Originally posted by @blood-on-the-tracks
Tragically young for anyone, made more poignant by the fact that she had so much more to give.
Her work was exceptional
The world lost a mathematician. Her husband lost a wife; her daughter lost a mother.
"I had better say something here about this question of age, since it is particularly
important for mathematicians. No mathematician should ever allow himself to forget
that mathematics, more than any other art or science, is a young man's game. ...
Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty.
There have been men who have done great work a good deal later; Gauss's great memoir
on differential geometry was published when he was fifty (though he had had the fundamental
ideas ten years before). I do not know an instance of a major mathematical advance initiated
by a man past fifty. If a man of mature age loses interest in and abandons mathematics,
the loss is not likely to be very serious either for mathematics or for himself."
--G.H. Hardy (_A Mathematician's Apology_)
As a counterexample, consider Zhang Yitang, a Chinese mathematician based in the USA.
In 2013, Zhang Yitang (who was born in 1955), an obscure lecturer at the University of
New Hampshire (which is not known as a research university) wrote a paper claiming an
astonishing result: the first finite bound on gaps between prime numbers. His proof
was confirmed, and Zhang won many awards (including a MacArthur 'genius' award).
So at age 57-58. Zhang Yitang made a 'major mathematical advance'.
(He's too old to be eligible for a Fields Medal, which his work would deserve otherwise.)