Intuitions about mathematical beauty: A case study in the aesthetic experience of ideas

Samuel G.B. Johnson, Stefan Steinerberger

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Abstract

Can an idea be beautiful? Mathematicians often describe arguments as “beautiful” or “dull,” and famous scientists have claimed that mathematical beauty is a guide toward the truth. Do laypeople, like mathematicians and scientists, experience mathematics aesthetically? Three studies suggest that they do. When people rated the similarity of simple mathematical arguments to landscape paintings (Study 1) or pieces of classical piano music (Study 2), their similarity rankings were internally consistent across participants. Moreover, when participants rated beauty and various other potentially aesthetic dimensions for artworks and mathematical arguments, they relied mainly on the same three dimensions for judging beauty—elegance, profundity, and clarity (Study 3). These aesthetic judgments, made separately for artworks and arguments, could be used to predict similarity judgments out-of-sample. These studies also suggest a role for expertise in sharpening aesthetic intuitions about mathematics. We argue that these results shed light on broader issues in how and why humans have aesthetic experiences of abstract ideas.

Original languageEnglish
Pages (from-to)242-259
Number of pages18
JournalCognition
Volume189
Early online date20 Apr 2019
DOIs
Publication statusPublished - 1 Aug 2019

Bibliographical note

Copyright © 2019 Elsevier B.V. All rights reserved.

Funding

We thank Woo-kyoung Ahn, Lance Rips, and Nadya Vasilyeva for discussion, and Asher Auel, Miki Havlickova, John Hall, Brett Smith, and Sarah Vigliotta for assistance with data collection. These studies were presented at the 40th Conference of the Cognitive Science Society and a subset of the findings were discussed in an informal commentary in the Mathematical Intelligencer magazine; we thank the conference attendees and Intelligencer editor for their interest ( Johnson & Steinerberger, 2018, 2019 ). This work was supported by a grant from the American Psychological Association awarded to the first author. Appendix A

Keywords

  • Aesthetics
  • Explanation
  • Psychology of mathematics
  • Reasoning
  • STEM education

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Language and Linguistics
  • Developmental and Educational Psychology
  • Linguistics and Language
  • Cognitive Neuroscience

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