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.

A person’s first duty, a young person’s at any rate, is to be ambitious, and the noblest ambition is that of leaving behind something of permanent value.

Bombs are probably more merciful than bayonets

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

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.

A chess problem is simply an exercise in pure mathematics.