The concept of mathematical beauty fascinates me – and lots of other people, as the long wikipedia article demonstrates – because it’s such a mix of opposites, the very quantifiable with the very non-quantifiable. There’s no question that some math work produces a response similar to the feeling you get from some artistic work, if you understand the mathematics.
But what if you don’t know the math? Does underlying “beauty” still shine through, like it does when you see a painting or listen to music?
An intriguing study tried to answer that by seeing whether mathematical proofs demonstrate any aesthetic feeling in non-mathematicians.
Science Daily has an excellent article about it (read it here).
For the study, they chose four mathematical proofs ( the sum of an infinite geometric series, Gauss’s summation trick for positive integers, the Pigeonhole principle, and a geometric proof of a Faulhaber formula, which I’d never heard of), four landscape paintings, and four classical piano pieces. They showed them to people, asked them to rate them on various aesthetic measures, and gave them questionnaires.
Steinerberger and Johnson were most impressed that these ratings could be used to predict how similar participants in the first group believed that each argument and painting were to each other. This finding suggests that perceived correspondences between maths and art really have to do with their underlying beauty.
Overall, the results showed there was considerable consensus in comparing mathematical arguments to artworks. And there was some consensus in judging the similarity of classical piano music and mathematics.
Small-scale social science studies like this should always be taken with more than just one grain of salt – they seem to be non-replicable with startling frequency – but it’s still interesting.