Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

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

But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

Mathematicians do not study objects, but the relations between objects.

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

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