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For some people, math can be a necessary headache. Yes, algorithms guide countless aspects of daily life. There are tips to calculate and hours to count. But unless someone's a specialist, they'll probably ignore complex math in any given situation if they can help it.
But Yale assistant professor of mathematics Stefan Steinerberger wants to challenge that perception. His new study shows that an average American can assess mathematical arguments for beauty just as they can pieces of art or music.
And he has the numbers to prove it.
Beauty is in the eye of the beholder, of course. But for Steinerberger and coauthor Samuel G.B Johnson, beauty is made up of nine separate components: seriousness, universality, profundity, novelty, clarity, simplicity, elegance, intricacy, and sophistication. They didn't come up with those criteria themselves, but expanded on ideas laid out in “A Mathematician’s Apology,” a 1940 essay by mathematician G.H. Hardy.
"The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics," Hardy wrote in his essay, which meant to draw distinctions between applied mathematics, as seen today in computer science and statistics, and what he called "pure," or theoretical, mathematics.
(Score: 4, Interesting) by AthanasiusKircher on Sunday August 18 2019, @06:01AM (2 children)
On a somewhat related topic, if you've never seen the book Proofs Without Words, I'd suggest a look. (The original book can be pricey, as I'm not sure it's in print. A quick search showed me a PDF available online -- though I'm not suggesting piracy, but if you just want to see what I'm talking about...)
In essence, it's a bunch of rather concise proofs, mostly presented geometrically and without verbal explanation. Some are creative; some are elegant or surprising in their approach. There are sequels available too with more proofs.
To relate to TFA: I think visual proofs are perhaps easier to think about aesthetically and compare to other types of art. It doesn't surprise me that the example given in TFA of a proof is a visual one.
(Score: 0) by Anonymous Coward on Sunday August 18 2019, @06:25AM
Getting a little further off topic, here's a pre-review of an upcoming book that looks interesting,
http://prettyugly.info/ [prettyugly.info]
(Score: 0) by Anonymous Coward on Sunday August 18 2019, @03:43PM
Many trig proofs are of the kind, often employing symmetry arguments.