The mathematician's patterns, like the painter's or the poet's, must be beautiful.

The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

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

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 public does not need to be convinced that there is something in mathematics.

It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.