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.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

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.

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

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

Mathematical discoveries, small or great are never born of spontaneous generation.