Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind."

I was at my best at a little past forty, when I was a professor at Oxford.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

It is rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility.

For any serious purpose, intelligence is a very minor gift.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.