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.‎

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

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

Intuition is more important to discovery than logic.

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.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.