Submitted via IRC for SoyCow1984
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: 0) by Anonymous Coward on Sunday August 18 2019, @04:38AM (9 children)
Schröedinger's Equation isn't exactly beautiful. but it is effective and is probably the minimally descriptive form of what it describes.
"E=mc²" is beautiful, but the full general relativity equation is a bit less so. or the tensor maths commonly used in that area to actually work 'in the 4th Dimension'.
Heaviside's versions of Maxwell's equations are beautiful (as is using differential calculus in much of EM)...compared to Maxwell's original versions...
then there is the abomination that is String theory.
(Score: 0) by Anonymous Coward on Sunday August 18 2019, @04:49AM (2 children)
Is a multi-terabyte proof the least or most beautiful math?
(Score: 3, Insightful) by Ethanol-fueled on Sunday August 18 2019, @05:43PM (1 child)
The most beautiful math is math you learn on your own terms rather than that drab repetitive academic slog most people pay to go through.
(Score: 2) by hendrikboom on Tuesday August 20 2019, @01:43AM
Yes, indeed. But if you have attention deficit it helps a lot to have a guide to lead your way.
And it helps to have someone pose interesting questions about what you're studying -- questions you'll learn something unexpected from.
(Score: 3, Insightful) by stormwyrm on Sunday August 18 2019, @06:14AM
Numquam ponenda est pluralitas sine necessitate.
(Score: 2) by maxwell demon on Sunday August 18 2019, @01:06PM (2 children)
If Schrödinger's equation is not beautiful, you've written it wrong. ;-)
H psi = E psi is very beautiful.
The trick to getting beautiful equations is to hide the ugliness behind single letters. :-)
The Tao of math: The numbers you can count are not the real numbers.
(Score: 0) by Anonymous Coward on Sunday August 18 2019, @03:02PM
So it's beauty and ugly at the same time. The perceived feature depends on the observer.
(Score: 0) by Anonymous Coward on Wednesday August 21 2019, @07:24AM
Yeah but that's not where it starts. Normally it starts with "here's a classical equation with shit-tons of formulas. Now watch.... we replace the equations with operators! Ta-da! Isn't it beautiful?!". Physics is full of that shit - not saying it's wrong, just the teaching of physics is wrong.
(Score: 2) by hendrikboom on Sunday August 18 2019, @01:45PM (1 child)
I've always appreciated Schrodinger's equation in operator form. Something like E psi = H psi. (or is it L instead of H? I forget.
As well as the relativistic version of the electromagnetic field equations expressed using differential forms: dF 0.
Basing physics on the proper mathematical concepts often makes it more elegant.
(Score: 2) by hendrikboom on Monday August 19 2019, @07:03PM
Of course the elegance of these equations isn't just a matter of using an abbreviation. It's because the notation used has a substantial body of theory that makes manipulation of the equations in this form easier that the traditional form involving nontrivial arrangements of partial derivative symbols.
(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.
(Score: 2) by deimios on Sunday August 18 2019, @07:23AM (1 child)
Beauty is in the eye of the beholder.
Beauty is what the group perceives to be beautiful be that biologically, sociologically or otherwise motivated.
(Score: 2) by The Mighty Buzzard on Sunday August 18 2019, @11:21AM
Yup. Incredibly complex things can be more aesthetically pleasing than simple things. Witness some funky with the cheeze whiz pool trick shots. Or the universe.
My rights don't end where your fear begins.
(Score: 2) by c0lo on Sunday August 18 2019, @01:22PM (1 child)
Meanwhile, zillions of non-beholders head to Facebook hourly.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 2) by takyon on Sunday August 18 2019, @04:20PM
They appreciate the raw beauty of the anti-social machine learning media surveillance colossus.
[SIG] 10/28/2017: Soylent Upgrade v14 [soylentnews.org]
(Score: 2) by legont on Monday August 19 2019, @04:05AM (1 child)
Beauty is way overused. What is universally understood and a good test for anything is quality. https://en.wikipedia.org/wiki/Zen_and_the_Art_of_Motorcycle_Maintenance [wikipedia.org]
We don't know what quality is, but anybody can separate quality from junk right away.
"Wealth is the relentless enemy of understanding" - John Kenneth Galbraith.
(Score: 0) by Anonymous Coward on Wednesday August 21 2019, @08:12AM
Feeeeeeel my junk, man. I mean the quality.
(Score: 0) by Anonymous Coward on Monday August 19 2019, @11:57AM (2 children)
The people who never get past the basic maths (like algebra I), never really get to appreciate the true beauty and joy you can get form math. Many get a taste of it in some of the geometry proofs in high school, but most never get to abstract algebra, topology, etc. That's where I first learned how beautiful math can be. Trying to describe it to others, the best I could come up with is "it's like art for smart people."
(Score: 2) by DannyB on Monday August 19 2019, @04:16PM
"Math (and science) are Hard! So let's just get rid of them!" -- Barbie from Mattel
"Yeah! Whatever she said!" -- Ken from Mattel
The lower I set my standards the more accomplishments I have.
(Score: 2) by hendrikboom on Tuesday August 20 2019, @01:34AM
And they are phasing out geometry as well. Anything obviously fun has to go!