms of the end of the late-1960s andearly-1970s.

My personal memories are from an ear-lier period – we had almost no contact dur-ing his final years. But I have to say thatwhen evaluating the life and career of aperson, one should take into account hiswhole life, and not only the last years.Those who speak of his anti-Semitism dur-ing his last years should remember that hehad several Jewish students, and that fur-thermore he tried to help V. A. Rokhlin,

which was unsafe at the time. (Aleksandrovand Kolmogorov also tried to help him.All three also tried to help Efremovich,who was not Jewish, so this does not sayanything about their attitude towards Jews,but it required the same valour as forRokhlin.) I think the latter outweighs.

Apart from these two paragraphs I seeno need to discuss LSP’s non-mathematicalactivities. In the end, these people areworth talking about only from the view-point of their scientific and educationalactivities.

I was LSP’s undergraduate and graduatestudent, and then worked in his depart-ment. I was never as close to him as histhree co-workers mentioned above, but it ishard to overestimate his influence on me.However, I think this influence was some-what unusual.

Pontryagin never taught me systemati-cally, and apart from the first few monthsof our acquaintance, not even non-system-atically. But he offered me several topicsto work on, first simple (not far beyond thelevel of exercises), then more and moredifficult: these turned out to be importantfor my growth. There were also a couple oftopics that he did not suggest but which I‘caught’ in the ambient creative atmos-phere around him. The influence of hisgeneral approach to mathematics mayhave been more important, but that is dif-ficult to describe.

Shortly before I became a student at theMSU, LSP decided to abandon topologyand switch to ordinary differential equa-tions. Actually, ODEs were not somethingnew for him. Many years before that, therewere contacts between Pontryagin andAndronov (a physicist, at least by educa-tion, who majored in physics at the MSU inthe 1920s). Around 1930 Andronov movedto Nizhnii Novgorod (then Gorkii), andthe transformation of this city into a signif-icant centre for mathematics and physics islargely due to him and his co-workers.(Incidentally, they also established thatLobachevsky was born in NizhniiNovgorod, but his scientific developmentstarted later – there was no university thereat that time; after his childhoodLobachevsky lived, studied and worked inKazan.) The collaboration betweenPontryagin and Andronov resulted in fourpapers: two by Pontryagin himself, one ajoint paper with Andronov, and the last ajoint paper with Andronov and anotherphysicist, A. A. Vitt, a student of Andronov.(Vitt was a victim of Stalin’s repression.)

A little later he wrote two papers on thezeros of quasipolynomials. Formally this isnot ODEs, but the stability of ODEs withdelay depending on the distribution ofthose zeros. However, all these works wereepisodes for LSP, although they were notepisodic for the theory of ODEs. He nowdecided to switch to ODEs completely,since he had no new ideas in topology andsome French papers with very strong newtopological results appeared at that time:the first announcements of these wereshort and the gist of the new methods wasdifficult to judge. Who knows: ifPontryagin could have established contact

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Anosov as a postgraduate

with French topologists, he might havecome up with new ideas, or at least com-bined his old ideas with those of theFrench. His approach was more geometri-cal, and we know that more geometricalideas, some going back to LSP’s works,were later added to the French algebraicmethods. But he was not permitted to goto France.

After his switch to ODEs, LSP had nochance to work with Andronov – the latterdied in 1952. But the first topic in ODEsthat LSP started to work on was ‘inherited’from Andronov – the theory of singularperturbations. Many different situationsarise in this theory. Some require ‘only’premises that are easy to guess, but fromthe very beginning Pontryagin concentrat-ed on the more difficult question (in whichAndronov was also interested), where theanswer was difficult to guess – the asymp-totics of solutions of differential equationsdescribing relaxation oscillations close todiscontinuous. While I was an undergrad-uate student, he offered me a simplerstatement which I managed to prove.Independently, the same was done by L.Flatto and N. Levinson, whose work waspublished earlier, but I considered a slight-ly more difficult version of the problem. Ithink that they purposely restricted theirpaper to the simpler version, because itrequired the same main ideas: if necessarythey could have proved my theorem. I donot know anything about Flatto, butLevinson was a well-known analyst and itwas an honour to do what he did. Still, mywork was a success for an undergraduatestudent: it was ‘a sophisticated exercise’that was useful for my development.Formally, it did not depend on anyoneelse, but in essence it was not based on newideas and methods.

Pontryagin lectured on ODEs to my class(it was a required part of the curriculum):this was the first time he had lectured onthis subject, or had taught a requiredcourse to a large audience. (Although hehad worked at the University before theAcademy’s move to Moscow, there wereprobably more students in one lecture hallthan in the whole department of mechan-ics and mathematics before – and topolo-gy, which he also taught at the Academy,was not a required course and did not havea large enrolment.) At the same time hewas preparing his well-known ODE text-book, and by the end of the school year wereceived a present – mimeographed copiesof the book. Publishing a book was differ-ent then – now you use a computer to writeanything you want and then print it out.The process then was much longer andrequired more work, in addition to theadministrative logistics. Many years later,when I began lecturing, I sometimes wroteout my lecture notes, but had only frag-ments by the end of the course. So, I can-not help but admire LSP’s responsibilityand ability to work.

Today’s ODE courses (at least at majoruniversities) more-or-less follow the high-lights established by LSP, which becamestandard. However, upon checking earliertextbooks, it is clear that Pontryagin’s

course was new, certainly in the USSR. (S.Lefschetz and V. Gurevich had alreadywritten somewhat similar books that wereunknown in the USSR. Although thesefirst attempts to modernise the ODEcourse did not have followers in the West,it was only after Pontryagin’s bookappeared that the situation started tochange. Lefschetz himself later turned hisbook into a longer graduate-level text.)

Pontryagin carefully prepared his lec-tures and tried to be comprehensible tomost of his students. Still, from time totime his lectures were difficult for quite afew. It was related in part to LSP’s lack ofteaching experience – before that, he hadtaught only topics courses in a differentsubject. There are still places in his bookthat are worth changing – but these are iso-lated shortcomings that could easily havebeen removed in subsequent editions;unfortunately, he did not do it.

LSP took a responsible attitude towardshis duties as a professor. For example,before exams there were review sessionsduring which students asked questions ifthey had not understood something in thecourse. Usually this involved straighteningout some issues, but LSP considered it nec-essary to repeat one or two of his lectures.

After a couple of years he got tired ofteaching a required course. He did notlecture poorly, but refused to teach thecourse and created a new one.

From the second half of the 1950s,Pontryagin worked mainly on optimal con-trol and later on differential games. I didnot take part in that work, since by then Ihad found my own field. I learned classi-cal ODEs mainly by reading myself – onlytowards the end was it complemented bythe topics courses of Kolmogorov, Arnoldand Sinai, but that was not the classical the-ory.

But the first nudge was from LSP, whorecommended that I read the mathemati-cal parts of Andronov and Khaikin’s Theoryof Oscillations. (It originally had Vitt as athird author, but after he was arrested hisname disappeared from the first edition.At first the cover page read ‘A. A.Andronov, A. A. Vitt and S. E. Khaikin’.When the cover page was reprinted, they

removed ‘Vitt’, but forgot to delete thecomma. Not to encourage politicallywrong conclusions, the suspicious commawas scraped off with a razor, but if onelooks carefully, there is less space after‘and’ than before, where there are visibletraces of scraping. I suspect that those whoforgot about the comma were penalized.)

This book had an extremely profoundinfluence on me – I had probably not beenso impressed by any other book. I thinkthere were two reasons for this. First, forthe first time I was reading not a text bookbut a monograph written by scientists, onea luminary and the other an exceptionallygifted educator (besides being a good sci-entist). Second, the two-dimensional qual-itative theory is quite impressive initially.(Before Pontryagin, there was almost nodiscussion of this field in a regular ODEcourse. It was covered in Poincaré’s collec-tion On curves defined by differential equations– Andronov urged its publishing – whichcontained detailed comments, and inQualitative theory of Ordinary DifferentialEquations by Nemytsky and Stepanov. Sincethe first book was ‘too special’, I read itonly several years later; the second, thoughundoubtedly rich in content (for its time)always bored me, I don’t know why, to thesame extent that as the Theory of Oscillationsabsorbed me.) Later generations of stu-dents were not as impressed by the mathe-matical chapters of Theory of Oscillations,since elements of the two-dimensionalqualitative theory were soon covered inmany textbooks and courses; after this, theTheory of Oscillations became a source with amore complete exposition of a subjectwhose basics were already known.

I studied many other aspects of the the-ory of ODEs by myself, from the works ofLyapunov, Perron and Bogolyubov. Ipractised searching the literature on sub-jects of interest to me, which was also use-ful. As I read, I tried to evaluate the workusing Pontryagin’s criteria: is it new inprinciple? or is it a useful refinement ofknown ideas and techniques? or neither?

I still believe that LSP’s best achieve-ments were in topology, and I caught himin decline – but the beginning of thedecline was slight and the level still veryhigh. My only critical comment on thatperiod relates less to his scientific activitythan to a certain mood that overcame him.He used to say that he studied real-lifeproblems (which he naively called ‘physi-cal’; what kind of physics is it when onedoes not have to know a single fundamen-tal physical law?); it was rather explicit,although not in the open, that others suchas Petrovsky, Bogolyubov or Gelfand hadpreviously worked on important appliedproblems but could not talk about them atthat time: at different times, and to a dif-ferent degree, all three were involved withthe Soviet atomic project. However, on thesurface everything looked decent. Iremember only one criticism of theseremarks of LSP. It was by Kolmogorov,who was also involved with physics andsome applications (the theory of shooting;turbulence, some questions connected tofluid dynamics and some applications of

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EMS March 2003 23

Anosov lecturing on complete uniform hyperbolicity

statistics of random processes, created byhim and N. Wiener). He said that there isa nice model for ordinary differentialequations – the geometrical picture of thebehaviour of trajectories in the phase space(Andronov coined the expressive termphase portrait), which carries so much infor-mation that there is no need for anythingelse, unlike partial differential equations,which require the knowledge of the physicsthey originated from.

I was far removed from higher circles,but I have the impression that Petrovskywas not particularly enthusiastic aboutLSP’s new direction. To some extent, hedisliked the emergence of a competitor ina field that he had ruled earlier (being theuniversity rector, he had no time forresearch, and at best could only followwhat was happening in mathematics); and

I cannot judge to what degree he felt thatLSP’s shortcomings, which for a whileappeared rather innocently in conversa-tions, but which later became more promi-nent: I am making the risky assumptionthat the former played the main role atthat time. LSP himself, after giving therestructured ODE course a couple of timesand written the corresponding textbook,did not make too much effort to overcomePetrovsky’s guarded attitude. But he hadachieved his goal – this course, whenoffered at a serious level, is now taught inthe style of Pontryagin everywhere in theworld. In addition to giving the newrequired ODE course, LSP and his co-workers held an accompanying seminar.This was initially a study group, but laterbecame a research seminar and movedfrom the MSU to MIAN. Its direct descen-

dent is the current seminar of MIAN’s DEdepartment.

Who were your student friends?Primarily these were the people with whomI studied the new field. First was S. P.Novikov. There were others among theregular participants of our topologicalseminars whose contribution to science(not necessarily to topology) was real,though not as great as Novikov’s:Averbuch, Vinogradov, Ivanovsky,Moishezon, Tyurina, and Fuks. I do notremember how regularly, but Zhizhchenkoand Melnikov also came; Manin and Golodparticipated in one of the study groups,but they were attracted to algebra, andsoon got pulled into it. It was only laterthat I drew closer to Arnold, Sinai andAlekseyev.

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EMS March 200324

The German Science Foundation DeutscheForschungsgemeinschaft (DFG) has establisheda new research centre in Berlin:Mathematics for key technologies:Modelling, simulation, and optimisation ofreal-world processes.The Centre is funded by DFG with 5 millioneuro per year, and is operated and cofi-nanced with 3 million euro per year by thethree Berlin Universities, the FreeUniversity (FU), Humboldt University (HU)and the Technical University (TU) as lead-ing institution, together with the tworesearch institutes, the Konrad-ZuseZentrum für Informationstechnik (ZIB) andthe Weierstrass Institute for AppliedAnalysis and Stochastics (WIAS). The cen-tre was opened on 20-22 November 2002 atthe Technical University of Berlin with athree-day workshop that started with aMathematical firework. This firework, withtalks for the general public including 3-Dmathematical visualisations, drew a spectac-ular audience of more than 1000 peopleand received a large and enthusiastic echofrom both audience and media.

History of the CentreIn August 2000 the DFG (as a result of fund-ing obtained through the UMTS licenceauction) started a new programme to estab-lish several centres of excellence in researchin Germany. The first call was open to allfields of research and drew more thaneighty proposals. In the first round threecentres were granted, with the topics Oceanrims in Bremen, Functional nanostructures inKarlsruhe, and Experimental biomedicine inWürzburg.

The second call in early 2001 was morespecific and was devoted to the topic ofModelling and simulation in science, engineeringand social science. A joint mathematics pro-posal was written by mathematicians fromthe Berlin universities and research centres,and coordinated by Martin Grötschel (TUand ZIB, Chair of the Centre), VolkerMehrmann (TU, Vice-Chair of the Centre),Peter Deuflhard (FU and ZIB), HansFöllmer (HU) and Jürgen Sprekels (HUand WIAS). There were 14 strong competi-

tors, many of them with participation fromother mathematics departments. In July2001 we learned that we were among thethree finalists, who then had to prepare adetailed proposal (a densely packed book of400 pages). In January 2002 the finalistshad to defend their proposals in competi-tion before an international group ofreviewers. The final decision in May 2002was based on the rule the winner takes all. Itsaw two very strong but disappointed run-ners-up who had spent as much time andenergy on their applications as we had.

Since the decision was made, the activitywithin the Centre has grown immensely.The administration of the Centre had to beset up and the facilities for the Centre arebeing prepared (it will occupy a large partof the mathematics building of TU Berlin).Furthermore, and most important, about 60researchers, 7 assistant professors and 7 fullprofessors, covering the areas of appliedanalysis, numerical analysis, stochastics, optimi-sation, visualisation, discrete mathematics andscientific computing have to be hired. Thecurrent grant is for four years and it has amaximum lifetime of 12 years, with twoevaluations on the way.

Mission of the CentreSince modern key technologies need moreand more complex modelling, simulationand optimisation techniques, and sinceinnovation cycles in technological develop-ment get shorter and shorter, it is essentialto have flexible mathematical models thatallow to master complexity, to react quickly,and to explore new smart options. Suchmodels can be obtained only via abstraction.This line of thought provides our globalvision: innovation needs flexibility, flexibilityneeds abstraction, abstraction is mathematics.But mathematics is not only the language ofscience, it provides theoretical insight, effi-cient algorithms and optimal solutions.Thus, key technologies and mathematicsinteract in a joint innovation process. Wethink that new products in key technologiesshould carry the stamp ‘Mathematics’inside.

The mission of the Centre is to strength-

en the role of mathematics in this interac-tive process. In order to achieve this, theCentre’s research program is application-driven, but we do basic research in mathe-matics and we envision that it will also havea strong impact on the development ofmany other areas of mathematics. We alsohope that the Centre’s activities will increaseinner-mathematical, inter-disciplinary andtrans-disciplinary cooperation.

The Centre focuses on the mathematicalfields of optimisation and discrete mathematics,numerical analysis and scientific computing, andapplied and stochastic analysis and, buildingon existing cooperations, it will address thefollowing key technologies:• Life sciences (computer-assisted surgery;

patient-specific therapies; protein database analysis; protein conformationdynamics)

• Traffic and communication networks (plan-ning of multi-level and multi-layer com-munication networks, planning of theUMTS radio interface, line planning,periodic time-tabling, and revenue man-agement in public transport)

• Production (shape memory alloys in air-foils, production of semiconductor crys-tals, methanol fuel cell optimisation, on-line production planning)

• Electronic circuits and optical technologies(quantum-mechanical modelling of opto-electronic devices, design of nano-pho-tonic devices, integrated circuits forfuture chip generations)

• Finance (measurement and hedging ofrisks, interaction models for asset pricefluctuation)

• Visualisation (discrete differential geome-try, image processing).

The Centre is not only a mathematicalresearch institution, but also aims at coop-eration with other sciences, engineeringand economics, and in particular with part-ners in commerce and industry.Furthermore, the Centre will also put astrong emphasis on changing the publicawareness for mathematics and will con-tribute to mathematical education at all lev-els.

The Centre has just begun to design anddevelop its web-presentation; for furtherinformation see: http://www.math.tu-berlin.de/DFG-Forschungszentrum

New rNew researesearch centrch centre in Berline in Berlin

The Israel Mathematical Union (IMU)represents 300 members, most of whomare individual members of the EMS.

The body of members includes facultymembers from the seven research uni-versities (Bar-Ilan University, Ben-Gurion University, Haifa University,Hebrew University, Tel-Aviv University,the Technion, and the WeizmannInstitute graduate school), from otherinstitutions for higher education inIsrael such as the Open University andundergraduate colleges, many of whichalso conduct research. Teachers’ col-leges (involved in the training of mathe-matics teachers for elementary schools)are also included among those repre-sented in the IMU. Graduate studentsfrom research universities are also mem-bers: many of them are mathematicians(having received their Ph.D. degrees)who are currently employed in Israel bythe high-tech, banking and aviationindustries. The IMU has a high concen-tration of members from the formerSoviet Union. It became a member ofthe EMS in 1991.

Some IMU members are internation-ally recognised mathematicians of thehighest level. Included among these areWolf Prizewinners Ilya Piatetski-Shapiroand Saharon Shelah, TuringPrizewinners Michael Rabin and AmirPnueli, Harvey Prizewinners IsraelAumann, Michael Rabin and HillelFurstenbe, and the Nevanlinna Prize

recipient Avi Wigderson. Three IMUmembers are recipients of the EuropeanPrize for Young Mathematicians: LeonidPolterovich (at ECM2), DennisGaitsgory (ECM3) and Semyon Alesker(ECM3). About 50 other IMU membershave given plenary and invited address-es at various International Congresses ofMathematics (ICMs) and EuropeanCongresses of Mathematics (ECMs).

Every two years new officers of theIMU are chosen, rotating among the dif-ferent research universities. The cur-rent positions are held by Tel-AvivUniversity faculty members Prof.Milman (President), Dan Haran(Secretary) and Gadi Fibich (Treasurer).The newly appointed positions, from theTechnion, include Alan Pinkus who willbecome the next President, along withthe incoming Secretary Eli Elias andBudget Officer Eli Aljadeff. Since theIMU became a member of the EMS, thefollowing presidents have held office:Yosef Zaks of Haifa University (geome-try), Larry Zalcman of Bar-IlanUniversity (complex analysis), SteveGelbart of the Weizmann Institute (auto-morphic forms) and Miriam Cohen ofBen-Gurion University (algebra).

Despite the small size of the country,mathematical activity in Israel is veryintense. This intensity is evidenced byour specialised research institutes (locat-ed in different departments), severalhundred graduate students, and fivemathematical journals published inIsrael: Israel Journal of Mathematics(Hebrew University), GAFA (Tel-AvivUniversity), Journal d’AnalyseMathématique (Bar-Ilan University),Integral Equations and Operator Theory(Ariel College), and Israel MathematicalConference Proceedings (Bar-IlanUniversity). In addition, Israel is host tointernational postdoctoral fellowshipprogrammes, many distinguished lec-ture series, visitor programmes, andinternational workshops and confer-ences.

Israeli mathematicians are involved inmany European Networks. On theinternational scene, several internation-al collaborations exist at governmentallevel, with research support andexchange programmes with countriessuch as Germany, Italy, France, theUSA, India and China.

For the most part, new Ph.D. recipi-ents may opt to take a 1- or 2-year post-doctoral position in Europe or the USA.Unfortunately, however, there are notenough positions in academia and as of

late some students are not returning toIsrael, indicating a small brain drain.During the high-tech bubble period,academia lost some manpower, but late-ly it seems to have stabilised.

The topics covered in Israel representall disciplines of modern mathematics –pure and applied, as well as mathemati-cal education. At the last EMS councilmeeting in Oslo, the IMU was upgradedto third category (meaning three repre-sentatives on the Council).

One of the festive events of the math-ematical life in Israel (from the late1970s) is the annual Wolf Prize ceremo-ny, which takes place in the Knesset (theIsrael Parliament). FriedrichHirzebruch, the first President of theEMS, received the prize in 1988, andLennart Carlson, the President of thescientific committee of 4ECM, receivedthe prize in 1992. Other mathemati-cians from EMS member states who havereceived the prize include Izrail M.Gelfand (Russia), Carl L. Siegel(Germany), Jean Leray (France), HenriCartan (France), Andrei N. Kolmogorov(Russia), Mark Grigor’evich Krein(Russia), Paul Erdõs (Hungary), LarsHormander (Sweden), Ennio De Giorgi(Italy), John G. Thompson (USA andUK), Mikhael Gromov (France), JacquesTits (France), Jurgen K. Moser(Switzerland), Laszló Lovász (USA andHungary), Jean-Pierre Serre (France),Vladimir I. Arnold (Russia and France).

The central IMU activity is the annual2-day meeting, covering many areaswith invited addresses on ‘hot’ topics,frequently given by distinguished math-ematicians from abroad; the ErodesPrize for Young Mathematicians isawarded during this event. In additionto the annual meetings, the IMU alsoholds regional specialised workshops.The most recent annual meeting tookplace at the picturesque and beautifuldesert location of Mitspe Ramon, not farfrom the observatory.

Mina Teicher [teicher@macs.biu.ac.il] isProfessor of Mathematics at Bar-IlanUniversity, Ramat-Gan 52900, Israel.

F. Hirzebruch receives the 1988 Wolf Prizein Mathematics from the President of theState of Israel, the late Chaim Herzog, at theKnesset (parliament) in Jerusalem, on 12May 1988.

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EMS March 2003 25

The IsraelThe IsraelMathematical UnionMathematical Union

Mina Teicher

Mina Teicher

History of the SocietyThe Society was founded in 1949 withthree aims: to publish, improve teaching,and unify terminology.

At that time, teachers in our elementaryand secondary schools were often qualifiedto teach both mathematics and physics.Now secondary school teachers, as a rule,specialise. There have accordingly beenrecent attempts to break the Society intotwo or three parts. But in Slovenia, withtwo million inhabitants, we find it morerational to work together, at least for now.This article will, of course, focus on themathematical achievements of the Society.

Slovenians have the mixed blessing to bethe westernmost South Slavic nation,wedged between Italy in the west andAustria in the north.

Several distinguished mathematicians ofthe past came from Slovenia. Jurij (Georg)Vega (1754-1802) produced improved log-arithmic tables that were immensely popu-lar, with the total number of editions goinginto hundreds. His four-volume course inmathematics and mechanics was translatedinto several languages and was a source ofknowledge, for example, for young JánosBolyai. Vega was essentially a self-taughtmathematician, who through a militarycareer managed to advance from a poorSlovenian peasant family to aristocracy.Next year we plan to celebrate the 250thanniversary of his birth with several events.

Franc Moènik (1814-92) wrote a best-selling series of high-quality mathematicaltextbooks (in German) for elementary andsecondary schools. These texts were trans-lated into many languages and used for

decades: the last revisions were printed justbefore WWII. Moènik, as an administra-tor, significantly increased the teaching ofSlovenian in our schools, then part of theAustrian Empire, which otherwisefavoured the German language.

Josip Plemelj (1873-1967) was a first-class mathematician. He worked in inte-gral and differential equations, as well as in

potential theory and analytic functions.When the University of Ljubljana openedjust after WWI, he became its first rector.Plemelj won two major prizes for his work,a German and an Austrian one. Theseenabled him to build a villa in his homeplace, the famous lake resort of Bled.Plemelj donated the villa to our Society.

Ivo Lah (1896-1979) was a demographerand statistician and an expert in actuarialmathematics. The Lah numbers in combi-natorics are named after him.

Plemelj’s student Ivan Vidav (born in1918) made a quantum leap in Slovenianmathematics. He had sixteen PhD stu-dents and managed to direct them intoseveral fields of mathematics, while doinggood research himself. (He was still pub-lishing original work four years ago.)Plemelj and Vidav set very high standardsfor lecturing at university level and I amproud to say that the tradition goes on.The Institute of Mathematics, Physics andMechanics (IMFM, www.ijp.si) in Ljubljanais an umbrella organisation for mathemat-ical research. Its 2001 yearbook listedmore than a hundred publications in(mostly high-quality) internationalresearch journals.

PeriodicalsSince 1951, the Society has published itsown magazine, Obzornik za matematiko, fizikoin mehaniko. Six editions every year pre-sent survey articles in Slovenian, as well asarticles on education and reports on theactivities of the Society, sometimes alsooriginal scientific work. Most of the 1100members of our Society are teachers whooften complain about the high level of thesurvey articles.

In 1973 the Society started to publishPresek (Intersection), a periodical for youngmathematicians, physicists andastronomers. It was an instant success,with a circulation of 20,000 every twomonths and special issues as well.Although we have managed to keep theprice low and the quality high, the circula-tion has now plummeted to 2600.University lecturers and teaching assistantswrite most of the contents. It is rather dif-ficult to find interesting material for read-ers in elementary schools, and many arti-cles turn out to be for the age group 17-18.

Books and teaching materialPublishing used to be an integral part ofthe Society. Now there is a separate pub-lishing house (DMFA-Zaloništvo,www.fmf.uni-lj.si/~zaloznistvo/), supervisedby our Society and the School ofMathematics and Physics (FMF) of the

SOCIETIES

EMS March 200326

Society of Mathematicians,Society of Mathematicians,Physicists and AstrPhysicists and Astronomers onomers

of Sloveniaof SloveniaPeter Legiša

Two stamps featuring Jurij Vega

Bled with Plemelj’s villa in the foreground

Josip Plemelj

University of Ljubljana. The popularSIGMA series started with Ivan Vidav’sSolved and Open Problems in Mathematics,which is still in print. Most of the 72 books(about 45 of them still available) are suit-able for bright students at secondaryschools. Most of these books are mathe-matical and original work. Recently, wehave had more translations.

Even more university textbooks andmanuscripts have been printed. The clas-sic one is Vidav’s Higher Mathematics, andthe author donated the royalties to thepublishing house. Two monographs are inEnglish (J. Vrabec, Bordism, Homology, andStiefel Whitney numbers and P. Pavešiæ, TheHopf Invariant One Problem).

Handbooks and exercise collections forelementary and secondary schools earn aprofit. D. Felda’s book 40 National MathOlympiads in Slovenia gives in English thetexts of problems in the national competi-tions, a topic to which we will return.

EducationThe Society helps to organise seminarsand workshops for teachers of mathemat-ics. It presents summer schools for themost gifted pupils, often in Plemelj’s villaat Bled. The Society has actively partici-pated in curriculum changes in secondaryschools, ensuring that no hasty decisionswere made.

For many years the Society providedspecial courses and lectures for students ofsecondary schools, given by university lec-turers and students. In my earlier years Iattended an excellent course on probabili-ty. The instructor (Prof. R. Jamnik) firstmade clear to us that there would be anexam at the end. He adapted to our lowerlevel and the course was a remarkable suc-cess – it convinced even those who other-wise did not like mathematics but unex-pectedly joined the course. The best par-ticipants earned books as prizes.

But I also listened to a mathematicianwho did not care about the reaction of thelisteners and was too fast even for thebrightest – a very frustrating experiencefor me and certainly not a good way toattract young people to mathematics.

CompetitionsThe most popular activities of the Societyare competitions for pupils and students ofsecondary schools. These have been goingright from the beginning, and haveexpanded enormously.

In the past, there were debates on theimpact of competitions. It turned out thatsome of the best competitors never got auniversity degree. Quick successes, arisingfrom their talents, did not prepare themfor the strenuous work at higher level.This now seems to be less of a problem, butthe best competitors do not always choosemathematics as their field of study.

Every year, about 60,000 pupils (50 percent of those who attend elementaryschools) participate in school competitions,which are now integrated in the EuropeanKangaroo. [For further information aboutthe European Kangaroo, see Paul Jaint’aarticle in issue 45] About ten per cent of

those in the 6th, 7th, and 8th class enterregional qualifications. The crème de lacrème – ten per cent of the best – competeat national level. About half of them winprizes.

At high-school level, about 5000 stu-dents participate in a similar three-levelcompetition, but the prizes are more struc-tured and limited.

Recently, we started separate competi-tions for students of technical schools(aged 15-18, about 3000 participants) andfor students of vocational schools (aged 15-17, 1600 competitors).

The 14th competition in RecreationalMathematics attracted several hundredcompetitors. It was supplemented by thethird competition in Space Visualisation.

In these competitions we collect a fee ofabout 1 euro per participant. This enablesus to maintain the on-line registrationscheme, print the diplomas, and so on.

Most of the budget of our Society comes

from the government (usually with delays),and most of it is spent on competitions, thelion’s share on the cost of sending a teamto the Mathematical Olympiad.

EventsEvery year the Society holds a meeting,lasting two or three days. We organise it indifferent regions of the country, so local

members can attend it without cost. Themeeting includes survey lectures, mostlyon elementary mathematics and mathe-matical education, but also on appliedmathematics. I listened to several veryinteresting talks, given by mathematicians,physicists and astronomers to a generalaudience. This is definitely one of theadvantages of working together.

Each year we reward distinguishedteachers and schools that excel in mathe-matical education. The Society has helpedto erect monuments or memorial plaquesto several Slovenian mathematicians. Italso helps to maintain the memorial roomfor Vega in his birthplace Zagorica, and anexposition on Plemelj in his villa.

Links For many years the Society has maintainedexcellent connections with mathematiciansin neighbouring Zagreb (Croatia). Wehave occasional contacts with colleaguesfrom Skopje (Macedonia) and now againwith colleagues from the (shrunken)Yugoslavia. (Slovenia was part ofYugoslavia from 1918 to 1990.)

In my view Italy and Austria have so farbeen mainly interested in attracting talent-ed students from our territory, but recent-ly, there has been research cooperationwith a centre in Austria (Leoben). Contactsdirectly across the border are weak: this isprobably linked to the fact that there areSlovenian populations in neighbouringareas of those two countries, a fact thatsome people find hard to admit. IfSlovenia joins the EU next year, we hopethat the situation will improve. The homepage of our Society iswww.dmfa.si.

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EMS March 2003 27

The two journals of the Society

The philosophy behind an emphasis onproblem solving is the educational truismthat telling is not teaching and listening isnot learning. I am a strong advocate ofthe precept that mathematics is not a mat-ter for immediate consumption: one canonly derive benefit from this subject if oneis doing it!

So, it is increasingly important forteachers and lecturers to offer new oppor-tunities for youngsters to stimulate theirinterest by coaching them in doing math-ematics. A vast supply of ideas, methodsand techniques lie dormant in problemsof Olympiad type. By attacking competi-tion problems, students can develop theirtalents for mathematical thinking.Mathematical talent and problem-solvingability are needed in today’s world inengineering, physics, chemistry and manyother sciences. In fact, with the applica-tions of mathematics in business, commu-nications, and the social sciences, there ishardly a field that does not require a goodbackground in mathematics.

This has been known in Bulgaria formore than 100 years, where they found itincreasingly important to invest time andresources in developing the mathematicalskills of a small but particularly talentedsection of its young persons. We canlearn a lot about the imaginativeness ofthe Bulgarian pioneers for encouragingparticularly gifted pupils and students. Inthe second part of his series, Prof. SavaGrozdev, from the Institute of Mechanics,Bulgarian Academy of Sciences, Sofia,describes the essential role that mathe-matics journals and summer camps play inthis continual national task of fishing outthose splendid young persons, in order tofurther their mathematical abilities.

Accompanying Measures (Sava Grozdev)The home journal Mathematics Plus

plays a lead in recruiting apt students. Itsmain goal is to identify highly talentedboys and girls, and for this purpose thejournal organises each year a junior con-test for pupils from grades 4-7. The trialis held in three rounds, each comprisingthree questions. Each stage is precededby two small articles in this journal,addressed first and foremost to those stu-dents who participate in the contest. Thearticles feature special topics that are usu-ally not on the curriculum; for example,squares and square numbers, induction ingeometry, the finite element principle,Euler’s formula, some invariants, andmathematical games. These articles aremeant to be studied by the young readingpublic, independently or with the help ofparents and teachers, at home or outsidelessons. Usually, these extra lessons areused in mathematics circles or special

classes that have been established in vari-ous Bulgarian cities and towns and arefrequented by students who are highlymotivated to problem-solving and eagerto do maths.

At least one of the problems in eachround is closely connected to the itemappearing in the journal at the same time.While working carefully through the arti-cles the contestants are provided withfresh knowledge and some tools necessaryfor solving the corresponding problem ora similar one. In addition to the ninequestions presented to the different agegroups, junior contestants especially areconfronted with a problem that ‘steps outof line’. This ‘Tenth Problem’ requiresingenious ideas and asks participants togo exploring. It usually allows challeng-ing and deep generalisations that can befound after some hard work and concen-trated examination.

Apart from individuals, groups of stu-dents and mathematical circles areencouraged to submit solutions. Theteachers in charge of a circle or working-group also play another significant part –for example, they give their young pro-tégés a hand when struggling with one ofthose fiddly Tenth Problems and provideadvice in coping with the difficult taskwriting down solutions to problems: thisassistance is useful for them, too. So,solving a Tenth Problem is an activity thatinvolves the whole team; teachers andpupils together learn new mathematicalfacts and are thus stimulated by fruitfulideas and tools. Sometimes, highly com-plicated tenth problems forge a closebond between coaches and their flock –but even a teacher may have to give up aparticularly stubborn problem.

The ‘Mathematics Plus’ junior contest iscarried out by written communicationbetween participants and correspondingmarkers. A special jury grades the papers,giving priority to the tenth problem.Those students who have worked well onall problems are invited, with their teach-ers, to a Summer Camp organised everyJuly. The Camp is free of charge for thoseselected. Some outstanding Bulgarianmathematicians are regularly asked to lec-ture on a special topic in this relaxed set-ting. These courses are usually enrichedwith general challenges and classicalmathematical problems, and include curi-ous facts connected with the history ofmathematics and the life of famous math-ematicians. The Summer Camp alwaysends in a festival, when many guests, stu-dents and teachers, can establish contactsamong themselves, or become friends.Most importantly, during their stay theyoung mathematicians will grow into theworld of mathematical science and society.

Later, a considerable percentage ofthose who found their way into one ofthese Summer Camps become membersof the Bulgarian team participating ininternational Olympiads – and after grad-uating from prestigious universities likeHarvard, Princeton, MIT and others, theymay start careers as a highly qualifiedmathematicians. The timely motivation ofjunior students has doubtless activatedthem towards individual research.

As a kind of levelling rod for theachievements of students at this early age,it is useful to know how they have per-formed in the Junior Balkan MathematicsOlympiad. In all five contests held up tonow, Bulgaria has been represented by 26students, and all came back with a medal.The other regular guests in the BalkanOlympiad are young people from Albania,Bosnia, Cyprus, Greece, Macedonia,Moldova, Romania, Turkey and Serbia.Since 2001 each participating country hasput forward a six-person team.

Already while a senior at school, manyof these students publish interesting trea-tises on specialist topics or create originalproblems. It is not unusual to encounteran author of several articles and challeng-ing questions in Mathematics Plus who isstill attending school. The Junior contest,and its counterpart for Senior students,appear in the journal as parallel contests.Each issue contains six problems for eachage group: these are well known for theirincreasing level of difficulty, and ‘breathethe spirit’ of an Olympiad. Usually, manyof the new problems come from the stu-dents. Their brainpower is impressive, asyou can see from the questions in the lastProblem Corner (issue 45).

The next six problems have been takenfrom the professionals.

PROBLEM CORNER

EMS March 200328

PPrroblem Corneroblem CornerContests frContests from Bulgaria, Pom Bulgaria, Part IIart II

Paul Jainta

PROBLEM CORNER

EMS March 2003 29

PROBLEM CORNER

EMS March 200330

It is now over sixty years since Eric TempleBell set out to write about mathematiciansin a way which would grip the imaginationof the educated public. His immenselyreadable book Men of Mathematics [4] wasfirst published in 1937 and is still in print.He was a man of strong opinions, not sim-ply reflecting the prejudices of a bygoneage, for example: ‘There is no morevicious academic hatred than that of oneJew for another when they disagree onpurely scientific matters. When two intel-lectual Jews fall out they disagree all over,throw reserve to the dogs, and do every-thing in their power to cut one another’sthroats or to stab one another in the back.’Moreover, he was not above distorting thefacts in the interests of making a goodstory. Although his book is looked downupon by the historians of mathematics, itcontinues to influence the impression thatordinary mathematicians have of the his-tory of their subject.

In his introduction Bell begins byemphasising that his book is not intended,in any sense, to be another history ofmathematics, and goes on: ‘The lives ofmathematicians presented here areaddressed to the general reader and toothers who might wish to see what sort ofhuman beings the men were who createdmodern mathematics.’ He continues:‘Two criteria have been applied in select-ing names for inclusion: the importancefor modern mathematics of a man’s work;the human appeal of the man’s life andcharacter. ... When these criteria clash ...the second has been given precedence, aswe are primarily interested here in mathe-maticians as human beings.’

Mathematical biography is a growingindustry these days. At least fifty of thegreat mathematicians of the past havebeen the subject of a full-scale treatment,usually either a Life and Work or a Life andTimes, and there are many more who meritthe attention of a biographer. Most ofthese books have been written by histori-ans of mathematics, who tend to write pri-marily for other historians. These seem tome too specialised to appeal to the ordi-nary mathematician, but others have beenwritten for a rather wider readership. Forexample, we have the biography ofCauchy [3] by Bruno Belhoste, which com-bines a good account of his life with anevaluation of his contribution to the devel-opment of mathematics; such books are ofinterest to anyone with some knowledgeof mathematics and its cultural history.

There are also a number of biographieswhich avoid technicalities and emphasise

the human side, such as the life ofHamilton by Hankins [6], of Galois byLaura Toti Rigatelli [19], of Courant [17]and Hilbert [18] by Constance Reid, ofHadamard [14] by Vladimir Maz’ya andTatyana Shaposhnikova, of Pólya [1] by G.L. Alexanderson, and of Zariski [16] by C.Parikh. Some of these books are morescholarly than others, but the best havebeen carefully researched and.one shouldnot be put off by catchy titles. The biogra-phies of Sonya Kovalevskaya by DonKennedy [12] and Ann Koblitz [13], that ofRamanujan [11] by Robert Kanigel, that ofStefan Banach [10] by Roman Kaluza, andthose of Abel [21] and Lie [22] by ArildStubhaug are also of this type. Theauthors have some mathematical back-ground, although not all would claim to beprofessional mathematicians: Kaluza, forexample, is a journalist and Stubhaug awriter. The life [15] of the Nobel LaureateJohn Nash by Sylvia Nasar is another suchexample. The author is an economist, nowprofessor of journalism at ColumbiaUniversity. Bell, of course, was a pioneerof science fiction as well as a professionalmathematician.

Sometime ago I began to think about writ-ing a Men and Women of Mathematics whichmight, I hoped, provide an alternative toBell’s book. This work has now appeared,under the title Remarkable Mathematicians[7]. For each of sixty subjects it provides abrief life which takes account of recentscholarship. They were chosen frommathematicians born in the eighteenth,nineteenth and early twentieth centuries.Among them, twelve different Europeancountries are represented, includingRussia. France and Germany are veryheavily represented. While Bell does notventure outside Europe, I have includedmathematicians from India and Japan, aswell as several from the United States. Istart with Euler and end with vonNeumann, whereas Bell begins in antiqui-ty and finishes with Cantor.

After digesting the relevant literature Ichose the subjects of the profiles with aneye to diversity and contrast. Most ofthem made important discoveries, but Iincluded some who contributed in otherways, for example Mittag-Leffler, Courantand Veblen. The majority spent at leastsome time teaching, with various degreesof success; several were the authors of suc-cessful textbooks. In the eighteenth cen-tury, when there were hardly any universi-ty posts for mathematicians, some occu-pied chairs in other subjects, such as

astronomy. Several made a living in quitedifferent professions, for example as engi-neers or lawyers or administrators. LikeBell I have tried to bring out the humanside, avoiding too much technical detailwhich can generally be found elsewhere.

The general question of whether anaptitude for the kind of abstract thoughtrequired for mathematics is in any senseinherited, and if so how, is an intriguingone. There is some evidence in favour;Francis Galton, in Hereditary Genius [5] dis-cusses the case of the Bernoullis, and thereare other less striking examples. A possi-ble reason why a genetic factor could beinvolved may be found in the medical lit-erature. Asperger syndrome [8] is a mildform of autism. Asperger people areattracted to mathematics; autistic tenden-cies run in families. It would be interest-ing to try and identify which of the greatmathematicians of the past were Aspergerpeople, like Newton, Einstein, Raman-ujan, and possibly Dirac.

The only woman mathematician whoappears in Men of Mathematics is SonyaKovalevskaya, who is included in the pro-file of Weierstrass. The prevailing preju-dice against women in science has taken along time to break down, and unfortu-nately the process is still not complete.Until the end of the nineteenth centuryand even beyond there were all kinds ofobstacles which made it difficult for awoman to become a scientist. Exceptionaldetermination was required; men werebelieved to have a monopoly of abstractthought. As a result, of my sixty subjects,only three are women, but there can be nodoubt that many other women had noopportunity to develop their mathematicalgifts.

Galton also mentions the common beliefthat the mothers of great men are moreinfluential on their development than thefathers. Gauss, Poincaré and Hilbertbelieved that their mathematical giftscame from their mother’s side of the fam-ily rather than the father’s side.

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EMS March 2003 31

MathematicalMathematicalBiographyBiography

IOAN JAMES

Regrettably, far too little is known aboutthe mothers of the great mathematicians,although some of them were clearlyremarkable women. The mother of Galoiswas described as ‘intelligent, lively, head-strong, generous and eccentric’, the moth-er of Ramanujan as ‘shrewd, cultured anddeeply religious’, and the mother of.Kolmogorov as ‘liberal and independent’.Others are simply stated to have been well-to-do, or from a wealthy family, or to havebeen well educated. Often we just knowtheir names, sometimes not even that.

Mathematical autobiography seems tobe quite a recent phenomenon, althoughvarious novels of Sonya Kovalevskaya arebased to a large extent on her own life.Another Russian who gave a vivid account[2] of his life story is P. S. Alexandroff.Other important examples are those ofLaurent Schwartz [20] and André Weil[23]. The idiosyncratic autobiography byNorbert Wiener [24], [25] should also bementioned. As Hans Freudenthal com-mented: ‘Wiener never had the slightestidea of how he appeared in the eyes ofothers.’ An autobiography is no substitutefor a biography.

A companion volume to RemarkableMathematicians, entitled RemarkablePhysicists [9], will follow shortly. Fourierand Laplace appear in both books; ofcourse, many physicists contributed great-ly to mathematics, and mathematicians tophysics. Because the interaction betweenthe two branches of science has been so

important I am thinking of combining themost interesting profiles from the twobooks into a third one in which mathe-maticians and physicists are treatedtogether.

References1. G.L. Alexanderson, The Random Walks of

George Pólya, Math. Assoc. of America,Washington DC, 1999.

2. A.S. Alexandrov, Pages from an autobiog-raphy, Russian Math. Surveys I 34 (1979),267-304; II 35 (1980), 315-358.

3. Bruno Belhoste, Augustin-Louis Cauchy,Springer Verlag, Berlin, 1991 (originallypublished in French).

4. E.T. Bell, Men of Mathematics, VictorGollancz, London, 1937.

5. Francis Galton, Hereditary Genius,Macmillan, London, 1869.

6. T.L. Hankins, Sir William Rowan Hamilton,Johns Hopkins Univ. Press, Baltimore,1980.

7. Ioan James, Remarkable Mathematicians,Cambridge Univ. Press, Cambridge, andMath. Assoc. of America, Washington DC,2002.

8. Ioan James, Singular Scientists, J. Roy. Soc.Medicine, 2003.

9. Ioan James, Remarkable Physicists,Cambridge Univ. Press, Cambridge, 2003.

10. R. Kaluza, Through a reporter’s eyes: The. lifeof Stefan Banach, Birkhäuser Verlag,Basel,1966 (originally published in Polish).

11. R. Kanigel, The Man who knew Infinity,Charles Scribner’s Sons, New York, 1991.

12. Don. H. Kennedy, Little Sparrow: a portrait

of Sonya Kovalevskaya, Ohio Univ. Press,Athens OH, 1983.

13. Ann Koblitz, A Convergence of Lives,Birkhäuser Verlag, Basel, 1983.

14. Vladimir Maz’ya and TatyanaShaposhnikova, Jacques Hadamard, aUniversal Mathematician, History ofMathematics 14, American and LondonMath. Societies, Providence RI, 1998.

15. Sylvia Nasar, A Beautiful Mind, Faber andFaber, London, 1998.

16. C. Parikh, The Unreal Life of Oscar Zariski,Academic Press, San Diego CA, 1991.

17. Constance Reid, Courant, Springer Verlag,Berlin, 1996 (originally published underanother title).

18. Constance Reid, Hilbert, Springer Verlag,Berlin, 1970.

19. Laura Toti Rigatelli, Evariste Galois (1811-1832), Birkhäuser Verlag, Basel, 1996.

20. Laurent Schwartz, Un Mathématicien auxPrises avec le Siècle, Editions Odile Jacob,1997.

21. Arild Stubhaug, Niels Henrik Abel and histimes, Springer Verlag, Berlin, 2000 (origi-nally published in Norwegian).

22. Arild Stubhaug, The Mathematician SophusLie, Springer Verlag, Berlin, 2002 (origi-nally published in Norwegian).

23. A. Weil, Souvenirs d’Apprentissage,Birkhäuser Verlag, Basel, 1991.

24. Norbert Wiener, Ex-Prodigy – My Childhoodand Youth, Simon and Schuster, New York,1953.

25. Norbert Wiener, I am a Mathematician – theLater Life of a Prodigy, Doubleday, NewYork, 1956.

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EMS March 200332

HELSINKI UNIVERSITY OF TECHNOLOGYInstitute of Mathematics

Two Professors of MathematicsHelsinki University of Technology invites applications for two positions as Professor in Mathematics at the Insituteof Mathematics, Faculty of Engineering Physics and Mathematics.

Helsinki University of Technology is located in Espoo, about 8 km from downtown Helsinki, the capital ofFinland.

When appointing a professor of the state university system of Finland, special emphasis is given to both researchand teaching competence and scientific leadership skills. Proficiency in Finnish, Swedish or English is required.Since the positions are full-time jobs, residence in the Helsinki area is necessary.

The applicants are required to a have demonstrated scientific competence in the following fields:

Position 1: Analysis (interpreted widely) or geometry

Position 2: Stochastic analysis and some other central subfield of mathematical analysis

For more details on the particulars, see the announcements (in English) on the web sitehttp://www.hut.fi/Yksikot/Hallitus/Virat/index.html

The applications should be addressed to the Council of Helsinki University of Technology and sent to:

Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland.

The deadline for the applications will be around 10 April 2003; see the above website for precise information.

Informal inquiries may be made to

Position 1: Prof. Juhani Pitkäranta: e-mail, Juhani.Pitkaranta@hut.fi

Position 2: Prof. Stig-Olof Londen: e-mail, Stig-Olof.Londen@hut.fi

This new mathematical journal is pub-lished under the auspices of the S. P.Timoshenko Institute of Mechanics of theNational Academy of Sciences (NAS) ofUkraine and the Laboratory for Industrialand Applied Mathematics (LIAM) at YorkUniversity (Toronto, Canada). Its aim isto publish original research articles ofexcellent quality in the broad area of non-linear dynamics and systems theoryincluding the following topics:

Analysis of uncertain systems; bifurca-tions and instability in dynamical behav-iours; celestial mechanics, variable mass,rockets; control of chaotic systems; con-trollability, observability, and structuralproperties; deterministic and randomvibrations; differential games; dynamicalsystems on manifolds; dynamics of sys-tems of particles; Hamilton and Lagrangeequations; hysteresis; identification andadaptive control of stochastic systems;modelling of real phenomena by ODE,FDE and PDE; non-linear boundary prob-lems; non-linear control systems, guidedsystems; non-linear dynamics in biologicalsystems; non-linear fluid dynamics; non-linear oscillations and waves; non-linearstability in continuum mechanics; non-smooth dynamical systems with impact ordiscontinuities; numerical methods andsimulation; optimal control and applica-tions; qualitative analysis of systems withafter effect; robustness, sensitivity and dis-turbance rejection; soft computing: artifi-cial intelligence, neural networks, fuzzylogic, genetic algorithms, etc.; stability ofdiscrete systems; stability of impulsive sys-tems; stability of large-scale power sys-tems; stability of linear and non-linearcontrol systems; stochastic approxima-tions and optimisation; symmetries andconservation laws.

The Editor-in-Chief is A. A. Martynyuk[anmart@stability.kiev.ua], S. P.Timoshenko Institute of Mechanics, NASof Ukraine, Nesterov Str., 3, MSR 680,Kiev-57, Ukraine. The Managing Editoris I. P. Stavroulakis [ipstav@cc.uoi.gr],Department of Mathematics, University ofIoannina, 451 10 Ioannina, Greece. TheEditorial Board is N. V. Azbelev (Russia),Chen Han-Fu (China), G. Dauphin-Tanguy (France), Duan Li (Hong Kong),J. H. Dzhalalow (USA), M. Fabrizio (Italy),H. I. Freedman (Canada), G. Georgiou(Cyprus), L. Hatvani (Hungary), N. A.Izobov (Belarussia), D. Ya. Khusainov(Ukraine), T. Kuepper (Germany), V. B.Larin (Ukraine), G. Leitman (USA), S.Leela (USA), O. S. Limarchenko(Ukraine), V. G. Miladzhanov(Uzbekiston), J. S. Muldowney (Canada),E. Noldus (Belgium), V. N. Pilipchuk(USA), M. D. Shaw (USA), P. D. Siafarikas(Greece), D. D. Siljak (USA), S.

Sivasundaram (USA), V. W. Spinadel(Argentina), Sree Hari Rao (India), N. M.Stavrakakis (Greece), R. Toscano (Italy),F. E. Udwadia (USA), T. Vincent (USA), V.V. Vlasov (Russia), Weiyong Yan

(Australia), Z. N. Zahreddine (UAE), V. I.Zhukovskii (Russia).

Submission of manuscripts: Authors areinvited to submit articles for publication.Instruction for contributors are on thewebsite: http://www.sciencearea.com.ua

Subscription Information: NonlinearDynamics and Systems Theory (ISSN 1562-8353) 2003, Vol. 3 (approx. 300pp.).Annual subscription rate: Institutional:US$278 or 300 euros; Individual: US$99or 100 euros. Orders should be sent tothe Editor-in-Chief or the ManagingEditor.

NEWS

EMS March 2003 33

CIME Courses 20036-13 July: Stochastic Methods in Finance, Bressanone, Bolzano (Joint course with the European Mathematical Society)Course directors:Profs. Marco Frittelli (Univ. di Firenze) and Wolfgang Runggaldier (Univ. diPadova).Lectures: Kerry Back (St. Louis): Partial and asymmetric information.Tomasz Bielecki (Northeastern Illinois): Stochastic methods in credit risk modeling, valu-ation and hedgingChristian Hipp (Karlsruhe): Finance and insuranceShige Peng (China): Nonlinear expectations and risk measures.Walter Schachermayer (Vienna): Utility maximization in incomplete markets

14-21 July: Hyperbolic Systems of Balance Laws, Cetraro, CosenzaCourse director:Prof. Pierangelo Marcati (Univ. de L’Aquila)Lectures: A. Bressan (Trieste): Viscosity solutions of systems of conservation lawsC.M. Dafermos (Providence): Conservation laws on continuum mechanicsD. Serre (Lyon): Shock profiles in scalar conservation lawsM. Williams (North Carolina): Stability of multidimensional viscous shocksK. Zumbrun (Indiana): Planar stability criteria for multidimensional viscous shock Waves

1-6 September: Mathematical Foundation of turbulent Viscous Flows, MartinaFranca, Taranto Course directors:Profs. M. Cannone (Univ. de Marne-la-Vallée) and T. Miyakawa (Kobe Univ.)Lectures: P. Constantin (Chicago): TheNavier-Stokes equations of viscous fluids and questions of tur-bulence theoryG. Gallavotti (Rome): Incompressible fluids and strange attractorsA. Kazikhov (Novosibirsk): The theory of strong approximation of weak limits via themethod of averaging with applications to Navier-Stokes equationsY. Meyer (Paris): Size estimates on solutions of nonlinear evolution equations and conse-quencesS. Ukai (Yokohama): The asymptotic analysis theory of fluid equations.

2-10 September: Symplectic 4-Manifolds and Algebraic Surfaces, Cetraro, Cosenza Course directors:Profs. Fabrizio Catanese (Bayreuth) and Gang Tian (M.I.T.) Lectures:B. Siebert and Gang Tian (Bochum and M.I.T.): Pseudo holomorphic curves and sym-plectic isotopyM. Manetti (Rome): Smoothing of singularities and deformation and differentiable type ofsurfacesD. Auroux and I. Smith (M.I.T. and Cambridge): Lefschetz pencils, branched covers andsymplectic invariantsP. Seidel (London): Lagrangian spheres and Dehn twists in dimension 4F. Catanese (Bayreuth ): Classification and deformation types of complex and real mani-folds

CIME can offer some fellowships. An on-line application form appears on the pagefor each CIME course: website C.I.M.E. courses are made possible thanks to the generous support received from:- Istituto Nazionale di Alta Matematica- Ministero Affari Esteri, Dir. Gen. Per la Promozione e Cooperazione Culturale- Ministero dell’ Istruzione, dell’Università e della Ricerca Scientifica e Tecnologica

NONLINEAR DYNAMICSNONLINEAR DYNAMICSAND SYSTEMS THEORAND SYSTEMS THEORYYA new International Journal of Research and Surveys

Please e-mail announcements of European confer-ences, workshops and mathematical meetings ofinterest to EMS members, to one of the followingaddresses: vberinde@ubm.ro or vasile_berinde@yahoo.com. Announcements should be writtenin a style similar to those here, and sent asMicrosoft Word files or as text files (but not as TeXinput files). Space permitting, each announce-ment will appear in detail in the next issue of theNewsletter to go to press, and thereafter will bebriefly noted in each new issue until the meetingtakes place, with a reference to the issue in whichthe detailed announcement appeared.

27-May 3: Spring School on Analysis:Variational Analysis, Paseky nad Jizerou,Czech RepublicInformation:e-mail: paseky@karlin.mff.cuni.cz website: http://www.karlin.mff.cuni.cz/katedry/kma/ss/apr03/ss.htm[For details, see EMS Newsletter 46]

28-June 20: Bimestre Intensivo:Microlocal Analysis and Related Subjects,Torino, ItalyTopics: short courses and specialist talks onthe following topics are scheduled: Perturbative methods in non-linear analysis;Pseudo-differential methods for evolutionequations; Quantization and harmonicnumerical analysis; Elliptic and hypoellipticequations.Scientific Committee: P. Boggiatto, I.Fujita, T. Gramchev, G. Monegato, A.Parmeggiani, J. Pejsachowicz, L. Rodino, A.Tabacco.Sponsor: INdAM (Istituto Nazionale di AltaMatematica), Italy.Location: Department of Mathematics,University of Torino; Department ofMathematics, Politecnico of Torino.Information: e-mail: indam@dm.unito.itwebsite http://www.dm.unito.it/convegniseminari/indam/bimestri.htm

2-3: X Encuentro de Topologia, Bilbao,SpainInformation: e-mail: xet@lg.ehu.es, website: http://www.ehu.es/xet[For details, see EMS Newsletter 46]

11-16: International Conference onGeneral Control Problems andApplications (GCP-2003), Tambov, Russia Information: e-mail: aib@tsu.tmb.ru,uaa@hmb.nnn.tstu.ru website: http://www.opu2003.narod.ru[For details, see EMS Newsletter 44]

11-18: Conference on TopologicalAlgebras, their Applications, and RelatedTopics, Bedlewo, Poland

May 2003

April 2003

Information: e-mail: ta2003@amu.edu.pl website: : http://main.amu.edu.pl/~ta2003[For details, see EMS Newsletter 44]

12-17: 23rd International Seminar onStability Problems for Stochastic Models,Pamplona, Navarra, SpainInformation: e-mail: stochastic@unavarra.eswebsite: http://www.unavarra.es/stochastic[For details, see EMS Newsletter 46]

25-31: Workshop on Singularity Theory,Edinburgh, UK Organisers: International Centre forMathematical SciencesInformation: e-mail: icms@maths.ed.ac.ukwebsite : http://www.ma.hw.ac.uk/icms/meetings/2003/singth/index.html

26-30: Fifth International Conference onSampling Theory and Applications(SampTA03), Strobl, Austria Information: web site: www.univie.ac.at/NuHAG/SampTA03/ [For details, see EMS Newsletter 45]

1-6: International Conference on GroupTheory, Gaeta, ItalyDedicated to Slava Grigorchuk on the occa-sion of his 50th birthdayTheme: combinatorial, geometric, anddynamical aspects of infinite groupsAim: presentation of recent developmentsconcerning combinatorial, geometric anddynamical aspects of group theoryScope: to bring together leading expertsand younger researchers to discuss recentdevelopmentsTopics: geometric group theory; ergodictheory; groups acting on trees and bound-aries; random walks; amenability; growth ofgroups, languages, and automata; groupsand fractals; L2-cohomology; bounded coho-mology; branch groups; groups generatedby finite automata; calculus of spectra; prob-lems of Burnside type; combinatorics ofwords.Main speakers: D. Anosov (Moscow); G.Baumslag (New York); M. Burger (Zürich);H. Furstenberg (Jerusalem); E. Ghys (Lyon);R. Grigorchuk (Texas and Moscow); M.Gromov (Paris); F. Grunewald (Düsseldorf);P. de la Harpe (Geneva); V. Jones(Berkeley); A. Lubotzky (Jerusalem); W.Lück (Münster); G. Margulis (Yale); A.Ol’shanskii (Vanderbilt Moscow); G. Pisier(Texas and Paris); S. Sidki (Brasília); A.Valette (Neuchâtel); A. Vershik (St.Petersburg); E. Zelmanov (San Diego andYale);Format: plenary talks, invited talksSessions: plenary lectures and parallel ses-sionsLanguages: English and FrenchOrganisers: L. Bartholdi, T. Ceccherini-Silberstein, Tatiana Smirnova-Nagnibeda

June 2003

and A. ZukLocal organisers: T. Ceccherini-Silberstein,A. Machi, F. Scarabotti and F. TolliProceedings: The conference proceedingswill be published in a special issue of theInternational Journal of Algebra andComputation. Deadline for submission is 1October 2003.Location: Hotel Serapo, Spiaggia di Serapo,04024 GaetaGrants: support for a limited number ofparticipantsDeadlines: deadline for abstract submissionwas 1 MarchInformation:gaeta@mat.uniroma.it; gaeta@math.kth.sewebsite: http://www-old.math.kth.se/math/users/gaeta/

1-7: Spring School in Analysis: FunctionSpaces and Applications, Paseky nadJizerou, Czech RepublicInformation:e-mail: pasejune@karlin.mff.cuni.cz website: http://www.karlin.mff.cuni.cz/katedry/kma/ss/jun03/ss.htm[For details, see EMS Newsletter 46]

2-6: Workshop on Derived Categories,Edinburgh, UK Organisers: International Centre forMathematical SciencesInformation: e-mail icms@maths.ed.ac.ukwebsite: http://www.ma.hw.ac.uk/icms/meetings/2003/dercat/index.html

13-22: Poisson Geometry, DeformationQuantisation and Group Representations(PQR2003), Brussels, BelgiumInformation: e-mail: pqr2003@ulb.ac.be;website: http://homepages.ulb.ac.be/~pqr2003/[For details, see EMS Newsletter 46]

18-19: Two-day Colloquium in honour ofEnrico Magenes, Pavia, ItalyTopic: On the occasion of the 80th birthdayof Professor Enrico Magenes, his former stu-dents at the University of Pavia are organis-ing a two-day colloquium in his honour inPavia. The programme consists of seven lec-tures by the following speakers: C. Baiocchi(Rome); J. M. Ball (Oxford); L. A. Caffarelli(Texas); G. Geymonat (Montpellier); P.-L.Lions (Paris); C. Verdi (Milano); A. Visintin(Trento). The Colloquium at the University of Paviaor at one of the University Colleges (to beannounced later) will take place from 18June at 3 pm to 19 June at 6 pm.Deadline: Those interested in participatingshould register by 15 April.Information:e-mail: magenes80@dimat.unipv.itphone/fax: +39 0382 505620 / +39 0382505602website: http://www.imati.cnr.it/~magen80/eng.htmlmail address: Prof. Marco Luigi Bernardi,Dipartimento di Matematica ‘F. Casorati’,Università di Pavia, Via Ferrata n.1, I-27100Pavia, Italy

18-28: Instructional Conference in theMathematical Analysis of Hydrodynamics,Edinburgh, UK Organisers: International Centre forMathematical Sciences

CONFERENCES

EMS March 200334

FForthcoming conferorthcoming conferencesencescompiled by Vasile Berinde

Information:e-mail: icms@maths.ed.ac.ukwebsite:http://www.ma.hw.ac.uk/icms/meetings/2003/hydro/index.html

19-22: 66th Workshop on General Algebra/ 66. Arbeitstagung Allgemeine Algebra(AAA66), Klagenfurt, AustriaTopics: universal algebra, classical algebraand applications of algebra Format: invited talks and contributed pre-sentationsSessions: plenary lectures and parallel ses-sionsRegistration: online registration form avail-able by the end of February 2003Organisers: H. Kautschitsch, W. More andJ. Schoißengeier Proceedings: it is intended to publish theproceedings of the conference as Volume 15in the series Contributions to General Algebra.All papers will be refereed. Location: University of Klagenfurt, A-9020Klagenfurt, Austria Grants: probably support for participantsfrom countries in a difficult economic situa-tion Information: e-mail: aaa66@uni-klu.ac.at; web site: www.uni-klu.ac.at/AAA66

20-27: Intermediate problems of modeltheory and universal algebra, Novosibirsk,RussiaInformation: web site: WWW2.nstu.ru/deps/algebra/erlogol[For details, see EMS Newsletter 46]

21-28: X International Summer Conferenceon Probability and Statistics (ISCPS) andthe Seminar on Statistical Data Analysis(SDA 2003), Sozopol, BulgariaTopics: Stochastic processes, limit theorems,financial mathematics, combinatorial analy-sis, theoretical and applied statistics, applica-tions in industry, economics, biology andeducation of statistics Organisers: Institute of Mathematics andInformatics of the Bulgarian Academy ofSciences, Faculty of Mathematics andInformatics of Sofia University and theBulgarian Statistical Society.Organising committee: N. Yanev (chair ofISCPS), D. Vandev (chair of SDA 2003), E.Pancheva, L. Mutafchiev, P. Mateev, M.Bojkova (secretary), E. Stoimenova.Location: Hotel Dolphin just on the beachof the gulf of SozopolInformation:website: http://stochastics.fmi.uni-sofia.bg

22-25: Conference on Applied Mathematicsand Scientific Computing(ApplMath03), Brijuni, CroatiaTheme: Numerical analysis and differentialequations in applied mathematicsAim: exchange of ideas, methods and prob-lems between various disciplines of appliedmathematicsScope: to present the state of the art in thefieldTopics: Splines and wavelets with applica-tions to CAGD, CAD/CAM, computer graph-ics and differential equationsMain speakers: L. Schumaker (USA), P.Costantini (Italy), J. J. H. Miller (Ireland)Format: keynote lectures, invited talks andcontributed presentationsSessions: plenary lectures and two parallelsessions

Call for papers: If you wish to present acontributed presentation, please submit anabstract according to the web instructionsProgramme committee: L. Schumaker(USA), P. Constantini (Italy), J. H. Miller(Ireland), Z. Tutek (Croatia), L. Sopta(Croatia), R. Scitovski (Croatia), K. Veselic(Germany), A. Mikelic (France)Organising committee: M. Marusic, M.Rogina, S. Singer, J. Tambaca (all fromCroatia)Proceedings: to be published by Kluwerpubl. co.Location: Island Brijuni, near Pula (Croatia)Grants: none so farDeadlines: for registration and abstracts, 30April; for manuscript 31 October 31Information: e-mail: ApplMath03@math.hrwebsite: http://www.math.hr/~rogina/ApplMath03

23-27: Workshop on Extremal GraphTheory (Miklos Simonovits is 60), LakeBalaton, Hungary Information: e-mail: extgr03@renyi.hu, website: http://www.renyi.hu/~extgr03[For details, see EMS Newsletter 45]

23-27: Equations aux derivees partielles etquantification, Colloque en l’honneur deLous Boutet de MonvelLocation: Institut de Mathématiques deJussieu, ParisInformation: website: http://www.institut.math.jussieu.fr/congres-lboutet/

23-28: Tools for Mathematical ModellingSt Petersburg, Russia (MATHTOOLS‘2003)Information: e-mail: lidiya_linchuk@mail.ru, website: www.neva.ru/journalMailing address: Lidiya Linchuk, MATH-TOOLS’2003, Dept. of Mathematics, StateTechnical University, Polytechnicheskaya st.29, St Petersburg, 195251, Russia[For details, see EMS Newsletter 46]

23-29: The Fifth International Conference‘Symmetry in Nonlinear MathematicalPhysics, Kyiv (Kiev), UkraineTopics: Classical, non-classical, conditional,approximate and other symmetries of equa-tions of mathematical physics, Symmetry inquantum mechanics, Quantum field theory,Gravity, Fluid mechanics, Mathematical biol-ogy, Mathematical economics, Symboliccomputations in symmetry analysis,Supersymmetry and its generalisations,Representation theory, q-algebras and quan-tum groups, Dynamical systems, Solitonsand integrability, Superintegrability and sep-aration of variablesScientific committee: A. Nikitin and A.Samoilenko (Co-Chairs, Institute ofMathematics, Kyiv), J. Beckers (Liège), G.Bluman (Vancouver), J. Carinena(Zaragoza), P. Clarkson (Canterbury), E.Corrigan (York), N. Debergh (Univ. ofLiege, Belgium), H.-D. Doebner (TechnicalUniv. of Clausthal, Germany), G. Gaeta(Milan), G. Goldin (Rutgers), B.K. Harrison(Utah), N. Ibragimov (Blekinge), V.Kadyshevsky (Dubna), J. Krasil’shchik(Moscow), A. Klimyk (Kyiv), M. Lakshmanan(Tiruchirappalli), P. Leach (Durban), W.Miller (Minneapolis), J. Niederle (Prague);P. Olver (Minneapolis), G. Pogosyan(Yerevan, Cuernavaca and Dubna),

I. Skrypnyk (Kyiv), M. Tajiri (Osaka), P.Winternitz (Montreal,), Yehorchenko (Kyiv),R. Zhdanov (Kyiv)Deadline: for registration 22 MayInformation:e-mail: appmath@imath.kiev.uawebsite: http://www.imath.kiev.ua/~appmath/conf.htmlor mirror http://www.bgu.ac.il/~alexzh/appmath/conf.html

24-27: Days on Diffraction ’03, StPetersburg, Russia Information:e-mail: grikurov@mph.phys.spbu.ru, website: http://mph.phys.spbu.ru/DD [For details, see EMS Newsletter 45]

25-28: International Congress‘Mathematics in the XXI Century. TheRole of the Mathematics Department ofNovosibirsk University in Science,Education, and Business’, NovosibirskAkademgorodok, RussiaInformation: e-mail mmf@math.nsc.ru, website: http://www-sbras.nsc.ru/ws/MMF-21/index.en.html[For details, see EMS Newsletter 46]

25-28: 7th WSEAS CSCC InternationalMulticonference on Circuits; Systems;Communications and Computers, CorfuIsland, GreeceInformation: website: http://www.wseas.org/conferences/2003/corfu

25-28: Current Geometry 2003, Naples,ItalySubject: Current geometry 2003, the IV edi-tion of the international conference on prob-lems and trends of contemporary geometry.Invited Speakers (provisional): E. Arbarello(Rome), M. Berger (Paris), P. Griffiths(Princeton), A. Sossinski (Moscow), A.Vinogradov (Salerno)Scientific Committee: E. Arbarello (Rome),F. Baldassarri (Padova), U. Bruzzo (Trieste),C. Ciliberto (Rome), A. Collino (Torino), M.Cornalba (Pavia), C. De Concini (Rome), B.Dubrovin (Trieste), L. van Geemen (Pavia),P. Griffiths (Princeton), V. Kac (Boston), K.O’Grady (Rome), C. Procesi (Rome), J.Stasheff (Chapel Hill), A. Vinogradov(Salerno). Organising Committee: A. De Paris(Naples), G. Rotondaro (Naples), G.Sparano (Salerno), A. Vinogradov (Salerno),R. Vitolo (Lecce).Sponsors: Istituto Italiano per gli StudiFilosofici, Naples; Università degli studi diSalerno; Gruppo Nazionale per le StruttureAlgebriche, Geometriche e le loroApplicazioni; Dipartimento di Matematicaed Applicazioni dell’Università degli Studi diNapoli ‘Federico II’Deadline: 15 MayInformation: e-mail: curgeo@diffiety.org orcurgeo@diffiety.ac.ruwebsite: http://www.diffiety.ac.ru/conf/curgeo03or http://www.diffiety.org/conf/curgeo03(mirror)

29- July 5: Workshop on Physics andGeometry of Three-dimensional QuantumGravity, Edinburgh, UK Organisers: International Centre forMathematical SciencesInformation: e-mail: icms@maths.ed.ac.uk

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website: http://www.ma.hw.ac.uk/icms/current/index.html

30-July 4: EMS School on DynamicalSystems, Porto, PortugalTheme: Dynamical systems Aim: A one-week training programme ondynamical systems and ergodic theory, lead-ing to an understanding of recent develop-ments in these areasTopics: Quantitative recurrence and dimen-sion theory; tessellations; reconstruction:(numerical) methods for the investigation ofrecurrent orbits and attractors from theirtime series; deterministic products of matri-cesMain speakers: L. Barreira (Portugal), J.-M.Gambaudo (France), F. Takens(Netherlands), M. Viana (Brazil)Format: Four intermediate-level coursesSessions: Five one-hour sessionsOrganising committee: J. Alves, V. Araújo,M. Carvalho, F. Moreira, J. Rocha (Portugal) Sponsors: EMSLocation: Department of Pure Mathematics,Faculty of Sciences, University of Porto - Ruado Campo Alegre, 687, 4269-007 Porto,PortugalGrants: Expected, but not yet confirmed,financial support from UNESCO.Information: e-mail: sds@fc.up.ptwebsite: http://www.fc.up.pt/cmup/sds

1-5: EuroConference VBAC 2003, Porto,Portugal Dedicated to Andrei TyurinTopics: the meeting will cover a range oftopics in the area of vector bundles on alge-braic curves, with special emphasis on mod-uli spaces and topologyMain speakers: J. Andersen (Aarhus), S.Bradlow (Urbana-Champaign), V. Balaji(Chennai), W. Goldman (Maryland), T.Hausel (Austin), L. Jeffrey (Toronto), L.Katzarkov (Irvine), F. Kirwan (Oxford), M.Reid (Warwick), M. Thaddeus (Columbia).Scientific Committee: L. Brambila-Paz, O.Garcia-Prada, P. Gothen, D. HernandezRuiperez, F. Kirwan, H. Lange, P. Newstead(Chair), W. Oxbury, E. Sernesi, C. SorgerOrganisers: Carlos Florentino(cfloren@math.ist.utl.pt) and Peter Gothen(pbgothen@fc.up.pt).Sponsors: European Commission, High-Level Scientific Conferences, ContractHPCF-CT-2001-00248; Research TrainingNetworks EAGER and EDGE; Centro deMatematica da Universidade do Porto;Centro de Matematica e Aplicacoes(Instituto Superior Tecnico, Lisbon);Fundacao para a Ciencia e a Tecnologia(Portugal) (*); Reitoria da Universidade doPorto (*); Departamento de MatematicaPura, Faculdade de Ciencias, Universidadedo Porto; (*) to be confirmed.Deadlines: to give a talk and/or apply forfinancial support, registration deadline was1 March; other registration 15 April Information: website: http://www.math.ist.utl.pt/~cfloren/VBAC2003.html

1-10: PI-rings: structure and combinatorialaspects (summer course), Bellaterra,Barcelona (Catalonia)Aim: to introduce the students in the struc-tural and combinatorial theory of algebrassatisfying polynomial identities (PI-algebras)

July 2003

Lecturers: V. Drensky (Bulgarian Academyof Sciences); E. Formanek (PennsylvaniaState University)Topics: Structure theorems of Kaplansky,Posner and Artin; ring of generic matrices;generic division ring and its relation withthe theory of central simple algebras; struc-ture of the centre of the generic divisionring; Amitsur-Levitzki theorem; constructionof central polynomials for matrices; polyno-mial identities of matrices and their relationwith invariant theory; Nagata-Higman theo-rem; Shirshov theorem; Regev theoremCoordinator: Ferran CedóScientific Committee: Pere Ara, DolorsHerberaOrganising Committee: Rosa Camps,Ferran CedóGrants: a limited number of grants for regis-tration and accommodation for young scien-tists and scientists from less favoured coun-triesDeadlines: applications for financial sup-port, 25 April; registration and payment, 31MayInformation: e-mail: PI-rings@crm.es website: http://www.crm.es/PI-rings

3-8: Wavelets and Splines, St Petersburg,RussiaTheme: wavelets and splines as tools forapproximation theory and applicationsAim: to exchange information on manyproblems related to the wavelet and splinetheoryTopics: wavelets and wavelet methods, sig-nal processing, spline theory and its applica-tions, related topics Main speakers: B. Kashin (Russia), A. Ron(USA), L. Schumaker (USA), P. Wojtaszczyk(Poland), Yu. Brudnyi (Israel), N. Din(Israel), A. Pinkus (Israel), M. Unser(Switzerland)Format: plenary 60- and 45-minute lectures,20-minute presentation and postersSessions: plenary sessions, parallel sessions,special session on bivariate splinesCall for papers: an electronic copy of theabstract should reach the organising com-mittee before 1 May. The abstract should beLaTeX-formatted in the style Article, shouldnot exceed one page, and should containtitle, names of the authors, official addressand e-mail addressOrganisers: St Petersburg branch of SteklovMathematical Institute and St PetersburgState UniversityProgramme committee: A. Averbuch(Israel), O. Davydov (Germany), Yu.Demjanovich (Russia), R. DeVore (USA), L.Gori (Italy), D. Leviatan (Israel), V.Malozemov (Russia), I. Novikov (Russia), A.Petukhov (USA), V. Zheludev (Israel), V.Zhuk (Russia)Organising committee: M. Skopina (Chair,Russia), S. Kislyakov (Vice-Chair, Russia), V.Malozemov (Russia), A. Petukhov (USA)Location: Euler International MathematicalInstitute, Pesochnaya nab.-10, 197022 StPetersburgDeadlines: for registration, 1 March; forabstracts, 1 MayInformation: e-mail: ws@imi.ras.ruwebsite: http://www.pdmi.ras.ru/EIMI/2003/ws

6-12: Journées Arithmétiques XXIII, Graz,AustriaTopics: all branches of number theory

Main speakers: J.-P. Allouche (France), Ch.Bachoc (France), M. Bhargava (USA), Ch.Breuil (France), J. Brüdern (Germany), A.Lauder (UK), K. Soundararajan (USA), S.Wewers (Germany), U. Zannier (Italy).Call for papers: participants are invited topresent a contributed talk of 20 minutes;abstract submission via Altas MathematicalConference Abstracts (http://atlas-confer-ences.com/), deadline 31 MayProgramme committee: E. Bayer Fluckiger(Switzerland), P. Debes (France), J.-M.Deshouillers (France), G. Frey (Germany), R.Heath-Brown (UK), H. W. Lenstra(Netherlands), P. Sarnak (USA), R.Tijedeman (Netherlands)Organising committee: S. Frisch, A.Geroldinger, P. Grabner, F. Halter-Koch, C.Heuberger, G. Lettl, R. Tichy (Graz)Proceedings: special issue of Journal deThéorie des Nombres de BordeauxLocation: Karl-Franzens Universität GrazDeadlines: for early registration (at lowerrates) 30 April; for registration: 15 June; forsubmission of abstracts: 31 MayInformation: e-mail: ja03@tugraz.atwebsite: http://ja03.math.tugraz.at/

9-12: XV Italian Meeting on Game Theoryand Applications, Urbino, ItalyInformation:e-mail: XVimgta@uniurb.it, website: www.econ.uniurb.it/imgta [For details, see EMS Newsletter 46]

13-28: VI Diffiety School in the geometryof Partial Differential Equations, SantoStefano del Sole (Avellino), Italy Theme: two series of courses, one for begin-ners and one for veterans, will be given. Thebeginners’ courses consist of a general intro-duction, analysis on manifolds and observ-ables, introduction to differential calculus incommutative algebras. Detailed pro-grammes have been published on our website. The veterans’ courses will discuss mod-ern geometric and homological methods inPDEs (including the elements of secondarycalculus) and their applications to integrablesystems and equations of mathematicalphysics. We will also organise a scientificsession on the research interests of the par-ticipants and to discuss starting pro-grammes, intended to involve interestedparticipants into our research projectsLecturers and tutors of the School: A. DeParis (Napoli), S. Igonin (Moscow), J.Krasil’shchik (Moscow), A. Verbovetsky(Moscow,), A. Vinogradov (Salerno), M.Vinogradov (Diffiety Institute), R. Vitolo(Lecce)Organising committee: D. CatalanoFerraioli, A. De Paris, C. Di Pietro, G.Manno, R. Piscopo, G. Rotondaro, A.Vinogradov, R. Vitolo. Sponsors: Diffiety Institute (Russia), IstitutoItaliano per gli Studi Filosofici, Municipalityof Santo Stefano del Sole (AV), ItalyDeadline: 10 JuneParticipation fee: 100 euro, to cover lodg-ing and living expensesInformation: e-mail: school@diffiety.org; website: http://www.diffiety.ac.ru orhttp://www.diffiety.org.

14-18: International Conference onAlgebras, Modules and Rings, Lisboa,Portugal [in memory of António AlmeidaCosta, on the centenary of his birth]Information: e-mail: lisboa03@cii.fc.ul.pt;

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web site: http://caul.cii.fc.ul.pt/lisboa2003/Subscribe to the conference mailing list athttp://caul.cii.fc.ul.pt/alg.announce.html[For details, see EMS Newsletter 46]

20-27: Hodge Theory in a New Century: AEuro Conference celebrating the Centenaryof Sir William Hodge (1903-1975),Edinburgh, UKOrganisers: International Centre forMathematical SciencesDeadlines: Registration 18 April; financialsupport, passed Information: e-mail: icms@maths.ed.ac.ukwebsite: http://www.ma.hw.ac.uk/icms/meetings/2003/HODGE/index.html

21-25: W³adys³aw Orlicz CentenaryConference and Function Spaces VII,Poznañ, PolandTopics: Banach space, geometry and topolo-gy of Banach spaces, operators and interpo-lations in Banach spaces, Orlicz spaces andother function spaces, decomposition offunction, approximation and related topics Main speakers:Conference in Honour of Orlicz: G. Bennet(USA), J. Diestel (USA), P. Domañski(Poland), F. Hernandez (Spain), N. Kalton(USA), B. Kashin (Russia), H. König(Germany), S. Konyagin (Russia), J. Kurzweil(Czech Republic), A. Pinkus (Israel), K.Urbanik (Poland), P. Wojtaszczyk (Poland); Function Spaces VII: J. Appell (Germany), D.Pallaschke (Germany), L. Persson (Sweden),B. Sims (Australia), T. Sukochev (Australia),H. Triebel (Germany) Call for papers: for an oral 20-minute com-munication, submit before 31 March anabstract of up to 200 words (.doc or .rtfextension) using the form at or mail to:Faculty of Mathematics and ComputerScience, Adam Mickiewicz University,Umultowska 87, 61-614 Poznan, Poland,with postscript “Orlicz100”. Programme committee: .for the Conference in Honour of Orlicz: Z.Ciesielski (Poland), L. Drewnowski (Poland),W. Johnson (USA), F. Hernandez (Spain), J.Lindenstrauss (Israel), N. Kalton (USA), J.Musielak (Poland), G. Pissier (France), A.Pe³czyñski (Poland), P. Ulyanov (Russia); for Funcion Spaces VII: J. Musielak, H.Hudzik and L. Skrzypczak (all Poland) Organising committee: Z. Palka (Chair), B.Bojarski (Vice-Chair), S. Janeczko (Vice-Chair), L. Skrzypczak (secretary), P.Domañski , H. Hudzik, J. K¹kol, I.Kubiaczyk, M. Masty³o, P. Pych-Tyberska, S.Szufla, R. Urbañski, J. Werbowski, A.Waszak, W. Wnuk (all from Poland) Proceedings: to be publishedLocation: the main building of the Facultyof Mathematics and Computer Science,Adam Mickiewicz University, PoznanDeadlines: for abstracts, 31 March; for reg-istration, 31 MayInformation: e-mail: orlicz@amu.edu.plwebsite: httm://orlicz.amu.edu.pl

3-9: Third International Conference:Creativity in Mathematics Education andthe Education of Gifted Students, Rousse,Bulgaria.Aim: to formulate the problem and defineglobally the directions of the developing of

August 2003

creative education in mathematics and infor-matics of gifted students Topics: see the websiteProceedings: to be published before theconferenceProgramme Committee: President: P.Vlamos (Greece); Scientific secretary: E.Velikova (Bulgaria); Members: H. Meissner(Germany), A. Agnis (Latvia), A. Warren(Australia), J. Becker (USA), F. Bellot-Rosado (Spain), V. Berinde (Romania), S.Bilchev (Bulgaria), M. Bartolini Bussi (Italy),C. Daniel (New Zealand), J.-C. Deledicq(France), S. Dimitrova (Bulgaria), S.Dodunekov (Bulgaria), I. Ganchev(Bulgaria), A. Gardiner (UK), M. Georgieva(Bulgaria), E. Gerganov (Bulgaria), D.Grammatikopoulos (Greece), K. Grigorova(Bulgaria), S. Grozdev (Bulgaria), M. Isoda(Japan), S. Kantcheva (Bulgaria), P.Kenderov (Bulgaria), K. Kreitht (USA), C.Lozanov (Bulgaria), K. Manev (Bulgaria), A.Momchilova (Bulgaria), O. Mushkarov(Bulgaria), D. Pavlov (Bulgaria), N. Rajkov(Bulgaria), N. Rovoz (Russia), I. Sharygin(Russia), E. Silver (USA), A. Soifer (USA), E.Stoyanova (Australia), J. (Bulgaria), P.Taylor (Australia), I. Tonov (Bulgaria), A.Ulovec (Austria), E. Vlamou (Greece)Organising Committee: B. Tomov(President); E. Velikova, S. Chernev, S.Bilchev (Vice-presidents); Members: R.Alexieva; G. Atanasova; K. Bankov; M.Beikov; A. Bojadzhiev; P. Bonchev; E. Buhm(Germany); M. Dikova; S. Dimitrov; J.Donkers (Netherlands); M. Drakakakis(Greece); G. Dushkov; V. Evtimova; A.Gardiner (UK); A. Georgiev; M. Georgieva;V. Gocheva; D. Grammatikopoulos (Greece);P. Hristova; V. Iliev; V. Jordanov; E.Kalcheva; J. Kandilarov; M. Karailieva; R.Kasuba (Lithuania); M. Kezas (Greece); N.Knoche (Germany); A. Kopankova; T.Kopcheva; M. Kunchev; M. Lambrou(Greece); M. Makiewicz (Poland); D.Milanova; T. Mitev; A. Momchilova; E.Perzycka (Poland); M. Petkova; N.Popivanov; M. Popova; A. Poulos (Greece);E. Rappos (Greece); P. Rashkov; T.Rashkova; E. Rashkova; R. Russev; A.Smrikarov; N. Strateva; J. Svrcek (CzechRepublic); M. Teodosieva; V. Tsonev; S.Tsvetanova; M. Todorova; A. Ulovec(Austria); V. Vaneva; V. Velikov; P. Vlamos(Greece); V. Voinohovska; A. Vrba (CzechRepublic).Organisers: Univ. of Rousse (Bulgaria),Union of Bulgarian Mathematicians(Rousse), ‘V-publications’ (Greece), VlamosPreparatory School (Greece), ResearchCenter for Culture and Innovation (Greece),World Federation of National MathematicsCompetitions (Australia), Ministry ofEducation and Science (Bulgaria),Mathematical High School (Rousse), Univ.of Veliko Turnovo (Bulgaria) Location: University of Rousse, BulgariaGrants: there will probably be support forparticipants from countries in a difficult eco-nomic situation, young gifted and PhD stu-dentsDeadlines: for registration, 30 June; forabstracts, 30 April Information: e-mail: conf_orgcom@ami.ru.acad.bg or emily@ami.ru.acad.bg website: www.cmeegs3.rousse.bg,www.ami.ru.acad.bg/conference2003/ www.nk-conference.ru.acad.bg

5-10: Workshops Loops ’03, Prague, CzechRepublicTheme: lectures on quasigroups, loops andLatin squaresLectures and Lecturers: Loop rings (E.Goodaire); self-distributive quasigroups, tri-linear constructions and cocyclic modules (T.Kepka, P. Nemec); Moufang loops and 3-nets (G. Nagy, P. Vojtechovsky); latin tradesand Hamming distances (A. Drapal); auto-mated reasoning in loop theory (J. D.Phillips); introduction to smooth loops (M.Kinyon).Format: four 90-minute lectures each dayProgramme and Organising Committee: D.Bedford (UK), O. Chein (USA), A. Drapal(Secretary, Czech Rep.), M. Kinyon (USA),G. Nagy (Hungary), M. Niemenmaa(Finland), H. Pflugfelder (Honorary Chair,USA), J. D. Phillips (USA), V. Shcherbacov(Moldova), P. Vojtechovsky (USA)Local Organising Committee: A. Drapal(Chair), S. Holub (social programme), P.Jedlicka (visas), T. Kepka (finances), P.Nemec (accommodation), D. Stanovsky(website, abstracts), P. Vojtechovsky (website,registration, abstracts)Sponsors: Charles University and the CzechUniversity of AgricultureLocation: Czech University of Agriculture,PragueNotes: see also Loops ’03Deadlines: for registration: 20 JuneInformation: e-mail: loops03@karlin.mff.cuni.czwebsite: http://www.karlin.mff.cuni.cz/~loops/workshops.html

10-17: Loops ’03, Prague, CzechRepublicTheme: quasigroups, loops, latinsquares, and related topicsAim: to highlightnew results in quasigroup theory, and to fos-ter connections to combinatoricsMain speak-ers: Galina B. Belyavskaya (Moldova), M.Kikkawa (Japan), A. Kreuzer (Germany), K. Kunen (USA), C.C. Lindner (USA), G. L. Mullen (USA), D. A.Robinson (USA), J. D. H. Smith (USA)Format: standard; contributed talks 30 or 15minutes longProgramme and Organising Committee: asfor previous conference (above)Local Organising Committee: as for previ-ous conference (above)Sponsors: Charles University and CzechUniversity of AgricultureProceedings: will be published inCommentationes Mathematicae UniversitatisCarolinae, and in Quasigroups and RelatedSystemsLocation: Czech University of Agriculture,PragueNotes: see also Workshops Loops ‘03Deadlines: for registration and abstracts: 20June; for survey papers: 15 April; for pro-ceedings papers: 10 OctoberInformation: e-mail: loops03@karlin.mff.cuni.czwebsite: http://www.karlin.mff.cuni.cz/~loops

11-15: Workshop on Finsler Geometry andIts Applications, Debrecen, HungaryTheme: Finsler geometry, spray geometry,Lagrange geometry, their generalisationsand applications in physics, biology, controltheory, finance, psychometry, etc.Advisory Board: P. Antonelli (Edmonton);G. S. Asanov (Moscow); D. Bao (Houston); S.S. Chern (Tianjin); P. Foulon (Strasbourg);

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R. S. Ingarden (Torun); R. Miron (Iasi); G.Patrizio (Firenze); Z. Shen (Indianapolis); H.Shimada (Sapporo); Z. I. Szabo (New York);L. Tamassy (Debrecen). Local organisers: S. Bacso, L. Kozma, and J.Szilasi (Debrecen)Information: e-mail: kozma@math.klte.huwebsite: http://www.math.klte.hu/finsler/

18-22: ENUMATH 2003, The EuropeanConference on Numerical Mathematics andAdvanced Applications, Prague, CzechRepublicTheme: numerical mathematics with appli-cationsAim: analysis of numerical algorithms aswell as their application to challenging sci-entific and industrial problemsMain speakers: A. Bermudez (Spain), R.Blaheta (Czech Republic), T. Gallouet(France), J. Haslinger (Czech Republic), R.Hiptmair (Germany), T. J. R. Hughes (USA),J. Rappaz (Switzerland), A. Russo (Italy), V.Schulz (Germany), A. Tveito (Norway)Format: invited talks and contributed pre-sentationsSessions: there will be plenary lectures,mini-symposia and contributed presenta-tionsCall for papers: to present a contributedpresentation, please submit an extendedabstract of up to one page in TeX or LaTeX Organisers: Charles University Prague,Faculty of Mathematics and Physics, Instituteof Chemical Technology Prague,Department of MathematicsProgramme Committee: F. Brezzi (Italy), M.Feistauer (Czech. Rep.), R.Glowinski(France/USA), R. Jeltsch (Switzerland), Yu.Kuznetsov (Russia/USA), J. Periaux (France),R. Rannacher (Germany). Scientific Committee: O. Axelsson(Netherlands), C. Bernardi (France),C.Canuto (Italy), M. Griebel (Germany), R.Hoppe (Germany), G. Kobelkov (Russia), M.Krizek (Czech Republic), P. Neittaanmaki(Finland), O.Pironneau (France), A.Quarteroni (Italy/Switzerland), C. Schwab(Switzerland), E. Suli (Great Britain), W.Wendland (Germany) Organising Committee: V. Dolejsi, M.Feistauer, J. Felcman, P.Knobloch, K.Najzar, E. Plandorova, J. Segethova (Czech.Rep.)Proceedings: to be publishedLocation: Institute of Chemical TechnologyPragueGrants: probable support for participantsfrom countries in a difficult economic situa-tion and young mathematiciansDeadlines: for registration, 30 April; forabstracts, 31 March Information:e-mail: enumath@karlin.mff.cuni.czwebsite: http://www.karlin.mff.cuni.cz/~enu-math/

18-22: 7th International Symposium onOrthogonal polynomials, Special Functionsand Applications, Copenhagen, DenmarkInformation: e-mail: opsfa@math.ku.dk,website: http://www.math.ku.dk/conf/opsfa2003[For details, see EMS Newsletter 46]

2-5: Symposium on Cartesian Set Theory,

September 2003

Paris, FranceInformation: e-mail: editions.europeenne @wanadoo.fr[For details, see EMS Newsletter 46]

2-6: Barcelona Conference on AsymptoticStatistics, Bellaterra, Barcelona, CataloniaInformation: e-mail: bas2003@crm.es website: http://www.crm.es/bas2003[For details, see EMS Newsletter 46]

12-16: International Conference ofComputational Methods in Sciences andEngineering (iccmse 2003), Kastoria,Greece Theme: computational methods in sciencesand engineering Aim and Scope: In recent decades many sig-nificant insights have been made in severalareas of computational methods in sciencesand engineering. New problems andmethodologies have appeared. There is apermanent need in these fields for theadvancement of information exchange. Thisundoubtedly beneficial practice of interdisci-plinary and multidisciplinary interactionsshould be expressed by an appropriate con-ference on such computational methods.ICCMSE 2003 aims at playing the aboverole and for this reason the aim of the con-ference is to bring together computationalscientists and engineers from several disci-plines in order to share methods, method-ologies and ideas Topics: these include (but are not limitedto) computational mathematics, computa-tional physics, computational chemistry,computational engineering, computationalmechanics, computational finance, computa-tional medicine, computational biology,computational economics, high performancecomputing, mathematical methods in sci-ences and engineering, industrial mathemat-ics, etc. Main speakers: H. Ågren (Sweden), J. Vigo-Aguiar (Salamanca); D. Belkic (Stockholm);E. Brändas (Uppsala); J. C. Butcher(Auckland); S. C. Farantos (Greece); U.Hohm (Braunschweig); A. Q. M. Khaliq(Illinois); G. Maroulis (Patras); A. Mylona-Kosma (Ioannina); S. Wilson (UK) Format: Plenary lectures (by invitation);original papers (selection based on extendedabstracts of 3-4 A4 pages); posters (selectionsimilar to original papers)Sessions: to be announcedCall for papers: send your abstract ordescription of session to iccmse@uop.grOrganisers: European Society ofComputational Methods in Sciences andEngineering (ESCMCE), Department ofInternational Trade TechnologicalEducational Institution of WesternMacedonia, Greece Programme (Scientific) committee: H.Agren, H. Arabnia (Georgia, USA), J. Vigo-Aguiar, D. Belkic, K. Belkic (SouthernCalifornia), E. Brandas, J. C. Butcher, A. Q.M. Khaliq (Illinois), G.Maroulis, S. Wilson, J.Xu (Pennsylvania) Organising committee: Th. Monovasilis,Eleni Ralli, Secretary of ICCMSE, I.Sinatkas, E. Siskos, Th. Themelis, K. Tselios,N. Tsounis Sponsors: European Regional DevelopmentFund, Region of Western Macedonia, Greece Proceedings: Extended abstracts will bepublished in a special volume of WorldScientific Publishing Company. The follow-

ing journals have accepted to publish select-ed Proceedings of ICCMSE 2003:Computational Materials Science (ElsevierScience), Journal of Supercomputing (Kluwer),Journal of Mathematical Chemistry (Kluwer),Communication in Mathematical and inComputer Chemistry (MATCH), Journal ofComputational Methods in Sciences andEngineering (JCMSE) (CambridgeInternational Science Publishing),Mathematical and Computer Modelling (ElsevierScience), Communications in Nonlinear Scienceand Numerical Simulation (Elsevier Science) Location: Kastoria, GreeceGrants: No grants available at this timeDeadlines: registration 30 April; abstractspassedInformation: iccmse@uop.grwebsite: http://www.uop.gr/~iccmse/ orhttp://kastoria.teikoz.gr/~iccmse/

15-21: First MASSEE Congress, Borovetz,BulgariaAim: to revive the traditional collaborationin mathematics and informatics (computerscience) among south-east European coun-tries Topics: I. Mathematical structures: logicsand foundations; algebra; topology; analysis;differential equations; geometry; stochasticsand probability theory; other related topics II. Applications of mathematics and infor-matics (computer science): mathematicalmodelling; operations research; waveletsanalysis and image processing; computation-al and numerical analysis; other related top-icsIII. Mathematical foundations of informatics(computer sciences): theory of computing;discrete mathematics in relation to computerscience; computing methodologies andapplications; algorithms; data mining; math-ematical linguistics; other related topicsIV. History and education in mathematicsand informatics: didactics of mathematicsand informatics (blackboard techniques andhypermedial methods); mathematical her-itage of south-east Europe; detecting anddeveloping mathematical talent; attractingtalent to science; other related topicsFormat: The congress will incorporate aseries of mini-symposia that emphasise top-ics of specific interest for the region: Organiser: the Mathematical Society ofSouth-East Europe (MASSEE): a recentlyregistered organisation comprising mathe-matical societies from Albania, Bulgaria,Bosnia-Herzegovina, Cyprus, Greece,Macedonia, Moldova, Romania andYugoslavia Location: Hotel Samokov, at the heart ofthe famous summer and winter resort ofBorovetz (55km south-east of Sofia)Information: website:http://www.math.bas.bg/massee2003/

16-20: Barcelona Conference on SetTheory, Bellaterra, Barcelona, CataloniaInformation: e-mail: set-theory@crm.es,web site: http://www.crm.es/set-theory[For details, see EMS Newsletter 46]

17-19: Conference on ComputationalModelling in Medicine, Edinburgh, UKOrganisers: International Centre forMathematical SciencesInformation: e-mail: icms@maths.ed.ac.ukwebsite: http://www.ma.hw.ac.uk/icms/current/index.html

CONFERENCES

EMS March 200338

Books submitted for review should be sent to the fol-lowing address: Ivan Netuka, MÚUK, Sokolovská83, 186 75 Praha 8, Czech Republic.

K. Alster, J. Urbanowicz and H. C. Williams(eds.), Public-Key Cryptography andComputational Number Theory, Walter deGruyter, Berlin, 2001, 331 pp., DM 256, ISBN 3-11-017046-9These proceedings are dedicated to the mem-ory of Rejewski, Rózycki and Zygalski, whobroke the military version of Enigma in 1933and gave its reconstructed version to theBritish and French in 1939. The book con-tains their photographs, but no paper describ-ing their activity. There are 20 papers in theproceedings, relating to various aspects of thescope of the conference.

Buchmann and Hamdy survey IQ cryptog-raphy, and Schnorr surveys the security of DL-cryptosystems and signatures against genericattacks. Patarin presents the concept of secretpublic-key schemes, where (in the case ofencryption) anybody can encrypt, but whereboth the key to decipher and the exact algo-rithm to decipher are secret. There is also a30-page carefully written overview of the XTRpublic key system by Lenstra and Verheul.Kucner and Kutylowski present a stochasticmethod of testing against stealing attacks bymanufacturers of cryptographic devices. S.Müller is concerned with security proofs basedon the factorisation problem in the sense ofIND-CCA (the indistinguishability-chosencipher text attack). Jacobson, Scheidler andWilliams investigate key exchange protocolsthat use real quadratic fields. Hoffstein andSilverman describe optimisation for NTRU,which is a cryptosystem based on ring theory.Niederreiter exhibits in a short survey severalinteractions of cryptography and the theory oferror-correcting codes.

The other papers are more or less purelymathematical. Couveignes discusses connec-tions between algebraic groups and the dis-crete logarithm, while Teske surveys algo-rithms to compute discrete logarithms.Elliptic and hyperelliptic curves are the subjectof contributions by Enge, Galbraith, Müllerand Pethö. The remaining three papers dealwith number theory: te Riele discusses the sizeof solutions n or the inequality ϕ(an + b) <ϕ(an), a and b coprime, Kubiak develops a pro-cedure which speeds up the extended binarygcd algorithms, and Dilcher surveys computa-tional and theoretical work done in the areasof Fermat and generalised Fermat numbers,Wieferich and Wilson primes, and Fermat andWilson quotients for composite moduli. (ad)

Y. André and F. Baldassarri, De RhamCohomology of Differential Modules onAlgebraic Varieties, Progress in Mathematics 189,Birkhäuser, Basel, 2001, 214 pp., DM 118, ISBN3-7643-6348-7The main topic of this book is the theory ofdifferential modules on algebraic varieties.The book offers fundamental results on directimages of regular differential modules by asmooth morphism (proofs of finiteness, basechange, regularity and monodromy theorems).There is also an algebraic treatment of the the-ory of regularity and irregularity in severalvariables, leading to elementary proofs of

main results on de Rham cohomology of dif-ferential modules. The authors use a new def-inition of relative algebraic de Rham cohomol-ogy with compact support and prove that itcoincides with the Dwork algebraic dual theo-ry. The final result of the book is a completeproof of general non-archimedean compari-son theorem for de Rham cohomology. As acorollary, it is shown that the functor of p-adicanalytification of connections is fully faithful.

The book will be of interest to specialists inarithmetic algebraic geometry, and may alsobe used as an introduction to the topicsdescribed above. (jbu)

G. E. Andrews, R. Askey and R. Roy, SpecialFunctions, Encyclopedia of Mathematics and itsApplications 71, Cambridge Univ. Press, 1999,664 pp., £55, ISBN 0-521-62321-9 An introductory chapter presents many factson gamma and beta functions, which form thenecessary basic tools for further treatment ofspecial functions, including a short informa-tion on their finite field analogues. Later (inChapter 8), the Selberg multi-dimensional ver-sions of beta integrals (including its finite fieldanalogue) are described. The next two chap-ters describe properties of the basic case ofhypergeometric series p+1Fp (mostly for p = 1or 2). A detailed study of Bessel functionsappears in Chapter 4. The following threechapters are devoted to properties of variousorthogonal polynomials, and Chapter 9 stud-ies spherical harmonics (including the relationof special functions to representation theory).Chapter 10 introduces a q-generalisation ofhypergeometric series, and includes q-versionsof the gamma and beta functions, the q-bino-mial theorem, Ramanujan formulas and atreatment of elliptic and theta functions.Relations to the theory of partitions form thesubject of Chapter 11. The final chapter isdevoted to identities of the Rogers-Ramanujantype. There are six appendices summarisingvarious tools used in the book. Each chapter isfollowed by a number of exercises.

The book is full of beautiful and interestingformulae, as was always the case with mathe-matics centred around special functions. It iswritten in the spirit of the old masters, withmathematics developed in terms of formulas.There are many historical comments in thebook. It can be recommended as a very usefulreference. (vs)

L. Barreira and Y. B. Pesin, LyapunovExponents and Smooth Ergodic Theory,University Lecture Series 23, American Math.Society, Providence, 2001, 151 pp., US$29, ISBN0-8218-2921-1This is a book on smooth dynamical systemswith a hyperbolic structure, written by twoexperts; in particular, several crucial resultswere proved by the second author. The classi-cal theorems of Lyapunov and Perron on thestability of non-autonomous systems of ODEshave started investigations into the Lyapunovexponents and their regularity.

The story is described in Chapters 1 and 2 –including, for example, the multiplicativeergodic theorem of Oseledets. Chapter 3 isdevoted to two main examples of (non-uni-form) hyperbolic systems, which stimulated thedevelopment of hyperbolic theory, namely

Anosov diffeomorphisms and geodesic flowson Riemannian manifolds. The last two chap-ters are based on Pesin’s results, and form theheart of the book. Local stable manifolds areconstructed in Chapter 4, where their absolutecontinuity (in the sense of Anosov) is proved.This is one of the main tools for the ergodictheory of smooth dynamical systems, and playsan important role in investigations of ergodicproperties of invariant hyperbolic measures inChapter 5.

The book contains many technically rathercomplicated results and is written for well-pre-pared readers (such as advanced graduate stu-dents working in dynamical systems) with agood knowledge of ODEs, differential topolo-gy and measure theory. Such a reader willsurely benefit by studying these lectures.(jmil)

E. R. Berlekamp, J. H. Conway and R. K.Guy, Winning Ways for Your MathematicalPlays, 1, 2nd ed., A K Peters, Natick, 2001, 276pp., US$49.95, ISBN 1-56881-130-6This first volume of a four-volume series is anelementary introduction to the theory of com-binatorial games, elementary in the sense thatconcepts, such as games, values, etc., aredefined naively rather than rigorously.

The book contains 8 chapters. Chapter 1introduces certain games and calculates theirvalues in complicated positions. Chapter 2,among others, introduces the game of Nimand the values of its positions – nimbers.Chapter 3 continues the exposition of valuearithmetic, studying nimber addition andintroducing the values of ↑ (up) and ↓ (down).Chapter 4 illustrates these ideas with a series ofexamples: Dowson’s chess, Treblecross etc.Chapter 5 introduces switch values, their tem-perature and their arithmetic, while Chapter 6shows how to deal with hot and big games.Chapter 7 discusses various versions ofHackenbush in more detail, and Chapter 8introduces the atomic weight of all-smallgames and related concepts. Each chapterends with references to further reading.

The book introduces numerous games withcolour illustrations. It does not assume anyparticular mathematical knowledge on part ofthe reader, but requires a certain degree ofabstract thinking and patience. (ab)

F. Borceux and G. Janelidze, Galois Theories,Cambridge Studies in Advanced Mathematics 72,Cambridge Univ. Press, 2001, 341 pp., £50, ISBN0-521-80309-8This book is based on a French manuscript,written by the first author as a record of hisideas; it is largely completed by results of thesecond author and his coauthors.

The authors briefly introduce the reader toclassical Galois theory and its tools, formulatedin modern mathematical language. The restof the book aims to provide deeper insight intomore advanced parts, such as the Galois theo-ry of Grothendieck. The reader will find herea well organised proof of the Galois theorem.The next part focuses on infinitary Galois the-ory. The true core of the book consists of thecategorical Galois theory of commutative rings(Stone duality, Pierce representation of a com-mutative ring, the adjoint of the spectrumfunctor, descent morphisms, etc.). The tech-niques of the second author are also used inthe chapter on covering maps. The conclud-ing chapter is devoted to thenon-GaloisianGalois theory, where the reader will find thefamous Joyal-Tierney theorem. The book iscarefully arranged and can be useful to any-body interested in algebraic methods. (lbe)

RECENT BOOKS

EMS March 2003 39

Recent booksRecent booksedited by Ivan Netuka and Vladimír Souèek

C. J. Budd and C. J. Sangwin, MathematicsGalore, Oxford Univ. Press, 2001, 254 pp.,£14.95, ISBN 0-19-850769-0 and 0-19-850770-4The aim of this book is to enthuse, inspire andchallenge young people in mathematics. Thematerial in this book is not covered by a typi-cal school syllabus. The main ideas are acces-sible to children from the age of eleven, whilesome parts of the book should interest andchallenge older school and university students,as well as their teachers and parents. Thebook consists of eight independent chapters,each formulating problems motivated by reallife and developing mathematical ideas thatcan be used to solve them. Many exercises areincluded.

In Chapter 1 mazes and labyrinths are stud-ied. After some short historical remarks, con-nections to graph theory, the problem of thebridges of Königsberg and the general methodfor solving all mazes are described. Chapter 2links group theory to study of patterns in danc-ing, bell-ringing and knitting. Chapter 3 con-tains some results in trigonometry. In Chapter4 some interesting mathematical theorems(mostly expressions of ð) are mentioned, withsome examples of magic tricks and the mathe-matics behind them. Chapter 5 shows howmathematics can apply to a problem of thebest design of castles: ideas on the isoperimet-ric inequality are presented, and the booklooks at properties of later designs of castlesand more modern fortifications. Chapter 6deals with codes, ciphers and the mathematicsused to break the codes: the Caesar andViginère ciphers are mainly discussed, withsome remarks about modern methods basedon prime factorization. Chapter 7 studies waysof representing numbers, with properties ofdifferent number bases (including negativeones). Chapter 8 introduces the properties oflogarithms. (ab)

I. Chavel, Isoperimetric Inequalities:Differential Geometric and AnalyticPerspectives, Cambridge Tracts in Mathematics145, Cambridge Univ. Press, 2001, 268 pp., £50,ISBN 0-521-80267-9The classical isoperimetric inequality com-pares the volume V(Ω) of a domain Ω in Rn

and the surface area A(∂Ω) of its boundary.There are several ways of interpreting thequantity A(∂Ω) – Hausdorff measure, perime-ter and Minkowski area – and the correspond-ing approaches to the proof of the isoperimet-ric inequality are presented. The Faber-Krahninequality on the smallest eigenvalue for theLaplace operator is deduced: among domainswith equal volumes, the minimum is attainedfor a ball. After this, the author turns to gen-eralisations to manifolds. He develops themethod of discretization and studies alsoisoperimetric constants for graphs, and relatesisoperimetric inequalities, Nirenberg-Sobolevinequalities, Nash-Sobolev inequalities andFaber-Krahn inequalities. Then he studiesthe large time heat diffusion on manifolds: themethod of proof again uses a discretisation.

The book is very useful in two ways. First, itnicely explains the story of the classicalisoperimetric inequality, a result with a big dis-proportion between the ease of formulationand difficulty of the proof. It is very useful thatthe reader can compare different approaches.Second, it presents a topical and interestingpart of global analysis on manifolds, relatingthe asymptotic behaviour of the isoperimetricinequality for large domains and large-timeheat diffusion. This second part contains deepresults obtained by the author. (jama)

I. Chiswell, Introduction to Lambda Trees,World Scientific Publishing, Singapore, 2001, 315pp., £48, ISBN 981-02-4386-3In a connected graph there is a natural dis-tance function, the minimum number of edgesin a path connecting given vertices. If thegraph is a tree, this distance has certain specif-ic properties. Generalising them to distanceswith values in a general ordered abelian groupL (instead of the group of integers), oneobtains the notion of a L-tree. Part of the book(less than a quarter) is devoted to an analysis ofthe notion and properties of L-trees as metricspaces. Most of the text is concerned with theirisometries, group actions on L-trees in general,and actions of special groups; in conclusion,Rip’s theorem is discussed.

The book is divided into six chapters.Chapter 1 introduces basic notions. Chapter 2is devoted to the definition and basic proper-ties of L-trees, and to R-trees (which play animportant role in the theory). Chapter 3, pre-sents some basic facts on isometries of L-trees(special features of individual isometries andtheir pairs, group actions as group of isome-tries, etc.). Chapter 4 is concerned with moreinvolved questions of group actions. Some spe-cial action groups are introduced andanalysed, and the spaces of actions on R-treesare discussed. Chapter 5 is devoted to actionsof free groups. Finally, Chapter 6 contains athorough discussion of Rip’s theorem (charac-terising finitely generated R-free groups) thatcan be approached using isometry groups onR-trees.

In the quarter-century since L-trees (andTits’ R-trees) were introduced, the theory hasdeveloped considerably. This monograph istimely and useful. (ap)

M. Cwikel, M. Engliš, A. Kufner, L.-E.Persson and G. Sparr (eds.), Function Spaces,Interpolation Theory and Related Topics,Walter de Gruyter, Berlin, New York, 2002, 462pp., EUR 138, ISBN 3-11-017117-1Interpolation theory is an important field offunctional analysis, which can be, roughlyspeaking, divided into its classical and modernparts. The main landmarks of the classicalinterpolation theory are the 1926 M. Riesz’sconvexity theorem, furnished later with thecelebrated complex-variable proof of O.Thorin (1939/48), and the 1939 theorem of J.Marcinkiewicz. Modern interpolation theory,whose foundations were laid in the early 1960s,has several fathers, including E. Gagliardo, A.Calderón, J.-L. Lions, S. G. Krein and J.Peetre. The last of these, Prof. Jaak Peetre ofLund, reached his 65th birthday on 29 July2000, and a delightful conference was held inLund a month later. The special spirit of thismeeting can be felt from the conference web-site.

This book, containing the conference pro-ceedings, is organised equally well. It has aninteresting introductory part, consisting of theEditors’ preface, an opening address by H.Wallin from which the reader can learn inter-esting facts (such as Peetre’s impressive per-sonal record in marathon races), a picture ofPeetre in his rose garden, a beautiful article‘Jaak Peetre, the man and his work’ by M.Cwikel, L.-E. Persson, R. Rochberg and G.Sparr, giving a comprehensive review ofPeetre’s work (including an unbelievable list of289 publications), and an essay ‘On the devel-opment of interpolation – instead of a historythree letters’, edited and/or translated byPeetre, including letters by O. Thorin, A.Zygmund and M. Cotlar that give a very inter-esting insight to the beginnings of interpola-

tion theory. The main part of the book contains contri-

butions from J.-L. Lions; A.B. Aleksandrov, S.Janson, V.V. Peller and R. Rochberg; J. Arazyand H. Upmeier; J. Brandman, J. Fowler, B.Lins, I. Spitkovsky and N. Zobin; M.J. Carroand J. Martín; M. Cotlar and C. Sadosky; D.Cruz-Uribe, SFO and M. Krbec; M. Engliš; T.Figiel and N. Kalton; V. Gol’dshtein and M.Troyanov; S. Kaijser and P. Sunehag; D.Lukkassen and G.W. Milton; V.G. Maz’ya andI.E. Verbitsky; C. Michels; E. Nakai; L. Pick;S.Yu. Tikhonov; H. Triebel; and a list of the 73talks given at the conference. The topics cov-ered by these contributions range from inter-polation theory, through function spaces, toapplications in operator theory. (lp)

O. Debarre, Higher-Dimensional AlgebraicGeometry, Springer, New York, 2001, 233 pp., 16fig., DM 96, ISBN 0-387-95227-6This book describes certain topics on theprogress in classifying algebraic varieties ofdimension at least 3. The first two chapters aredevoted to the standard definitions and resultson nef, big and ample Cartier divisors andspaces of morphisms of a fixed algebraic curveto a fixed algebraic variety. Chapters 3, 4 and5 deal with various aspects of the geometry ofsmooth algebraic varieties with many rationalcurves – in particular, uniruled or rationallyconnected varieties. It is proved, for example,that Fano varieties are rationally connected.Chapters 6 and 7 take a first step toward theMori minimal model programme of classifyingalgebraic varieties, proving the cone and con-traction theorems. (pso)

P. Dolbeault, A. Iordan, G. Henkin, H. Skodaand J.-M. Trépreau (eds.), Complex Analysisand Geometry: International Conference inHonor of Pierre Lelong, Progress in Mathematics188, Birkhäuser, Basel, 2000, 241 pp., DM 118,ISBN 3-7643-6352-5This is a collection of 18 papers written in hon-our of the 85th birthday of Pierre Lelong. Themeeting, organised on this occasion in Paris,was also the closing conference for theEuropean network ‘Complex analysis and ana-lytic geometry’.

The first contribution (by H. Skoda)describes the main topics of Lelong’s research,and includes his complete bibliography.Further papers are written by J. Siciak, J.-P.Demailly, G. Bassanelli, M. Christ, K.Diederich and T. Oshawa, K. Diederich and J.McNeal, G. Herbort, U. Hiller, S. Webster, C.Laurent-Thiébaut and J. Leiterer, T.C. Dinh,P. Dingoyan, E. Mazzilli, E. Bedford and M.Jonsson, G. Tomassini, F. Berteloot and J.Duval, C. Epstein and G. Henkin. At the endis a list of ten open problems in the field, for-mulated by participants at the meeting. Thebook will be of interest to mathematiciansworking in the field. (vs)

L. T. Fernholz, S. Morgenthaler and W.Stahel (eds.), Statistics in Genetics and in theEnvironmental Sciences, Trends in Mathematics,Birkhäuser, Basel, 2001, 183 pp., DM 130, ISBN3-7643-6575-7This book is a collection of twelve papers,based on contributions to the 1999 Workshopon Statistics and Science, held at the CentroStefano Franscini in Ascona. It provides fur-ther proof of the crucial role of statistics inmodern genetics and environmental science,and will be useful for anyone interested in sta-tistical applications or methodology in thisarea of research. The articles range fromapplied statistics to theoretical results with tied

RECENT BOOKS

EMS March 200340

connection to environmetrics. The book starts with three articles on

applied stochastical genetics. This part coversquantitative genetics, with applications to plantbreeding, DNA microarray analysis after stan-dardisation, and variance component estima-tion with an uncertain link between individualsand their parents. The next four articles pre-sent non-trivial statistical applications in chem-istry. The authors face problems of censoreddata and severe outliers, when estimatingchemical concentration, risk under low doseexposure, age-dependent risk of carcinogene-sis, and atmospheric chemistry. The appliedpart of the proceedings concludes with ananalysis of the problem of small objects on theEarth’s orbit. The last four papers can be clas-sified as theoretical: written with applicationsto the environmental sciences in mind, thesearticles deal mainly with multivariate data androbust techniques. Here one can find treat-ments of robust principal components, robustinverse regression, regression depth or τ-esti-mate for linear regression.

The book provides a sample of possibleapplications of statistics for statisticians inter-ested in how their methods are used. Othersfrom different areas can learn how to use sta-tistics in their work. (dh)

H. Freistühler and G. Warnecke (eds.),Hyberbolic Problems: Theory, Numerics,Applications, 8th Internat. Conference inMagdeburg February/March 2000, Vols. I, II,International Series of Numerical Mathematics,140/141, Birkhäuser, Basel, 2001, 472 and 469pp., EUR 80 each volume, ISBN 3-7643-6709-1and 3-7643-6710-5The book, in two volumes, is the Proceedingsof the Eighth International Conference inMagdeburg, in 2000. It contains about onehundred refereed papers presented at thisconference. Most of these are concerned withnon-linear hyperbolic equations of conserva-tion laws.

The papers can be divided into threegroups. Those from the first group are con-cerned with such theoretical aspects of hyper-bolic problems as the existence and uniquenessof solutions, asymptotic behaviour, large-timestability or instability of waves and structures,various limits of solutions, the Riemann prob-lem, etc. In particular, non-linear conservationlaws are treated. One can see a considerableprogress in mathematical theory on the onehand, but the results published here indicatethat mathematicians are struggling with anumber of difficult open problems. The sec-ond group of papers is devoted to numericalanalysis of hyperbolic problems – for example,development of numerical schemes, investiga-tion of their stability and convergence. Thesepapers study finite differences, finite elementand finite volume schemes, investigateschemes with special properties, and pay atten-tion to adaptivity, domain decomposition,multi-resolution and artificial dissipation. Thethird group of articles is oriented to a widerange of applications, such as one-phase andmultiphase flow, shallow water problems, high-speed flow, relativistic magnetohydrodynam-ics, low Mach number flow, elasticity, thermo-dynamics, electromagnetic fields, etc.

The books contain a large amount of mater-ial and give an excellent overview of the con-temporary state of art in the area of hyperbol-ic problems. They will be of interest toresearchers and students of applied andnumerical mathematics, computational fluiddynamics and computational physics, scientistsand engineers engaged in applied mathemat-

ics and scientific computing. (mfei)

S. Feferman, J. W. Dawson, Jr., S. C. Kleene,G. H. Moore, R. M. Solovay and J. vanHeijenoort (eds.), Kurt Gödel: CollectedWorks, Vols. I and II, Oxford Univ. Press, 2001,473 and 407 pp., each volume £26.50, ISBN 0-19-514720-0 and 0-19-514721-9These two volumes present a comprehensiveedition of all Kurt Gödel’s published works inthe period 1929-74. The first volume coversthe period 1929-36 and begins with his disser-tation, previously available only through theUniversity of Vienna. Each article or group ofarticles is preceded by an introductory noteplacing it into historical context and clarifyingit. The members of the editorial board, andsome outside experts, are the authors of thesenotes. Each article originally written inGerman is printed with an English translation.The first volume starts with SolomonFeferman’s bibliographical essay on Gödel’slife and work. In each volume, there are exten-sive lists of references, as well as interestingphotographs.

The books are carefully and beautifully pro-duced and offer rich material, illuminating notonly the outstanding work of Gödel, but alsothe whole mathematical logic of the twentiethcentury, including some philosophical and his-torical aspects. Some questions from physicsare also discussed. (jmlc)

M. Gardner, Gardner’s Workout: Training theMind and Entertaining the Spirit, A K Peters,Natick, 2001, 319 pp., US$35, ISBN 1-56881-120-9This is a remarkable book. It is a collection of41 articles that the author wrote for academicjournals and popular magazines. It also con-tains ideas of the author on ‘how to teach mathto pre-college students without putting them tosleep’. Let us pick out a few characteristicpoints. • There is an old picture of a baker, whobaked a square cake and sold a quarter of it.Four hungry kids enter the shop to buy the restof it. Could they tell how to cut it into fourpieces of the same size and shape? • Another problem: ‘Cut an equilateral trian-gle into three similar parts, no two congruent’is easily solved. It is probably unique, thoughno proof is known. • One afternoon, while sitting in a car waitingfor my wife to finish supermarket shopping, Ilocated a pencil and paper and drew on thesheet the unique lo shu, or magic square madewith distinct digits 1-9. … Back home I beganexperimenting… (How typical of a marriedmathematician!).

It remains for the reader to find a lonelyisland, an unlimited quantity of paper and aneternal pencil, together with this book. It willsurely produce a paradise for anybody whowants to enjoy the pleasure of the creative workin his brain. (lbe)

J. M. Gracia-Bondía, J. C. Várilly and H.Figueroa, Elements of NoncommutativeGeometry, Birkhäuser Advanced Texts, Birkhäuser,Boston, 2001, 685 pp., DM 138, ISBN 0-8176-4124-6 and 3-7643-4124-6The branch of mathematics now called non-commutative geometry is a far-reaching gener-alisation of the Gelfand-Naimark theorem stat-ing that, for a commutative C*-algebra A, thereis an isometric *-isomorphism between thealgebra A and the set of continuous functionson the set of characters of A. In a sense, anynon-commutative C*-algebra gives rise to analgebra of functions on a non-commutative

topological space constructed as the spectrumof A.

The book is divided into four parts, com-prising 14 chapters. The first part contains asummary of the basics of C*-algebras, such asthe Gelfand-Naimark theorem, the Tannaka-Krein reconstruction theorem, Serre-Swan cat-egorical equivalence between vector bundlesand projective modules over unital commuta-tive algebras, K-theory and its Bott periodicityfor C*-algebras, Morita equivalence of C*-alge-bras, etc. The second part contains some con-structions of universal algebras that are behindthe real analysis foundations of non-commuta-tive geometry – in particular, universal formsand connections, cycles and their Chern char-acters, together with Hochschild cohomology.The third part is devoted to ingredients ofnon-commutative Spin geometry, built uponthe notion of a spectral triple. The fourth partdiscusses possible applications of this machin-ery in the realm of mathematical and theoreti-cal physics, including descriptions of non-com-mutative gauge theories and perturbativequantum field theories. The book containsproofs of almost all assertions, as well as manyexplicit examples illustrating the theoreticaldevelopments described. (pso)

M. R. Grossinho, M. Ramos, C. Rebelo, L.Sanchez, Eds., Nonlinear Analysis and itsApplications to Differential Equations, Progressin Nonlinear Differential Equations and TheirApplications 43, Birkhäuser, Boston, 2001, 380pp., DM 188, ISBN 0-8176-4188-2 and 3-7643-4188-2The book contains many of the talks deliveredat the Autumn School on Non-linear Analysisand Differential Equations, held at the CMAF,University of Lisbon, in 1998. The school con-sisted of short courses and a seminar.

The first part of the book contains the fol-lowing short courses: An overview of themethod of lower and upper solutions for ODEs(C. De Coster and P. Habets); On the long-time behaviour of solutions to the Navier-Stokes equations of compressible flow (E.Feireisl); Periodic solutions of systems with p-Laplacian-like operators (J. Mawhin);Mechanics on Riemannian manifolds (W. M.Oliva); Twist mappings, invariant curves andparabolic differential equations (R. Ortega)and Variational inequalities, bifurcation andapplications (K. Schmitt). The second partcontains 21 contributions from various topics,related in one way or another to either ordi-nary or partial differential equations. The top-ics in the ODE part include spectral theory forthe 1-dimensional p-Laplacian, application of atime-map in boundary-value problems, non-linear oscillations, non-linear resonance, andmore. The topics in the PDE part include sym-metries of positive solutions to equationsinvolving the higher-dimensional p-Laplacian,bifurcation theory and its applications to theMonge-Ampère operator, application of thedual method to the Tricomi problem, the tele-graph equation, an abstract concentration-compactness method, and degree and indextheories on the Nielsen numbers. In bothparts, problems from the calculus of variationsand optimal control appear naturally – forexample, in Lipschitz regularity of minimisers(ODE part) or optimal control for some ellipticequations of logistic type (PDE part). Finally,we mention the dynamics of delayed systemswhich appears in connection with asymptoticexpansion and Hopf bifurcation. (lp)

P. Hájek (ed.), Gödel ‘96, Lecture Notes inLogic 6, A K Peters, Natick, 1996, 322 pp.,

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US$50, ISBN 1-56881-153-5This volume contains the proceedings of a con-ference held in Brno on the 90th anniversaryof the birth of Kurt Gödel. It is divided intotwo parts: the first, ‘Invited papers’, contains 9papers, and the second part, ‘Contributedpapers’, has 13 papers. The contributionsreflect many areas substantially influenced ortouched by Gödel’s work. They mainly illumi-nate or develop some of Gödel’s results andideas concerning mathematical logic and thefoundations of mathematics. Some contribu-tions discuss aspects of his results and opinionsin physics, as Ellis’s ‘Contributions of K. Gödelto Relativity and Cosmology’ and Stöltzner’s‘Gödel and the Theory of Everything’. Othercontributions refer to Gödel’s philosophicalopinions, as, for example, ‘Gödel’s OntologicalProof Revisited’ by Anderson and Gettings.The authors of invited papers are S. Feferman,M. Baaz, G.F.R. Ellis, B.A. Kushner, C.Parsons, P. Pudlák, W. Sieg and J. Byrnes, G.Takeuti and M. Yuasumoto, and A. Wisser. Awide area of Gödel’s work is covered, and thecontents could inspire a large community ofresearchers. (jmlc)

V. P. Havin and N. K. Nikolski (eds.),Complex Analysis, Operators, and RelatedTopics, Operator Theory Advances and Applications113, Birkhäuser, Basel, 2000, 408 pp., DM 198,ISBN 3-7643-6214-6 This book is dedicated to the memory of afamous analyst, S. A. Vinogradov. The firstpaper (by V. P. Havin and N. K. Nikolski)describes Vinogradov’s life and mathematicalwork and includes his complete list of publica-tions. The next two papers are English trans-lations of two of his articles (summaries of themain results of his Ph.D. and doctoral theses).There are 27 contributed papers from variousbranches of real, complex and harmonic analy-sis, using points of view and methods fromfunctional analysis and operator theory. Thereare both survey papers and research papers,and one short paper is of a personal character.(vs)

H. Hedenmalm, B. Korenblum and K. Zhu,Theory of Bergman Spaces, Graduate Texts inMathematics 199, Springer, New York, 2000, 286pp., 4 fig., DM 109, ISBN 0-387-98791-6Although Bergman spaces (spaces of square-integrable holomorphic functions) resemblethe familiar Hardy space on the unit circle,they are much less manageable and their theo-ry is still far from being complete. This bookdeals exclusively with the Bergman space onthe unit disc and presents an exposition of thecurrent state of the theory, including severalrecent advances that took place in the 1990’s.

After introducing the basic tools and con-cepts (Bergman projections, the Berezin trans-form, Carleson measures), the main topics dis-cussed are the factorisation theory and zerodivisors on the Bergman space (due to the firstauthor), zero sets and the growth spaces A-α(due to the second author), interpolation andsampling (the work of Seip and others), invari-ant subspaces of higher index and theBeurling-type theorem of Aleman, Richter andSundberg, the construction of invertible non-cyclic functions (after Borichev and the firstauthor), and the solution of the dominationproblem via weighted biharmonic Green func-tions with respect to log-subharmonic weights.(This last result, due to Hedenmalm,Jakobsson and Shimorin, appears here for thefirst time in full.) The authors deliberatelyabstain from treating the operator-theoreticaspects, thus avoiding overlap with the third

author’s book Operator theory in function spaces(Marcel Dekker, New York 1990).

The exposition is beautifully organised andvery lucid and well written. Although someimportant topics close to the spirit of the bookhave been omitted (such as the recent proof ofthe so-called Korenblum conjecture), the bookis surely indispensable for anyone activelyworking in the area of Bergman spaces, whilemaking good reading for any mathematicalanalyst. (meng)

H. Heuser, Lehrbuch der Analysis, 1, 14.Auflage, B.G. Teubner Verlag, Stuttgart, 2001,643 pp., EUR 29,90, ISBN 3-519-52233-0This outstanding textbook covers all basic top-ics of first-year mathematical analysis at uni-versities: differential and integral calculus, andrelated topics such as sequences, series, and anintroduction to differential equations. Besidesthe theory, the book offers numerous applica-tions in physics, chemistry, biology, agricul-ture, technics, medicine, psychology, warfare,etc. The purpose is to show how powerful amathematical approach is and how rich theapplications can be, as well as to show what astimulating influence these sciences can havefor mathematics. There are about 1000 exer-cises and problems in the text (the more diffi-cult ones are marked), some of them solved atthe end of the textbook.

The three chapters on applications are real-ly worth while: it is easy to have run through‘dry’ theory without a single application. Aquestion then arises, as to whether readers canapply anything from what they have justlearned. The depth, width, skill and refine-ment make this book highly valuable, not onlyfor students of pure mathematics and studentsof other areas that need it, but also for profes-sional mathematicians and lecturers who canfind here a lot of inspiration. Of course, wecan hardly expect less from a book that hasattained its fourteenth edition and has therebyproved beyond any doubt its high standardand popularity. (jdr)

J. W. P. Hirschfeld (ed.), Surveys inCombinatorics, 2001, London MathematicalSociety Lecture Note Series 288, Cambridge Univ.Press, 2001, 301 pp., £27.95, ISBN 0-521-00270-2This volume contains nine invited talks pre-sented at the 18th British CombinatorialConference, held at the University of Sussex inJuly 2001. It also contains a memoir of C.Nash-Williams, who died in January 2001, writ-ten by J. Sheehan, and the list of Nash-Williams’s publications. Four survey articlesdeal with graph theory and matroids, threewith combinatorial designs and finite geome-tries, one with computational Pólya theory, andone with the Penrose polynomial.

B. Mohar surveys classical and recent resultsrelated to graph minors and graphs on sur-faces. M. Molloy discusses progress on twoproblems in random structures: how manyedges must be added to a random graph untilit is almost surely k-colorable, and the analo-gous question for satisfiability in the random k-SAT problem. J. Oxley writes on the interplaybetween graphs and matroids (2-connected-ness, removable circuits, minors and infiniteantichains, branch-width). D.R. Woodalldescribes results on list colorings: in the firstpart he surveys mostly proper colorings, and inthe second part he gives a number of newproofs and conjectures on improper list color-ings. I. Anderson discusses results on combi-natorial designs with cyclic structure. A. R.Calderbank and A. F. Naguib describe applica-

tions of quadratic forms in wireless communi-cation problems: the bridge between the twosubjects are orthogonal designs (known also asspace-time block codes), and Hurwitz’ famoustheorem of classifying normed algebras (reals,complex numbers, quaternions, and octo-nions) finds its way into applied mathematics!J. A. Thas focuses on the most importantresults on partial m-systems and m-systems offinite classical polar spaces. L. A. Goldberg’scontribution is concerned with the computa-tional difficulty of three problems: for a per-mutation group acting on a finite set, to countthe orbits exactly and approximately, and tochoose an orbit uniformly at random. M.Aigner ‘surveys in a leisurely pace’ connectionsof the Penrose polynomial, developed as a toolfor attack on the 4-colour problem, to graphtheory, binary space, Tutte polynomial, Gaussproblem, Hopf algebras, and invariants in knottheory. (mkl)

J. Hong and S.-J. Kang, Introduction toQuantum Groups and Crystal Bases, GraduateStudies in Mathematics 42, American Math. Society,Providence, 2002, 307 pp., USD$49, ISBN 0-8218-2874-6This book deals with some aspects of quantumgroups, defined as the spectra of no-commuta-tive Hopf algebras given by one-parameterdeformations of universal enveloping algebrasof Kac-Moody algebras. In the first part, theLusztig representation theory of deformed uni-versal enveloping algebras is recalled.Chapters 4 and 5 develop the theory of crystalbases, following the combinatorial approach ofKashiwara and geometric approach of Lusztig.The next chapters discuss the structure of crys-tal graphs of finite-dimensional integrable rep-resentations of deformed universal envelopingalgebras via semistandard Young tableaux.The final three chapters describe a connectionbetween representation theory of deformeduniversal enveloping algebra of affine algebrasand solvable lattices and vertex models. (pso)

A. A. Ivanov and S. V. Shpectorov, Geometryof Sporadic Groups II: Representations andAmalgams, Encyclopedia of Mathematics and itsApplications 91, Cambridge Univ. Press, 2002,286 pp., £50, ISBN 0-521-62349-9This is the second half of a two-volume set,which contains the proof of the classification ofthe flag-transitive P- and T- geometries. Thegeometries involved are those in the sense ofTits: an incidence system of subsets of differenttypes.

The existence of the geometries was estab-lished in the first volume of the treatise. Themain theorem of the second volume consists inthe proof that the amalgam of maximal para-bolics obtained from a flag-transitive automor-phism group of a P- geometry or T-geometry isisomorphic (as an amalgam) to the amalgam ofmaximal parabolics obtained from one of theknown cases. The book is written with obviouscare and the arguments are usually not difficultto follow. The authors have also taken carewith summaries and overviews that ease under-standing of the general strategy of the proof.The only deficiency worth mentioning seemsto be the index, which contains too few items:it also contains no list of symbols, which meansthat a considerable amount of time can bewasted searching for the first appearance of asymbol or a notation convention. (ad)

T. Iwaniec and G. Martin, Geometric FunctionTheory and Non-linear Analysis, OxfordMathematical Monographs, Clarendon Press,Oxford, 2001, 552 pp., £75, ISBN 0-19-850929-4

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Geometric function theory studies mappings ffrom an open set ΩΩ in Rn to Rn. If f has inte-grable Jacobian J(x, f) and satisfies the distor-tion inequality |Df|n ≤ K(x) J(x, f) a.e., where Kis a non-negative finite measurable functionand Df is the weak gradient in the sense ofSobolev, then f is said to be a mapping of finitedistortion. Such mappings appear naturally asminima of various variational problems, or ele-ments of classes of deformations. Their topo-logical and geometric behaviour recalls thebehaviour of holomorphic functions. The firsthistorical step towards this theory was the gen-eralisation from conformal to quasiconformalmappings. In the 1960s, Reshetnyak devel-oped the theory of quasiregular mappings(mappings with bounded distortion). His classof mappings allows branching, and thus pro-vides a joint generalisation of the theory ofholomorphic functions and the quasiconformaltheory. Geometric function theory is now a sig-nificant part of analysis, with links to manyother parts of mathematics (differential geom-etry, global analysis on manifolds, topology,partial differential equations, calculus of varia-tions, and harmonic analysis).

The book begins with an overview of the the-ory. After some preliminary material, theauthors prove the generalised Liouville theo-rem, and then study continuity and its modulusfor mappings of finite distortion. The part oncompactness of families of mappings of finitedistortion is related to polyconvex calculus ofvariation, with results important in the theoryof elasticity. As a preparation for further treat-ment, large parts of the theories of differentialforms, Beltrami equations, and Riesz trans-forms are developed. The authors present theHardy estimate of the Jacobian and theGehring result on reverse Hölder estimates.After an excursion to theory of non-linearelliptic PDEs, they return to the theory of map-pings of bounded distortion and prove theirproperties (openness, discreteness, positivity ofthe Jacobian, branching behaviour, removablesingularities, and theorems of Picard andMontel type).

The approach of the authors is entirely ana-lytical, relying on methods of PDE theory, geo-metric measure theory, the theory of functionspaces and harmonic analysis. They skip themethod of moduli of curve families, which iswell covered by other books. This book dis-cusses all important results of the theory.Notwithstanding, most of the material is new,at least in the degree of generality or in themethods of proof. This book makes life easierfor all mathematicians interested in quasicon-formal theory and all its generalisations, analy-sis of mappings between Euclidean spaces ormanifolds, and all related areas. Even special-ists in quite distant fields can find inspirationby studying the far-reaching methods here.The book is well written and may comfortablybe read by advanced students. (jama)

L. Kérchy, C. Foias, I. Gohberg and H.Langer (eds.), Recent Advances in OperatorTheory and Related Topics, Operator TheoryAdvances and Applications 127, Birkhäuser, Basel,2001, 669 pp., DM 330, ISBN 3-7643-6607-9A conference in memory of B. Sz.-Nagy (1913-98) was held in Szeged in August 1999. Thisvolume in the Birkhäuser series on operatortheory contains 35 articles, partly proceedingsand partly research papers by the conferenceparticipants. One special article, by L. Kérchyand H. Langer, briefly describes the scientificresults of Sz.-Nagy, who was one of thefounders of modern operator theory. A thirdof the papers describe the current state of the

method of unitary dilatations. This theory andits later extensions to functional models (doneby Sz.-Nagy with C. Foias) provide one of themain research directions in modern operatortheory. Other papers are devoted to furtherparts of operator theory, such as operatorinequalities and orderings, spectral theory,Banach algebras and their applications tophysics, stochastic processes and system theo-ry. Several papers emphasise the connectionsbetween complex function theory and operatortheory.

This book is oriented mainly to experts, butits scope is wide enough to show the richness ofproblems and methods of operator theory toother interested readers. (jmil)

E. Kleinert, Units in Skew Fields, Progress inMathematics 186, Birkhäuser, Basel, 2000, 79 pp.,DM 68, ISBN 3-7643-6293-6This book presents the theory of arithmeticgroups. In particular, it includes a treatmentof unit groups of orders in skew fields, whichare finite-dimensional and central over therational field. The goal is, in the author’swords, ‘to stimulate the interest in the topic bypresenting a synopsis of methods and results’.

The book starts with a description of skewfields, which are considered in the subsequenttheory. The necessary theorems on simplealgebras over global fields are stated but notproved. The exposition proceeds with Hey’stheorem and Weyl’s reduction theory. The fol-lowing chapters touch several features of thestudied groups, such as Zariski-density, thefiniteness theorem of Margulis and Kazhdan’sproperty. The final chapters use crossed prod-ucts and results by Tits to construct importantexamples and show some methods for findingunits. The main open problems are discussed.The book is not of an introductory character,and will be appreciated mainly by researchersin arithmetic groups and neighbouring areas.(rb)

K. P. Knudson, Homology of Linear Groups,Progress in Mathematics 193, Birkhäuser, Basel,2001, 192 pp., DM 118, ISBN 3-7643-6415-7This is a highly specialised monographdesigned for researchers and postgraduate stu-dents preparing themselves for work on thehomology of linear groups. It is well knownthat the main impetus for this study were thehigher algebraic K-groups of rings introducedby D. Quillen.

In Chapter 1 the author presents results,now already considered classical, on the coho-mology of the general linear groups: these arelinked with famous mathematicians like A.Borel, Dwyer, Friedlander, Lichtenbaum andQuillen. Chapter 2 deals with stability resultsconcerning the homology of general lineargroups: t he main result here is the importanttheorem of W. van der Kallen. Chapter 3 thenconcentrates on the description of low-dimen-sional homology (up to dimension 3). Themain theme of Chapter 4 is groups of rankone. Finally, Chapter 5 is a survey on resultsconcentrated around the Friedlander-Milnorconjecture (homology of algebraic groupsmade discrete).

Reading this book requires a lot of prerequi-sites, especially from algebraic topology, groupcohomology, algebra and algebraic geometry.On the other hand, the author has succeededin writing a lively text and has tried his best tomake the reading easier, so that a reader withpossible gaps in his knowledge can proceedfurther and is ready to learn more in order tounderstand this book. He also advises a read-er how to understand some notions without too

much preparation (for instance, using specificexamples instead of general notions), and hasadded three appendices on the homology ofdiscrete groups, classifying spaces and K-theo-ry, and étale cohomology. Each chapter is fol-lowed by exercises (some quite difficult). Thebibliography has 134 items up to the year2000. This book represents a very good intro-duction into contemporary research in thisinteresting field. (jiva)

I. Lasiecka and R. Triggiani, Control Theoryfor Partial Differential Equations: Continuousand Aproximation Theories II. Abstr.Hyperbolic-like Systems over a Finite TimeHorizon, Encyclopedia of Mathematics and itsApplications 75, Cambridge Univ. Press, 2000, pp.645-1067, £60, ISBN 0-521-58401-9This is the second part of an intended three-volume treatise on the state-space approach toquadratic optimal control theory for linearpartial differential equations in Hilbert statespaces. While the first volume was devoted toparabolic-like equations yielding analytic semi-groups in abstract formulations, this secondvolume considers autonomous hyperbolicequations and the Petrovski-type equations,and the finite-time horizon case (the infinitehorizon will appear in Volume 3). A semi-group approach to a control problem dependson regularity properties of the input-state map– the trace regularity in the authors’ terminol-ogy.

The first chapter of this volume (actuallyChapter 7, since the numbering is through thewhole treatise) contains various formulations ofthis hypothesis. Chapters 8-10 study theresulting differential Riccati equation, givingpointwise feedback synthesis of an optimalcontrol, within three different frameworks,which differ by continuity or discontinuity ofthe input-state map and the observation oper-ator. These special cases come from differenthyperbolic-like equations: typically, Neumannboundary control and Dirichlet boundaryobservation for the second-order hyperbolicequations (Chapter 8), a coupled system of awave equation and a Kirchhoff equation withpoint control (Chapter 9), Dirichlet boundarycontrol for the second-order hyperbolic equa-tion and the Schrödinger equation (Chapter10). Like the first volume, this part is mainlybased on numerous results of the authors, onboth abstract and concrete equations.

The reader will find much important infor-mation on various aspects of semigroup theoryand on the regularity of solutions of hyperbol-ic equations. Most of the proofs are carefullypresented, but some preliminary knowledge ofPDE techniques (such as interpolation theory)is needed. A review of the first volumeappeared in EMS Newsletter 38. (jmil)

P. Lounesto, Clifford Algebras and Spinors,London Mathematical Society Lecture Note Series239, Cambridge Univ. Press, 1997, 306 pp.,£27.95, ISBN 0-521-59916-4This is the second edition of a book that firstappeared in 1997. It offers a systematic anddetailed treatment of many topics connectedwith Clifford algebras and the correspondingspinor spaces. Different parts of the book canbe used for different purposes.

The first chapters are suitable for beginners,starting with repetitions of complex numbers,vectors, scalar products, bivectors, exteriorproduct and quaternions. Relevant topicsfrom theoretical physics are reviewed in thenext few sections (electromagnetic theory, spe-cial relativity, the Dirac equation, various typesof spinors, Fierz identities). Real Clifford alge-

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bras are introduced in the second half of thebook, where all their basic properties areshown, including a discussion of Witt rings andBrauer groups. Matrix realisations of Cliffordalgebras, periodicity questions and the use ofClifford numbers in the Vahlen description ofconformal maps form the next topic. Thebook ends with a short summary of basic factsfrom Clifford analysis, the Chevalley construc-tion of Clifford algebras (including characteris-tic 2) and relations between octonions and tri-ality.

The first part of the book is elementary andcan be used for undergraduate study, while thesecond part is more advanced and can bewarmly recommended to students orresearchers interested in the topic. (vs)

K. Matsuki, Introduction to the Mori Program,Universitext, Springer, New York, 2002, 478 pp.,61 fig., EUR 74,95, ISBN 0-387-98465-8The aim of this book is to introduce the Moriprogramme, which can be regarded as aneffective approach toward the biregular and/orbirational classification framework of higher-dimensional algebraic varieties. The first partof the book is devoted to the Enriques classifi-cation of algebraic surfaces in the framework ofthe Mori programme. Unlike algebraic curves,in the case of algebraic surfaces there are manynon-singular representatives in each birationalequivalence class. The operations of blowingup and blowing down lead in two complexdimensions to the machine of the minimalmodel programme, producing either a mini-mal surface or a ruled surface. The importantcharacterisation of the minimal model is thatits canonical divisor is nef. Various features ofthe Mori programme in dimension 3 or higherare discussed in the rest of the book. Here theclassification naturally and inevitably forces theextension of category of the non-singular vari-eties to the varieties with some specific singu-larities. The most important are the notions ofcanonical and terminal singularities, togetherwith their logarithmic generalisations. Therelation between any two of various minimalmodels is that they are connected by asequence of flops, the codimension 2 opera-tions with close connection to flips. (pso)

E. Menzler-Trott, Gentzens Problem.Mathematische Logik imNationalsozialistischen Deutschland,Birkhäuser, Basel, 2001, 411 pp., EUR 43, ISBN3-7643-6574-9This is the most extensive and detailed biogra-phy of Gerhard Gentzen (1909-45), based onan enormous number of documents, extractsfrom correspondences, personal recollectionsand communications, reviews of Gentzen’spapers, and Gentzen’s reviews of papers ofother logicians – all carefully reproduced andcommented on. It also partially elucidates hislast days: his arrest in May 1945 in Prague andhis death in prison in August 1945. The devel-opment of his proof theory and natural deduc-tion are discussed at length. The book alsocontains three Gentzen’s lectures on the con-cept of infinity, the consistency of mathematics,and the foundations of mathematics (pub-lished, but not easily available), and anAppendix gives a concise introduction to theproof theory, written by Jan von Plato. All thisis embedded in the general political and ideo-logical situation in Germany during thenational-socialistic regime. The history of therelationship between logic and mathematics onone hand, and politics and ideology on theother, is carefully described and well docu-mented, and general philosophical implica-

tions are discussed. There are many pho-tographs, tables, documents and a detailed bib-liography. This is a really valuable book. (jfi)

J. Oikkonen and J. Väänänen (eds.), LogicColloquium ‘90, Lecture Notes in Logic 2, A KPeters, Natick, 1993, 305 pp., US$50, ISBN 1-56881-132-2This volume contains the proceedings (includ-ing invited speakers) of the 1990 EuropeanSummer Meeting of the Association forSymbolic Logic, held in Helsinki. There areeighteen papers, some of them devoted to newor generalised logic foundations, intuitionistic,modal and temporal logic. Among the othersare Hintika’s ‘New foundations for mathemati-cal theories’ and Gabbay’s ‘Labelled deductivesystems: a position paper’. Other papers coverfurther branches of mathematical logic, such asmodel theory, proof theory, computability the-ory and set theory, including Buchler andNewelski’s ‘On the geometry of U-rank 2 type’and Cooper’s ‘Definability and global degreetheory’. The papers cover a wide spectrum oftopics. (jmlc)

J.-P. Pier (ed.), Development of Mathematics1900-1950, Birkhäuser, Basel, 1994, 729 pp.,DM 118, ISBN 3-764-32821-5 and 0-817-62821-5To write comments on the history of mathe-matics in the second half of the 20th century isa difficult task, due to the enormous growth inthe number of working mathematicians. Theaim of this book is to contribute to such a pro-ject with a collection of essays on evolution incertain fields.

A few contributions are devoted to the foun-dation of mathematics, set theory, logic andtopology and their applications in variousparts of mathematics (J.-Y. Girard, J.-P.Ressayre, B. Poizat, F.W. Lawvere and S.Sorin). Papers by E. Fouvry, M. Waldschmidt,J.-L. Nicolas and C. Ciliberto discuss topicsfrom number theory and its applications.Graphs and their applications in other fieldsare discussed by C. Berge. Riemannian geom-etry is the topic of a paper by M. Berger. Apaper by M.-F. Roy surveys results in real alge-braic geometry. Various versions of K-theoryare discussed by M. Karoubi. Two papers by V.Arnold are devoted to the local theory of criti-cal points of functions and to dynamical sys-tems. Relations between thermodynamics andchaotic dynamical systems are studied by V.Baladi. B. Mandelbrot discusses questions infractal geometry. A review by J. Dieudonné isdevoted to mathematics during the last 50years in France, while one by V. M. Tikhomirovdiscusses Moscow mathematics in this period.A paper by M. Smorodinsky treats questions ininformation theory, and I. Chalendar and J.Esterle discuss some questions in functionalanalysis. Fourier analysis is treated by P.L.Butzer, J.R. Higgins and R.L. Sten, andwavelets by S. Jaffard. PDEs are discussed by J.Sjöstrand and R. Temam (microlocal analysis,Navier-Stokes equations). The calculus of vari-ation is the topic of a paper by F.H. Clarke.Several complex variable theory and plurisub-harmonic functions are discussed by P.Dolbeault and C. Kiselman. Random process-es, branching processes, Brownian motion,random walks, statistics and stochastic analysisare treated by P.-A. Meyer, M. Yor, J.-F. LeGall, Y. Guivarc’h, K.D. Elworthy, G.R.Grimmett, L. Le Cam and B. Prum. The bookconcludes with interviews with A. Douady, M.Gromov and F. Hirzebruch, and various bibli-ographic and other data. It is important toknow our own history, and this book con-

tributes very well to this aim. (vs)

F. Schweiger, Multidimensional ContinuedFractions, Oxford Univ. Press, 2000, 234 pp.,£70, ISBN 0-19-850686-4 This is a well-written monograph, written byone of the leading experts in the field. It con-tains a study of the properties of multidimen-sional continued fractions, which can bedescribed by fractional linear maps, togetherwith their relations to other fields of mathe-matics and its applications. The authordescribes individual algorithms (due to Jacobi-Perron, Güting, Brun, Selmer, Poincaré, etc.)and studies their periodicity and convergenceproperties. There is an interesting discussionon the Schweiger generalisation of the Kuzmintheorem to higher dimensions. The book endswith chapters on the dimension of exceptionalsets (a generalisation of Good’s theorem) andsome applications. It can be warmly recom-mended to all readers interested in this diffi-cult theory. (bn)

S. Yu. Slavyanov and W. Lay, SpecialFunctions. A Unified Theory Based onSingularities, Oxford Mathematical Monographs,Oxford Univ. Press, 2000, 293 pp., £65, ISBN 0-19-850573-6There are various ways of treating a very broadfield of special functions in a systematic way.This book uses the classifications based on sin-gularities of the corresponding differentialequation, and is written in a very nice and sys-tematic way.

Basic facts about linear second-order ordi-nary differential equations with polynomialcoefficients in the complex plane areexplained in the first part of the book. Thisincludes a discussion of regular and irregularsingularities, confluence and reductionprocesses, and a generalised Riemann schemefor description of type of the considered equa-tion. The next two chapters form the core ofthe book, where the authors treat the classicalhypergeometric class of equations and theHeun class of equations. A number of applica-tions to problems in physics is given in Chapter4. In the final chapter, the authors show thatPainlevé equations of different types are Euler-Lagrange equations for quantum systemsdescribed by different types of Heun equa-tions.

The main aim of the book is to be a tool forpractical use for applied mathematicians,physicists and engineers. It offers a very sys-tematic treatment, without too many proofs,and can be complemented by software that isavailable separately. The book has a lot ofhelpful pictures, diagrams and tables. (vs)

I. J. Sobey, Introduction to InteractiveBoundary Layer Theory, Oxford Applied andEngineering Mathematics 3, Oxford Univ. Press,2000, 332 pp., £45, ISBN 0-19-850675-9This book is devoted to a better understandingof the laminar steady plane flows of aNewtonian fluid in the presence of the bound-ary. Due to two-dimensional geometries, theflow is described by the stream function whichis then constructed via asymptotic expansions(matched asymptotic analysis techniques). Inparticular, the triple deck method proves to bea useful tool in understanding the behaviour offluid near the points of laminar separation.The following special flowsare studied indetail: flow around a flat plate (infinite orfinite), external flow about a circular cylinder,and flows in (symmetric and asymmetric) chan-nels; the historical development of each prob-lem is underlined. From the point of view of

RECENT BOOKS

EMS March 200344

mathematical analysis of fluid mechanics equa-tions, the content of the book is closely relatedto an interesting open problem: whether in twospatial dimensions the solutions of the Navier-Stokes equations subjected to the no-slipboundary conditions converge, as the viscosityvanishes, to the solution of Euler equationswith zero normal component of the velocity onthe boundary. This book provides variousphysical/engineering/historical insights on thistopic. (jomal)

R. P. Stanley, Enumerative Combinatorics, 2,Cambridge Studies in Advanced Mathematics 62,Cambridge Univ. Press, 1999, 581 pp., £45, ISBN0-521-56069-1The book is a continuation of Volume 1 (1986),starting with Chapter 5 (Trees and the compo-sition of generating functions) and continuingwith Chapter 6 (Algebraic, D-finite, and non-commutative generating functions) andChapter 7 (Symmetric functions). The finalchapter has two appendices on Knuth equiva-lence, jeu de taquin, and the Littlewood-Richardson Rule (by S. Fomin) and the charac-ters of GL(n, C)). Each chapter has its own setof exercises with solutions – altogether 261 ofthem, but in fact many more when subexercis-es are counted. The references to these andthe bibliographies to the chapters constitute agiant survey of the literature on enumerativecombinatorics.

What else can be added to the commentsupon this excellent book? Perhaps a quotationfrom G.-C. Rota’s foreword: ‘Every once in along while, a textbook worthy of the namecomes along; (...) Weber, Bertini, van derWaerden, Feller, Dunford and Schwartz,Ahlfors, Stanley.’ The paperback edition con-tains a new short section with errata andaddenda to some of the exercises. (mkl)

J. Tanton, Solve this: Math Activities forStudents and Clubs, Classroom ResourceMaterials, Math. Assoc. of America, Washington,2001, 218 pp., £20.95, ISBN 0-88385-717-0This is a collection of problems and exercisesfrom recreational mathematics, and is dividedinto three parts. Thirty chapters in Part I con-tain many funny and interesting problems,from sharing a pile of candies, via ‘interesting’surfaces and turning one’s T-shirt inside outwith one’s hands clasped together, to mapcolouring and chessboard problems. Parts IIand III then contain hints, solutions, furtherthoughts and further reading on the problemsof Part I. This book is accessible to anyoneinterested in recreational mathematics. (ab)

H. Triebel, The Structure of Functions,Monographs in Mathematics 97, Birkhäuser, Basel,2001, 422 pp., DM 196, ISBN 3-7643-6546-3For more than the past three decades, books byProf. Hans Triebel of Jena have been land-marks of the theory of function spaces, differ-ential operators and interpolation, whichnobody seriously interested in the area couldpossibly dream of overlooking. They formedan important part of the literature that I wasadvised to study as a research student almosttwenty years ago, and still appear among therecommendations to my own students nowa-days. These books have always been wellknown for the precise way in which they arewritten, for the incredible amount of informa-tion they contain, and for the original style ofexposition (recall the ‘Steps’ of proofs, to namejust one example). Over the years, I have seenonly one objection that could possibly be madeabout the author’s style, that certain parts ofone book or another are a bit difficult to read.

The book under review has no such weakness,and in my opinion the way the material is pre-sented is ‘limiting’ in the following sense: if anymathematical author were given the sameamount of information to be covered, it wouldbe a very hard challenge (if not impossible) towrite a better text. The mathematical ideas areexposed in a witty, reader-friendly, narrativestyle which makes reading of the book a verypleasant experience. All the important results,deep as they are, are followed by a thoroughdiscussion of the subject, putting it into histor-ical context and revealing plenty of links toother, often seemingly distant, areas – linksthat would probably be overlooked otherwise.Occasionally, alternative proofs are given inorder to improve the reader’s insight into thesubject. The historical context is often com-plemented by a touch of geography; the authorhas an impressive knowledge of both westernand eastern, mainly Russian, literature. Thereader can thus learn more about the well-known fact that many important results pub-lished in Russian journals passed unnoticed,only to be rediscovered independently in theWest a few years later. These parts of the bookare of independent interest, even for a non-mathematician.

The main theme of the book is a constructiveapproach to function spaces (here called the‘Weierstrassian approach’) and its applications.Some parts of the book might be considered acontinuation of the author’s earlier bookFractals and Spectra, but in general the book isself-contained. As the author assures us in thepreface, the four chapters of the book aredevoted to the study of links between quarko-nial decompositions of functions on one side,and three other contemporary topics (sharpinequalities and embeddings, fractal ellipticoperators, and regularity theory for certainsemi-linear equations) on the other. Theauthor states that the book is based on recentresearch carried out by him and his co-work-ers. One would have therefore thought thatthe book is more a scientific monograph than,say, a textbook for Ph.D. students, but the bookis so well written that it can also be a good aidfor an interested reader who might not be anexpert in the field of function spaces but who iswilling to spend a little effort to study this won-derful and interesting book. (lp)

A. Uchiyama, Hardy Spaces on the EuclideanSpace, Springer Monographs in Mathematics,Springer, Berlin, 2001, 305 pp., DM 171, ISBN4-431-70319-5This book is based on a typewritten manuscriptcompleted by Akihito Uchiyama in 1990. Theauthor died prematurely in 1997 before hecould publish the material, and several of hisfriends and colleagues then proceeded withthe publication. Through their efforts thebook is now available for a broad mathematicalpublic.

An excellent preface should not be skippedby the reader. It is a witty, moving and clever-ly written essay which takes us to early-1980sChicago when Fourier analysis was undergoinga stormy development and an impressivegroup of the world’s top superstars in the areawere gathered there (A. Calderón, A.Zygmund, R. Fefferman, F. Browder, W.Beckner, to name just a few). The descriptionof the atmosphere is very convincing.

The book is devoted to the study of Hardyspaces by real-variable methods. The text isclearly meant more as a scientific monographthan, say, as lecture notes for beginners: theexposition is rather technical and does notcontain too much verbal explanation. Having

said this, a reader who is willing to put in someeffort will obtain an explanation of the ideas,methods and main results in Fourier analysisduring the last three decades, including theground-breaking duality result of C.Fefferman. In an introductory section, there isa graphical description of the cross-depen-dence of the sections, as well as advice as towhich of the sections might be safely skippedby the reader. The book has 28 sections, anappendix, and an impressive list of references,including an (even more impressive) list of sig-nificant contributions by the author, publishedin first-class journals. The introduction is wellwritten, giving a perfect description of whatshould be expected from the subsequent text,and also presenting a brief and very usefulintroduction to the world of Hardy spaces.The first thirteen chapters contain severalcharacterisations of the Hp spaces, includingthose involving certain special convolutionoperators, culminating with the perhaps mostnotorious one (on the real line), which involvesthe Hilbert transform. Within the material liedeep sophisticated methods developed sincethe 1970’s, including the arguments, now con-sidered classical, which employ all kinds ofvariations on maximal operators, atomicdecomposition, Hardy-Littlewood-Fefferman-Stein inequalities, good λ-inequalities, subhar-monicity of functions, basic concepts of theLittlewood-Paley theory, and much more. Thecharacterization of a Hardy space on a real lineby the Hilbert transform is a point of departurefor the analysis that follows, aimed (amongplenty of other things) at a generalisation ofthis result to a higher-dimensional situation:this material can be found in the subsequentfourteen sections (14-27). The last eight sec-tions (21-28) contain the main results of thebook, connected with the decomposition ofBMO due to Fefferman and Stein. The authorgives a constructive proof of this result thatenables him to obtain surprisingly deep exten-sions. (lp)

V. I. Voloshin, Coloring Mixed Hypergraphs:Theory, Algorithms and Applications, FieldsInstitute Monographs 17, American Math. Society,Providence, 2002, 181 pp., $49, ISBN 0-8218-2812-6This book is a collection of results (obtainedmostly by Vitaly Voloshin himself) on a newtype of hypergraph colouring, the so-called‘mixed hypergraphs’. A proper vertex-colour-ing of a given mixed hypergraph must respecttwo types of opposite constraints: some of theedges must not be monochromatic, while someof the edges must not be rainbow.

Mixed hypergraphs were introduced by theauthor in 1992, and since then the field hasgrown significantly and many interesting con-nections to other colouring problems havebeen discovered; the last chapter of the book isdevoted to these connections. In some aspects,colouring mixed hypergraphs is analogous tothe usual colouring, while in others it is com-pletely different – for example, there exists amixed hypergraph on six vertices that can becoloured with two and four colours but has noproper coloring with exactly three colours.The field is developing so rapidly that theauthor could not include some recent results,and several problems listed as open have sincebeen solved.

The book is self-contained and very read-able. It is clearly organised: each of the twelvechapters is devoted to a single concept or a sin-gle class of mixed hypergraphs. Anybody inter-ested in graph or hypergraph colouring willfind this book interesting. (dkr)

RECENT BOOKS

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