I just read 'A Mathematician's Apology' where Hardy touches on this at one point. If you want to consider someone's opinion on your question (besides cperciva), consider Hardy's (because he was a great mathematican and a brutally honest person). Briefly, Hardy thought the ability to make deep contributions to mathematics erodes after middle age. He cites Euler, Abel, Ramanujan, et al. Hardy mentions Gauss who was old (55, I think) when he made a major contribution but, Hardy notes, the idea for it had germinated while Gauss was young. I personally think Nature plays a bigger part than nurture when it comes to mathematical ability (of the rarer kind). Ramanujan is a classic example. He had pretty much no nurture. Way before anyone knew or cared, he was producing stunning mathematical insights.