A while back, I had briefly stopped at the age-old question of beauty's place in art - and, just as quickly, walked past without so much as a backward glance. However, I have now regained my bearings, and feel that I am ready to tackle this juicy question full on. So, I will make a fool-hardy attempt to construct a composite view of beauty by breaking it down and applying it to one art form in particular - mathematics.
Okay, so now you're probably wondering "Why math"?
Well, no...more likely, you're probably wondering "Holy crap! Since when is math an art!?"
Yes, dear reader, it is true, though it may not be recognized as such due to its long-time association with science - not to mention failed tests, bad report card marks, and skinny nerds in coke bottles and suspenders. However, to mathematicians, schools have been going about things the wrong way; no one who really enjoys math pursues it because it's useful - they pursue it for its own sake, because it brings beauty and pleasure to their lives. True, math has nudged its way deep into the sciences, economics, and other applied fields, but just because it can be useful in a few applications doesn't mean that's all it's good for. Take graphic design, for instance; its use is primarily practical, but beneath its polished, Type-A pedigree lies a shared lineage with the great works of Dali, Picasso, and other titans of creativity.
However, that said, math is distinct among the other arts in one crucial manner - it is, in essence, a "discovered art", as opposed to a "created art". Mathematicians will say that they are deducing art from the natural (or imaginary) world via the rules of mathematical logic. It's all very left-brained, to be sure, but theirs is an approach that suites nicely our purposes for defining beauty; since mathematicians "discover" their art, it's much easier to peg down rules for identifying beauty as it manifests, as opposed to - say - a painter, who creates and redefines art and beauty with every passing style and generation.
The above should not be taken as a formal defense of math as an art, nor as a complete explications of its methodological differences with the other creative arts - those would require far more space than I'm willing to allocate here. Still, from there we can move ahead to consider beauty's role in art since, believe it or not, mathematicians are obsessed with beauty. We won't tackle all this in one go, but rather distribute our thoughts over four posts, each centered around what I believe to be the primary components of mathematical beauty: brevity, symmetry, profundity, and truth. The question of why these four will, hopefully, be answered over the course of the discussion, starting with brevity and ending with the familiar (and tantalizing) junction of truth and beauty.
Any artists/writers/mathematicians/musicians - feel free to dive in with your own ideas on what beauty is and how it relates to art. So until next time...