The researchers’ nine dimensions elaborated from Hardy’s six were: seriousness, universality, profundity, novelty, clarity, simplicity, elegance, intricacy, and sophistication. Hardy, which discusses mathematical beauty. They derived these criteria from “A Mathematician’s Apology,” a 1940 essay by famous mathematician G.H. The first task required a sample of individuals to match the four math proofs to the four landscape paintings based on how aesthetically similar they found them the second required a different sample to do the same but instead comparing the proofs to sonatas and the third required another unique sample of people to independently rate, on a scale of zero to ten, each of the four artworks and mathematical arguments along nine different criteria plus an overall score for beauty. Johnson divided the study into three parts. One of the four mathematical arguments used in the study, as it was displayed to participants. 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. “It was a match made in heaven.”įor the study, they chose four each of mathematical arguments, landscape paintings, and piano sonatas. “I had some diffuse notion about this, but Sam immediately got it,” said Steinerberger. art and music, and if this would hold true for an average person, not just a career mathematician like himself. 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. “A lot of my work is about how people evaluate different explanations and arguments for things,” he explained. Johnson studies reasoning and decision making. in psychology at Yale when he connected with Steinerberger. 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. Yale professor of psychology Woo-Kyoung Ahn replied to Steinerberger and, after further discussion, gave him the name of a psychology graduate student with whom she thought he would get along.Įnter Samuel G.B. “Three or four students came up to me afterwards and asked, ‘What did you mean by this?’ And I realized I had no idea what I meant, but it just sounded sort of right. “As it turns out, the Yale students who do math also do a statistically impressive amount of music,” said Steinerberger. 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.” 300 individuals had better-than-chance agreement about the specific ways that four different proofs were beautiful. The beauty they discerned about the math was not one-dimensional either: Using nine criteria for beauty - such as elegance, intricacy, universality, etc. Yes, actually - and not just by mathematicians, reports a new study in Cognition.Ĭoauthored 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. 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?
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