It is far better to foresee even without certainty than not to foresee at all.

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

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

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

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

Chance ... must be something more than the name we give to our ignorance.