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

Samuel G.B. Johnson; Stefan Steinerberger

doi:10.1016/j.cognition.2019.04.008

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

Samuel G.B. Johnson, Stefan Steinerberger

Yale University

Research output: Contribution to journal › Article › peer-review

23 Citations (SciVal)

335 Downloads (Pure)

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 language	English
Pages (from-to)	242-259
Number of pages	18
Journal	Cognition
Volume	189
Early online date	20 Apr 2019
DOIs	https://doi.org/10.1016/j.cognition.2019.04.008
Publication status	Published - 1 Aug 2019

Bibliographical note

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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10.1016/j.cognition.2019.04.008

Johnson & Steinerberger in press.PDFAccepted author manuscript, 1.02 MBLicence: CC BY-NC-ND

Cite this

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

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this