Perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.

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

No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.

Mathematics is not a contemplative but a creative subject.

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

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.