Mathematics is a discipline for young people.
Most of the greatest mathematicians in history started very early their work and, often, they had the best results when still very young.
I believe, anyway, that there is still some space for older mathematicians…
After some research, I ended up with this funny list:
- Joan Birman got her PhD when she was 41, she did a great job in several areas among which braid theory;
- Eugène Ehrhart got his PhD when he was… 60;
- Albrecht Fröhlich worked on Galois theory (there is even a prize named after him); he got his PhD when he was 36;
- George Green was an autodidact that did undergrad studies when he was 40; apparently Albert Einstein commented that Green had been 20 years ahead of his time.
A more scientific study examined the correlation between age and scientific creativity but I believe that, after all, it is not only a matter of age.