Be advised: this thread is not for serious in-depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.
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Notes -
Yitang Zhang didn't prove that the lim inf of the prime gap was 2 (which would have verified a 150 year old conjecture), but he was the first to prove it was finite, at age 58. Listing and Moëbius were in their 50s when they formalized the idea of non-orientable surfaces (which I would consider to be literally "producing" math rather than just "solving" it). The first version of the Weierstrass Approximation Theorem (which led to whole fields of the most economically valuable results in mathematics, in my biased applied-math+engineering opinion) was proven when Weierstrass was 70.
But, damn, are they the exceptions who prove the rule, so long as we leave that "basically" qualifier intact? Kolmogorov was in his 50s when he solved Hilbert's thirteenth problem, but that was in joint work with a 19 year old student. Euler, Gauss, and Cauchy were doing great work in their old age, but arguably only after doing greater work as younger men. Searching for mathematical discoveries by importance and then looking up age (rather than searching specifically for discoveries made at older ages), the bulk do seem to be between 25 and 45.
I wonder if the trend is moving older (because things that were groundbreaking discoveries 300 years ago are basic undergrad background today and you need to learn much more to get to the cutting edge) or younger (because subsidized institutional math research gets more output but at the cost of making older mathematicians spend all their time teaching and mentoring and writing proposals and hiring and so on, while their grad students and postdocs are the ones who can actually focus on the work).
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