Eugenia Cheng may be my mathematical opposite. She did a great interview with Peter Rowlett in which she bubbles over with enthusiasm for category theory. She explains that she couldn’t stand applied math, but stuck with math because she believed there was something there she could love. The further she moved from applicable math, the happier she became. Abstract algebra was a big improvement, but still too concrete. When she discovered category theory, she was home.
Category theory is a sort of meta-mathematics. It aims to identify patterns across diverse areas of math the way a particular area of math may identify patterns in nature. I like the idea of category theory, but I get that deer-in-the-headlights look in my eyes almost immediately when I look at category theory in any detail.
I enjoy pure math, though I prefer analysis to algebra. I even enjoyed my first abstract algebra class, but when I ran into category theory I knew I’d exceeded my abstraction tolerance. I moved more toward the applied end of the spectrum the longer I was in college. Afterward, I moved so far toward the applied end that you might say I fell off the end and moved into things that are so applied that they’re not strictly mathematics: mathematical modeling, software development, statistics, etc. I call myself a very applied mathematician because I actually apply math and don’t just study areas of math that could potentially be applied.
I appreciate Eugenia Cheng’s enthusiasm even though I don’t share her taste in math. I have long intended to go back and learn a little category theory. It would be great mental exercise precisely because it is so foreign to my way of thinking. Cheng’s interview inspired me to give it one more try.
Update: After this post was written, I did give category theory another try, and gave up again. Then a couple years later I finally committed to digging into category theory and have found practical uses for it.