mathematical lifespan

"The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished." Thus wrote Alfred Adler in an article "Mathematics and Creativity" in The New Yorker Magazine (1972) echoing a common belief that mathematicians tend to do their best work before the age of 30, physicists before the age of 40, and biologists before the age of 50 (though there are exceptions!). The mathematical physicist Freeman Dyson put it more succinctly: "Young men should prove theorems, old men should write books." On the other hand, there are compensations for early burn-out, as G. H. Hardy pointed out (in A Mathematician's Apology): "Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean."