The Universal Aesthetics of Mathematics

  • Samuel G. B. Johnson
  • Stefan SteinerbergerEmail author

Can a proof be objectively beautiful? It is not a surprising claim that the search for beauty, both in theorems and in proofs, is one of the great pleasures of engaging with mathematics.

Quite often the similarity to beauty in the visual arts or music is made explicit:

The mathematician’s patterns, like those of the painter’s or the poet’s, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way (G. H. Hardy [2]).

Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is (Paul Erdős [3]).

A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature (H. Poincaré [8]).

Theorems can be “deep,” “profound,” “surprising,” or “derivative” and “boring”; conjectures can be “daring,” “bold,” “natural,” and...


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of Marketing, Business and Society School of ManagementUniversity of BathBathUK
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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