Thoughts on aging's effect on learning and intelligence

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Ok, that mathematics thing is something I read a while back. Let me ask you something though, since I know nothing about the state of modern mathematics. When I think of genius I don't just picture someone who solved a tough proof or made some kind of advancement that happens every few years.

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Some 'tough proofs' are hundreds of years in the making or more. For example, Fermat's Last Theorem, the Green-Tao theorem on the infinitude of primes in given arithmetic progressions, Poincare's conjecture (this is just under 100 years). An answer to the Riemann hypothesis (age: about 175 years) would be more profound than all of the above combined.

By the way, Wiles was over 40 when FLT was settled, Green and Tao were about 28 and 30 when they established the Green-Tao theorem, and Perelman was just under 40 when he solved Poincare.

This doesn't answer your question of course. Here are some major 'revolutions' in math in the last 100 years or so.

Grothendieck lays the foundation for modern algebraic geometry - about 30 at the time.
Ito constructs the Ito integral (stochastic integration) - under 30 at the time
Kolmogorov builds probability theory in a rigorous way - about 30 years old at the time
Lebesgue defines the Lebesgue integral - under 30 at the time

It would certainly seem to appear that a lot of the great breakthroughs in math in the last 100 years or so were done by very young, brilliant individuals.