Quote 4 of 9

From A Mathematician's Apology, by G.H. Hardy

No mathematician should ever allow himself to forget that mathematics,
more than any other art or science, is a young man's game.  To take a
simple illustration at a comparatively humble level, the average age
of election to the Royal Society is lowest in mathematics.

We can naturally find much more striking illustrations.  We may
consider, for example, the career of a man who was certainly one of
the world's three greatest mathematicians.  Newton gave up mathematics
at fifty, and had lost his enthusiasm long before; he had recognized
no doubt by the time that he was forty his great creative days were
over.  His greatest ideas of all, fluxions and the law of gravitation,
came to him about 1666, when he was twenty-four--'in those days I was
in the prime of my age for invention, and minded mathematics and
philosophy more than at any time since'.  He made big discoveries
until he was nearly forty (the 'elliptic orbit' at thirty-seven, but
after that he did little but polish and perfect.

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.
		-- Part 4, pp. 70-72

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