Mathematics as a Creative Mathematics as a Creative ArtArt

By Stephanie SundbergBased on the article by P.R.Halmos in

“Readings for Calculus”

Math is an art?Math is an art?

• In this article, P.R. Halmos proposes that mathematics is a creative art and that mathematicians are artists, not number crunchers. He discusses two fields: Pure Math (mathology) and Applied Math (mathophysics).

• Halmos presents many analogies for mathematics from the fields of music, art, and English.

• The best analogy for a mathematician is a painter.

Why Does Halmos Think Math is a Creative Art?

Why Does Halmos Think Math is a Creative Art?

“[Mathematics] is a creative art because mathematicians create beautiful new concepts; it is a creative art because mathematicians live, act, and think like artists; and it is a creative art because mathematicians regard it so” (pg. 180).

Mathology and MathophysicsMathology and Mathophysics

• Mathology: Pure Math—the development of theorems and rules, or “math for its own sake”-- requires the mind of a creative artist in order to make a significant contribution.

• Mathophysics: Applied mathematics is a branch of math that deals with applying math concepts to other areas such as biology, physics and statistics.

• After making this distinction, Halmos discusses only Mathology.

Math is like chess because…?Math is like chess because…?

• Halmos states it has an elaborate technical language and is completely deterministic.

• Chess—like mathematics—requires problem solving, evaluation, critical thinking, intuition and planning. (Should undergraduate students study chess to improve their critical thinking skills?).

• Trivia: Rosalyn Katz of New Jersey passed bills Bill #S452 and #A1122 in the senate. The legislature declared “…chess increases strategic thinking skills, stimulates intellectual creativity, and improves problem-solving ability. ”

Math is Like Music because…?Math is Like Music because…?• “The Mozart Effect”.• Tones can be represented

as functions: The superposition principle allows the decomposition of "any" periodic function as a sum of multiples of sin(n t), with n = 1, 2, 3, ...

• The multiples are the Fourier coefficients of the given function. This leads to Fourier Analysis.

• Beauty, intricacy, neatness, elegance, and satisfaction are suggested by Halmos.

• Math forms the basis of all musical scales.

Math is Like Literature because…?Math is Like Literature because…?

• There is often hidden math in literature. George Orwell once wrote “Any writer who is not utterly lifeless moves upon a kind of parabola, and the downward curve is implied in the upward one. “

• Who said: "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is--oh dear! I shall never get to twenty at that rate!" ?

• Answer: Alice in Wonderland

• Halmos thinks one reason they are alike is because society isn’t willing to subsidize pure language and pure math very much (theorists of both must earn their ‘bread and butter’ by teaching while theorizing in their spare time).

The PainterThe Painter

• The closest analogy is perhaps between mathematician and painter.

• Physical reality is the origin of both.

• Every time a mathematician hears “I could never balance my checkbook”, a painter hears “I could never draw a straight line”.

• Old art is as good as new art, and old math is just as relevant today as it was in the time of the Babylonians.

A Brief BiographyA Brief Biography

• Paul Richard Halmos was born in Budapest, Hungary in March, 1916. He is recognized for his outstanding contributions to operator theory, ergodic theory, and functional analysis.

• He emigrated to Chicago and due to some confusion with the differences between European and American grades, he entered the University of Illinois at age 15 to study Chemical engineering.

• “I hinted to the school authorities that I had completed three years of secondary school, and I was believed. ... a year and a half later, at the age of fifteen, I graduated from high school.”

ReferencesReferences

Paul Halmos picture/bio: http://www.algebra.com/algebra/about/history/Paul-Halmos.wikipedia

Paul Halmos Quotation: http://www-groups.dcs. st-and.ac.uk/~history/Mathematicians/ Halmos.html

Microtonal Music Theory: www.tonalsoft.com

Mathematics and Music: http://www.math.niu.edu/~rusin/papers/uses-math/music/

Mathematics as a Creative Mathematics as a Creative ArtArt

By Stephanie SundbergBased on the article by P.R.Halmos in

“Readings for Calculus”