> There are common prejudices and cliches about mathematicians and
> aging. I would appreciate any exact citations, either about the
> older years of specific mathematicians, or generalizations about
> what happens as mathematicians get older. Thank you very much.
I would like to add an example of those aging mathematicians who
contributed to mathematics in later years.
It concerns Abraham de Moivre (1667-1754) who found his presumably most
important result in 1733 when he was 66. The theorem is now known as the
local central limit theorem. Interestingly it can be shown that de Moivre
did not find this theorem any earlier. It was the result of a competition
with James Stirling concerning the solution of a problem which had been
posed by a philomath, one of de Moivre's students, in 1721. De Moivre had
found a preliminary solution already in the 1720ies. The final breakthrough
came with the development of an (asymptotic) series for log (n!) by
Stirling and de Moivre around 1730.
I hint to these details because they show that de Moivre remained
mathematically active for a comparatively long period until he found the
above mentioned theorem.
Different from the situation presupposed by Hardy for a mathematician to
turn to other fields of interest than mathematics in a certain age de
Moivre seems to have had no choice. He had to stay competitive as a problem
solver in order to attract noble coffee house frequenters as paying clients
for his instructions.
There is an biographical anecdote going with de Moivre which has nothing to
do with your question but might still be to your liking. It stems from
Matthew Maty, de Moivre's most important biographer. Accordingly de Moivre
in old age used to sleep every day a bit longer until the sleeping phase
had reached 24 hours.
Ivo