6th
Notes from Princeton
July 7, 2011
I’m currently at Princeton attending a Summer Program in Analysis and Geometry. Today was the second day of lecture of the first week, the topic for the week is The Geometry of General Relativity. I’ve been introduced to ideas and topics that I’ve never heard of before; Riemannian manifolds, geodesics, the list goes on. I have very little idea of what it is that we’re talking about in lecture. We’re using lots of notation that I’ve never used before, furthering my confusion. The language of mathematics is very complex, the less of it you know, the less chance you have of understanding anything.
Yes, I’m a math major. Which means I’m arrogant, cocky and egotistical. But only about what I know, or what I project to know. That which I don’t know is such a vast quantity. This week I’ve begun to realize that there is so much mathematics that I’ll never know, and could never hope to understand. And this thought alone has depressed me greatly. It’s not as though I fancied myself a mathematician akin to the character Charlie Eppes on the show Numb3rs, whose knowledge on a breadth of subjects seems endless. But I suppose that I never really thought about it. The only thing I can really hope to do in math is to be the expert on a very narrow topic, in one particular area. This of course would be a fantastic accomplishment, and no doubt the pinnacle of my career, yet the chances are slim to none. More likely I’ll end up a tenure professor at a middle tier university, making meager advances in a wide field will little progress. Even that in itself is not that unappetizing to me, as there are many things I wish to accomplish in my life that have nothing to do with math. Really, the worst thought is that eventually, I will pick a specialty. Two, at the most. And those will be the only subjects that I’ll be able to understand with some depth. Sure, if I wanted I could study hundreds of topics. But there will always be more to learn, more than I could possibly study in a hundred lifetimes. Math is such an infinite topic. The realization that there is a limit to my knowledge of the subject is the scariest thought I’ve ever come across.
