Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.

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.

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.

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.

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

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

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.

Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.

How is an error possible in mathematics?

It is through science that we prove, but through intuition that we discover.

Facts do not speak.

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.

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.

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