GHH was a leading mathematician of his time.
“I still say to myself when I am depressed, and find myself
forced to listen to pompous and tiresome people, 'Well, I have done one thing
you could never have done, and that is to have collaborated with both
Littlewood and Ramanujan on something like equal terms.”
“In these days of conflict between ancient and modern
studies, there must surely be something to be said for a study which did not
begin with Pythagoras, and will not end with Einstein, but is the oldest and
the youngest of all.”
“It is not worth an intelligent man's time to be in the
majority. By definition, there are already enough people to do that.”
“A mathematician, like a painter or poet, is a maker of
patterns. If his patterns are more permanent than theirs, it is because they
are made with ideas.”
“Reductio ad absurdum, which Euclid loved so much, is one of
a mathematician's finest weapons. It is a far finer gambit than any chess play:
a chess player may offer the sacrifice of a pawn or even a piece, but a
mathematician offers the game.”
“No mathematician should ever allow him 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 later; … [but] I
do not know of a single instance of a major mathematical advance initiated by a
man past fifty. … A mathematician may still be competent enough at sixty, but
it is useless to expect him to have original ideas.”
“The Greeks were the first mathematicians who are still
‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but
Greek mathematics is the real thing. The Greeks first spoke a language which
modern mathematicians can understand: as Littlewood said to me once, they are
not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another
college’. So Greek mathematics is ‘permanent’, more permanent even than Greek
literature. Archimedes will be remembered when Aeschylus is forgotten, because
languages die and mathematical ideas do not. ‘Immortality’ may be a silly word,
but probably a mathematician has the best chance of whatever it may mean.”
“The seriousness of a theorem, of course, does not lie in
its consequences, which are merely the evidence for its seriousness.”
