[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

A chess problem is simply an exercise in pure mathematics.

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

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.

Most people can do nothing at all well

No one should ever be bored. … One can be horrified, or disgusted, but one can’t be bored.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.