I’m enjoying the fact that the primary purpose of this summer for me is to work on math–that at this stage in my education and mathematical life, I don’t have to worry so much about what comes of that work. The doing, for now, is enough.
I’ve approached and retreated from the frontiers of frustration several times over the past few weeks, defined and redefined what the heck I’m actually trying to do with these problems, bashed through lots of calculations to find that they are mostly inconclusive but suggest new directions. Doing math the last several years, I’ve learned to take at least a minute or two to savor the feeling of making a new discovery–since, most often, it turns out to be wrong, sometimes only in details and sometimes more fundamentally. Lately I’ve been waking up in the early hours of the morning with some regularity with thoughts that my proofs are wrong. Sometimes I actually get up to work through the details or check them out–and sometimes that even helps me be assured that I was, in this case, actually right.
Research is frustrating for everyone almost all the time, it seems. But right now, even with the frustration, it’s just so refreshing to not have the problem set and lecture grind. And to be able to spend time away from research problems reading up on interesting areas and techniques in mathematics and immersing myself in the culture and history of mathematics, as both profession and area of inquiry, a little bit more.
I’m reminded why I wanted to study math in the first place, and that I want to continue to study it, wherever that may lead in the end.