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

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.

If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

Every man who is not a monster, a mathematician, or a mad philosopher, is the slave of some woman or other.

The pure mathematician, like the musician, is a free creator of his world of ordered beauty.

The human race may well become extinct before the end of the century. Speaking as a mathematician, I should say the odds are about three to one against survival.

Mathematical reasoning may be regarded…

Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

Some mathematician said: ‘Pleasure lies not in discovering truth, but in seeking it.