Quotations: A Baker’s Dozen

This semester I have taken to the habit of writing a quote of the day on the board for my Geometry for Teachers class. When possible, I choose a quote germane to the lecture topic, but a good number of them refer to mathematics more broadly. As I’ve looked though my notebooks, my favorite texts, and my memory for my favorite quotes, the ones that have helped me define for myself what mathematics means and why it is beautiful, it’s occurred to me that some of these bear mention here.

  • “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” — John von Neumann
  • “Do you know why the sun doesn’t revolve around the Earth? Because the idea is not beautiful enough.” — Einstein, in Steve Martin‘s Picasso at the Lapin Agile
  • “A mathematician is a device for turning coffee into theorems.”  Alfréd Rényi (but often misattributed to his friend Paul Erdös)
  • “Everything should be made as simple as possible. But no simpler.” Albert Einstein
  • “Pure mathematics, may it never be any use to anyone.” — Henry J. S. Smith (a toast)
  • Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to forsee their consequences.” E. C. Titchmarsh
  • “It is one of man’s curious idiosyncracies to create difficulties for the pleasure of resolving them.” — Joseph de Maistre
  • “Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle. . . . ” Jacques Hadamard
  • “The trouble with integers is that we have examined only the very small ones.  Maybe all the exciting stuff happens at really big numbers, ones we can’t even begin to think about in any very definite way.  Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed.  Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.” Ronald Graham
  • “The art of doing mathematics consists in finding that special case which contains all the germs of generality.” David Hilbert
  • “We often hear that mathematics consists mainly of ‘proving theorems’. Is a writer’s job mainly that of ‘writing sentences’?” Gian-Carlo Rota
  • “The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.”  Aristotle
  • “As for everything else, so for a mathematical theory: beauty can be perceived but not explained.” Arthur Cayley

P.S.

Somehow I managed to publish an incomplete version of the previous post, several drafts back. If you read this post and thought I might have lost my marbles, the correct version of the post is there now.

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