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

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

But for harmony beautiful to contemplate, science would not be worth following.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.