I want to take a moment to talk about some of the social problems that come with mathematics. This is a subject which illicits more hatred from the average American than any other. Math causes high school students to lose sleep, college students to change majors and graduate students to struggle for days and days on problems that have already been solved. Isn’t that interesting? For the sake of knowledge, we each struggle to solve something on our own that the general knowledge of the world already understands. But I guess that’s true in every field isn’t it? So I return my attention to the voluminous halls of mathematics:
I recently read a biography about Erdös wherein the author discussed how Erdös would visit ailing mathematicians in order to challenge them with problems. He seemed to do this to force them to return their to their prior confidence in themselves. It seems to me, that the biggest hurdle in higher level math, is self-doubt. At my university, it takes an awful lot before the program will kick a student out. However there are students every year who drop out before they reach their PhD. Where do these other students go? What is it that causes students to leave? I think it has a lot of to with self-confidence. My probability professor at Smith College, Prof Henle was fond of telling us that a mathematician must be two things:
confident and humble
The longer I do math the more I understand how true this statement is. But I also think it is very easy to slip away from humble and become self-deprecating.
Mathematics is intriguing because it is the right degree of difficulty. People who work towards a PhD don’t do it because they want to get paid a lot of money. The people who want money actually stop before their PhD and do something “easier”, like insurance or finance. Math is fun when it feels solvable and I think that getting a graduate education is about pushing the boundaries on which math looks like fun. The more hard things someone completes, the more fun it seems to do hard things. I suspect this is because one feels like she has a better chance at completing them given her previous work. So from doing hard things she develops confidence. And by having the hard things be challenging she learns to be humble.