The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.

As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or "scholarship candidates," but "Fellows of another college."

A science or an art may be said to be "useful" if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.

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.

If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.