chzbrgr, that’s what they say about early accomplishments in mathematics, but I don’t think that career studies bear that out.
Look at Andrew Wiles’ age when he proved Fermat’s theorem: 42, when the unflawed proof was published
Terence Tao is 42 now and still publishing
Manjul Bhargava is 43 now. At 41, he and a co-author proved the Birch and Swinnerton-Dyer conjecture “for a positive proportion of elliptic curves,” according to Wikipedia. A proof of the Birch and Swinnerton-Dyer conjecture that covers all cases is worth $1,000,000 from the Clay Mathematics Institute, as one of its seven millennium prize problems (https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture).
This is not to say that mathematicians are “over the hill” when they hit their 50’s either. I can’t locate it now, but I remember an article in Science about a Purdue professor of mathematics who proved a notable theorem when he was in his 50’s, and it was the peak of his accomplishment up to that time.
I think the stereotype that mathematicians only contribute significantly when young may come from a few effects: First, a young person may have a truly novel way of looking at things, and he/she “picks off” the problems that are most susceptible to proof in that way. After a while, the problems get harder and deeper. A young (or youngish) person proves something major, and thereafter is only interested in even more challenging problems, that may or may not yield (Einstein perhaps exemplifies this). I have my own conjecture: Andrew Wiles is currently working on the Riemann conjecture. Then, there is the importance of unfettered concentration, in mathematics. This is easier (in my view) before one has a family, mortgage, etc., to say nothing of graduate students to direct, classes to teach, grant proposals to write, university committees . . .
Here’s a suggestion: Go over to the local university’s math department, look for faculty members over 35, and ask them if they are doing any worthwhile mathematics now. (No, wait, don’t do that.)