2022-08-13

• I had a wonderful experience recently reading a math book. It was that feeling of seeing unexpected connections, and coming to better understand how I make sense of things around me. I have loved math, in some capacity, for a long time. In grade school, it fed my young ego when I was able to complete the times tables faster than most other kids. That felt good, but is no longer the thing I enjoy about the subject (eventually you run into people who do the times tables faster than you could imagine, and your ego has to find something else to latch onto). In high school, math was an outlet for my ego to feel like a good student, who was filling his role in the right way. Of course, i am no longer in the role of “good student” and I no longer feel this way about math. In college, I began to develop a deeper and genuine love of the aesthetic aspects of math. Theorems began to have resonance in a way that is still hard to describe. The best I can do is to say that theorems started to feel like they had shapes, and the relationships between them felt something like pegs going into properly sized holes. This is still approximately how I feel about my love of math. Recently, I was dabbling in a book about Geometry. It was structured, like many math books, in a pretty challenging way. It stated a theorem upfront, as if it was obvious, and then said “if this isn’t obvious, we’ve included a proof in the back.” Naturally, it’s a little bit of an ego bruise to get sent to the back of the book, but I’ve been down this road before many times and know not to take that too personally. Of course, the proof in the back was also not particularly clear. I had to really chew on it. This chewing is, of course, a necessary and important piece of the art of mathematics. But eventually, I figured out how the proof worked, and it was very satisfying. Then I stopped and asked myself “wait, what just happened there? What did I do to figure this out?” And I realized that I applied some thinking from Computer Science/the tech world to get the clarity I needed to understand the math. Basically, when faced with the ambiguity in the math statements in front of me, I responded by trying to gather as much raw data about the situation as I could, and then seeing if any insights would pop out. The proof in question was, unsurprisingly for a geometry book, all about circles and triangles. I was confused about why various triangles were even created as being relevant to the proof. I was confused until I framed those seemingly random triangles as actually coming from important pieces of data in the problem. So like, a triangle formed with one point in the center of the circle is likely to be helpful in understanding the claim precisely because the center of the circle is an intrinsically important part of the circle. And then looking around for other points/information that would be important intuitively/intrinsically helped frame the statements in the proof in a way that seemed much more intuitive and much more like they were headed in a meaningful direction. And that led to me understanding the whole system. And it was a beautiful moment. Not only did I discover a connection between circles and triangles that I didn’t understand before, but I discovered a connection between computer problems and math problems, and came to have an increased appreciation for the way in which I make connections from seemingly disparate concepts.

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