Is Math a Young Person's Game?

In a review of Proof, Lee quotes an old mathematician as saying that creativity ends at 23 (presumably taking with it the capacity to do brilliant mathematical work) and wonders whether this means he is over-the-hill.

I've heard this a lot, also - the idea that math is a young man's (ahem!) game, that if you haven't made your contribution by age 30 you never will, etc. What's not clear to me about this common assertion is whether the actual imagined culprit is chronological age per se or years spent working in the discipline. Since it seems likely that the majority of mathematicians complete grad school while they are still young, in general, being young in years also means being early in one's career, and being old in years means being farther along in one's career. (I guess a mathy person might call this a multicollinearity problem.)

I'm not even remotely convinced that either version of this belief is true, but if it's less an issue of having an old vs. young brain (e.g., information processing speed, working memory capacity) and more about being new to the field, energized, and in life circumstances that promote doing a lot of math (e.g., being "married" to math rather than having an actual spouse, kids, and so on) vs. established, complacent, tenured, and caught up with other distractors, then "older" math grad students like Lee and Tam are not over-the-hill, mathematically.

I have to admit, as a social psychologist (in training), I enjoy / am infuriated by the stereotypes associated with mathematicians, both from those outside of and within the discipline.

Anyway, ultimately, this is an empirical question, and one that mathematicians (even mathematicians in plays) are sadly not well-placed to answer.