Beauty in Math, Doh!
I saw an episode of the Simpsons a long time ago in which Bart was mistaken for a genius and went to a school for the gifted. In one class the following exchange takes place (lifted from this web site)
Ms.M: So y = r3/3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.
Class: [chuckles]
Ms.M: Don't you get it, Bart? Derivative dy = 3 r2 / 3, or r2 dr, or r dr r. Har-de-har-har, get it?
It blew me away! There was differential calculus on The Simpsons, and it was correct; although it is non-standard to write the differential dr in the middle of the answer, who cares. I always thought this was strange until I saw this Science News article on clever math in the Simpsons. For example, The Simpsons also once showed an apparent violation of Fermat's theorem - it will appear to check out on a typical calculator, but the difference is below most calculators' round off error:
178212 + 184112 = 192212 (close, but NOT true!)
For some reason this made me wonder if one could think of math as art. Maybe one can tackle it from a different angle - is math beautiful? Sure I think fractals are beautiful. And the Golden Ratio is considered to correspond to aesthetically pleasing dimensions in natural structures like conch shells. Many claim to recognize its influence in art, but this is often disputed and I tend to side with the skeptics.
These are aesthetic arguments, but is Math intrinsically beautiful? G.H. Hardy thought so and wrote about this in his wonderful book 'A Mathematician's Apology'. As an example of intrinsic beauty in math, Hardy pointed out Euclid's proof that there are infinitely many prime numbers; I'll try to do a decent job here:
Suppose pn is the largest of a complete sequence of n total prime numbers. Then form a new number: ((p1*p2*...*pn) + 1). This new number is not divisible by any of the n prime numbers. Therefore this new number is either itself prime, and therefore is also larger than pn, or is divisible by a prime number larger than pn. Therefore for any prime pn there must exist an even larger prime number.