A bunch of traffic seems to be coming over from Terry’s blog, so while the math people are here, one more comment about why the cult of the genius is bad for mathematics. When a student, especially a first-year, really impresses me, I often suggest that they consider majoring in math. And too often what I get in response is, “My math classes are my favorite ones and I’m really having fun, but I can’t be a math major because I didn’t win the Olympiad / win Intel / take calculus in 4th grade.” I don’t think other fields of study have this problem, at least not as severely — I’ve never heard anyone say “I can’t go to medical school because I’m not like those people who can instantly figure out how to palpate a gallbladder correctly and who knew the diagnostic criteria for a hundred tropical diseases when they were eight.” But in math we’ve unfortunately allowed the impression to persist that all of us in the business are former child prodigies, touched at birth with the math stick.
Consider, for instance, the list of participants in the 1988 International Mathematical Olympiad, which includes both me and Terry. There are lots of notable mathematicians on here — at a quick run-through, I count 13 names I know as working research mathematicians today. This means, of course, that of the many hundreds of excellent mathematicians in our age cohort, only a tiny minority even participated in the IMO. And even among this group of contest-lovers, success in research doesn’t require success at the Olympiad — one of the most distinguished members of the group, Elon Lindenstrauss (now a full professor at Princeton) finished with a score of 17 out of 42, right in the middle of the pack.
If you’re in college and you like learning math, study math! It doesn’t matter that there’s someone out there who’s better at it than you. That’ll be the case no matter what path you choose. And if you decide that the academic life is not for you — and it isn’t for everyone — you’ll be very well-positioned to apply for a wide spectrum of jobs and higher degree programs.