Mathematics is the art of giving the same name to different things.
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
It is through science that we prove, but through intuition that we discover.
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.
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.
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
Geometry is not true, it is advantageous.
Mathematicians do not study objects, but relations between objects.
If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
The mind uses its faculty for creativity only when experience forces it to do so.
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.
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.
If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws.