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Monday, August 12, 2019

Study shows we like our math like we like our art: beautiful | Arts & Humanities - Yale University

A beautiful landscape painting, a beautiful piano sonata — art and music are almost exclusively described in terms of aesthetics, but what about math? Beyond useful or brilliant, can an abstract idea be considered beautiful? by Kendall Teare, Assistant Communications Officer at Yale University. 

A "cold and austere beauty" has been attributed to the compound of five cubes
Photo: Wikipedia, the free encyclopedia 
Yes, actually — and not just by mathematicians, reports a new study in Cognition.

Coauthored by a Yale mathematician and a University of Bath psychologist, the study shows that average Americans can assess mathematical arguments for beauty just as they can pieces of art or music. The beauty they discerned about the math was not one-dimensional either: Using nine criteria for beauty — such as elegance, intricacy, universality, etc. — 300 individuals had better-than-chance agreement about the specific ways that four different proofs were beautiful.

This inquiry into the aesthetics of mathematics began when study co-author and Yale assistant professor of mathematics Stefan Steinerberger likened a proof he was teaching to a “really good Schubert sonata.”...

Enter Samuel G.B. Johnson, study co-author and now an assistant professor of marketing at the University of Bath School of Management, who was still completing his Ph.D. in psychology at Yale when he connected with Steinerberger. Johnson studies reasoning and decision making. “A lot of my work is about how people evaluate different explanations and arguments for things,” he explained.

Steinerberger said Johnson understood immediately how to design an experiment to test his question of whether we share the same aesthetic sensibilities about math that we do about other modalities, i.e. art and music, and if this would hold true for an average person, not just a career mathematician like himself.

I had some diffuse notion about this, but Sam immediately got it,” said Steinerberger. “It was a match made in heaven.”

For the study, they chose four each of mathematical arguments, landscape paintings, and piano sonatas. Because the similarities between math and music have long been noted, Johnson explained, they also wanted to test people using another aesthetic modality — art in this case — to see if there’s something more universal about the way we judge aesthetics.

Additional resources
Samuel G.B. Johnson, Stefan Steinerberger. Intuitions about mathematical beauty: A case study in the aesthetic experience of ideas. Cognition, 2019; 189: 242 
DOI: 10.1016/j.cognition.2019.04.008

Source: Yale University