Chess problems are the hymn-tunes of mathematics.

Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism".

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

The case for my life... is this: that I have added something to knowledge, and helped others to add more

Real mathematics must be justified as art if it can be justified at all.

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.

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.