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

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.

No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game

Bombs are probably more merciful than bayonets

No one should ever be bored. … One can be horrified, or disgusted, but one can’t be bored.

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

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.