This summer, rather than
selling my soul to some corporate overlord and grinding myself into the dirt to make some big bucks working on Wall Street, I chose to stay at my college and do some academic research. I was assigned a mentor and we worked together to simulate the kind of project that one would take on in grad school or as a post doc. Eventually, we settled on the topic of random polytopes. Essentially, that means that you pick a bunch of points in , take their convex hull, and see what happens. The results are the 11+ page pdf I linked at the top of this post.
I can’t say I was thrilled with the project. Due to a couple of unfortunate lapses in communication, I got stuck with a topic which I did not find particularly interesting. (From what I gathered, the program administrators did not tell my mentor about my research preferences, nor did they inform him that he was supposed to do most of the legwork getting background material and a well-defined question prepared.) We also spent a large chunk of our time just doing background reading, finding what seemed like a feasible question, and then realizing that someone had already solved it in greater generality. When we finally did reach questions which had not been exhaustively answered, they were, simply put, way too hard to answer, especially within the span of five weeks. As a result, the paper I produced is purely expository. I am of the opinion that it brings some clarity and intuitive understanding to the results which we survey, but I suppose I’m biased.
Despite all this, I certainly enjoyed myself more than I have at any other job/internship. I think that research may be a good fit for me, if I can just find a field which intrigues me enough. I think perhaps a *slightly* more applicable area of math–for instance, theoretical statistics or random matrix theory–is more my speed. Even though I find answering abstract questions rewarding, if I’m going to devote as much time and energy to a project as I did to this one, I’d like a compelling reason to plod forward when the going gets tough. As I’ve heard on many occasions, perseverance is far more critical to research than sudden miraculous inspiration.
Overall, I think it was a positive experience. I got some more practice writing a technical paper, at the very worst, and I did learn about some pretty interesting stuff. (See the part in the paper about affine perimeter, and the part about making a convex chain in a triangle.) I think I’d like to give it another try moving forward, and next time I’ll do a better job of picking a damn project.