| I disagree with most of your points, though you're more qualified to talk on the subject than I am. | All the easy math has been done. How easy are we talking about? While I was in high school, I remember a news article about some other high-school-age kids that happened to a solve a long-standing and relatively simple problem in geometry involving triangles. I can't remember the specifics, nor can I find anything about it now, but I think there are still plenty of relatively entry-level problems to work on. | It is probably impossible for someone at a midpoint in their lives to suddenly develop an interest in math and make a meaningful contribution. http://en.wikipedia.org/wiki/List_of_amateur_mathematicians It's a pretty crappy list, and most of the names are from centuries past, but there are a couple of interesting entries there. | Do you have to be gifted to run in an Olympic Marathon? Your example of Olympic marathons is specifically a zero-sum game, whereas mathematics is not. | But then again, anytime a new field opens up there's hundreds of PHD students across the world that jump into it looking for a new bit of math to write their thesis on. This seems to contradict your previous point that mathematics has become inaccessible. There are a few differences between a grad student and a sufficiently dedicated hobbyist, and none of them are genetic, nor are any of them necessarily bound by a particular age bracket. Indeed, someone in middle age could attend university on a specific curriculum, and in a few years be looking at the same problems as the PHD students. The older person might have some advantages in self discipline or experience in tangential fields. |
This raises an interesting empirical question: is there a significant deterioration in brain performance after about 40 years of age or so? Anecdotally it would seem to be the case. The Fields Medal is the highest award in Mathematics and it has an age cap of 40, but the rule hasn't raised controversy because almost all the worthy contenders have been under 40 anyway. However, some people have hypothesized that the dominance of the young is the result of other career and family concerns distracting people in middle age. That could well be the truth, and I hope it is. It would be interesting to know the answer.