In high school I had an art professor who said to me, “The only way to truly know something is to sketch it.” The idea is when you draw something with your own hands you are forced to look at it more carefully. Fine artists tend to sketch the same object over and over again in order to better capture an idea. One of my favorite examples of this is Robert Delaunay, a cubist painter in the early 20th Century, who painted the Eiffel tower repeatedly in attempt to capture the vertigo he felt when he was near it.
I find myself currently studying for finals and I’m really drawn to writing and rewriting theorems and proofs. Somehow as I write something over and over I glen more truth out of the statement. The first time I look at something I don’t notice the little details; whether it’s a mu or a nu in a particular equation. As I rewrite the theorem I find myself thinking, “well gosh, why does this converge almost everywhere instead of pointwise?” By sketching the proof, perhaps laying it out in different ways in my notebook, I begin to truly know it. I can complete similar sketches of related objects, just as Delaunay may have done with the nearby buildings, in order to better know the object of his painting. And so, artistically I sit, proof sketching my analytical and (to some) emotionless subject in the same manner as the finest artists capture a vision of grandeur. As I sketch Urysohm’s Lemma I wonder: who would ever imagine math is not a creative process?