It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
I still say to myself when I am depressed and 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 Littlewood and Ramanujan on something like equal terms.
I am interested in mathematics only as a creative art.
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.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.
There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
Young men should prove theorems, old men should write books.
317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.
No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.