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

The mind uses its faculty for creativity only when experience forces it to do so.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

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.

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

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

Every good mathematician should also be a good chess player and vice versa.