A window into a mathematician’s mind

One day I had 20 minutes to kill, and decided to just draw a cityscape.

I got to the category theory class (also affectionately known as “general abstract nonsense”) with five minutes to spare before the lecture, so I kept going. A friend sat down next to me, looked at the page, and just asked “are you just going to draw windows?”

A mathematician is asked to hammer two nails into a wall. One nail is already halfway in; the other is untouched. The mathematician looks at them, picks up the untouched nail, hammers it in perfectly, then stops. When asked why he didn’t finish the half-hammered one, he replies:

“That case is already reduced to the general problem.”

Mathematics is pretty unique in that you want to do things only once. Or, that is a point of view common among mathematicians; for most people, mathematics is “computation”. To be good at computations, you need to do a lot of reps, like muscle training. Well, to be a mathematician you need to do a lot of proofs to be able to come up with your own proofs. Proofs are all unique in their own way, in stark contrast with computations. Unless you consider “computation” in one of its higher forms, such as performing integration on exotic functions. Or, on the other side, you can build a proof factory by creating systems for which you can prove some property through a generic proof template. In fact, proofs and computations are just different perspectives on the same activity, but they feel like very different activities depending on the level of abstraction.

When drawing on paper, you cannot make a general window and derive all the others as special cases. You have to draw them. These repetitive, simple activities feel soothing and meditative, or tedious and unnerving. I can take either point of view. When contemplating the tediousness, I feel this becomes like an abyss swallowing the whole of human life. But in the flow of things, drawing is my own retreat to my inner sanctum. This is what life really is about; mathematics is the weird abnormality in life. This is what makes us “human”; empathy and kindness are what make us animals.

In any case, I could not bring myself to continue the drawing.