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

In the old days when people invented a new function they had something useful in mind.

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

All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.‎

A small error in the former will produce an enormous error in the latter.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.