>There was recently some headline news about an older mathematician that made a significant breakthrough. Other than that one outlier, have there been many impo

>There was recently some headline news about an older mathematician that made a significant breakthrough. Other than that one outlier, have there been many important contributions made by people after the age of, say, 45? There is one other effect beyond ability: people over 45 rarely take up new interests. There are plenty of cases of people who continue working in the same field through their 40s and 50s and continue to make advances, but there are many fewer cases of an individual beginning to work in a field after 40 and going on to make a major discovery. In pure math, possibly the most aesthetic-driven technical field (it is impractical by definition), this effect might be especially strong. Richard Hamilton (not to be confused with William Rowan Hamilton of action-principle fame) initiated the application of the Ricci flow to the geometrization conjecture in 1982 at 39 and continued his work through the '90s, being credited by Perelman as making crucial contributions to the final solution of the Poincare conjecture in three dimensions. He's probably the most prominent example. >It is very hard to find an instance of a first-rate mathematician who has abandoned mathematics and attained first-rate distinction in any other field. Chomsky? Szilard? Maybe even Wolfram?