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

One does not ask whether a scientific theory is true, but only whether it is convenient.

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.

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

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.

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

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know