When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.

It is with logic that one proves; it is with intuition that one invents.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.

When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.

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

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