In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

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

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.

There are no solved problems; there are only problems that are more or less solved.

But for harmony beautiful to contemplate, science would not be worth following.

Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

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.