Mathematics as a Creative Art

1
Mathematics as a Creative Art

• By Stephanie Sundberg
• Based on the article by P.R.Halmos in Readings
  for Calculus

2
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.

3
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).

4
Mathology and Mathophysics

• Mathology Pure Maththe 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.

5
Math is like chess because?

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

6
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.

7
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 isnt 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).

8
The 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.

9
A 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.

10
References

• Paul Halmos picture/bio http//www.algebra.com/al
  gebra/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/mu
  sic/

11
Mathematics as a Creative Art

• By Stephanie Sundberg
• Based on the article by P.R.Halmos in Readings
  for Calculus