mathematics in the 20th and 21st century. in 20th century, mathematics became a major profession ...
TRANSCRIPT
MODERN MATHEMATICS
mathematics in the 20th and 21st century
introduction
in 20th century, mathematics became a major profession
hundreds of specialized areas
development of computers enabled mathematics to expand
mathematics progressed more than ever
Hilbert and 23 problems
David Hilbert (1862-1943) – German mathematician
“The Problems of Mathematics” – introduced in 1900
interest in physics
worked on general relativity
Who among us would not be happy to lift the veil behind which is hidden the future; to gaze at the coming
developments of our science and at the secrets of its development in
the centuries to come? What will be the ends toward which the spirit of
future generations of mathematicians will tend? What methods, what new facts will the
new century reveal in the vast and rich field of mathematical thought?
David Hilbert, 1900, Paris
four colour theorem
problem proposed in 1852 by Francis Guthrie
Haken and Appel
proved the four colour theorem in 1976
Wolfgang Haken –born in 1928, Berlin
Kenneth Ira Appel – born in 1932, New York
game theory and two John’s
John von Neumann (1903-1957) – American mathematician
interests: set theory, game theory, computer science, hydrodynamics of explosions
minimax theorem in 1928
member of Manhattan project
John Forbes Nash, Jr. – born in 1928, West Virginia
interest: game theory, differential geometry, partial equations
games: Hex in 1947 and So Long Sucker in 1950
“Nash equilibrium” Nobel Prize in Economics in 1994 A Beautiful Mind – Oscar winning
movie
game theory
attempts to mathematicly capture behavior in strategic situations
Theory of Games and Economic
Behavior in 1944
awards in mathematics why is there no Nobel Prize in
Mathematics?
Millenium Prize Problems - presented in 2000
Fields Medal - awarded since 1936
Abel Prize – first awarded in 2003