Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

All of mathematics is a tale about groups.

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

Experiment is the sole source of truth.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.