Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

It is not order only, but unexpected order, that has value.

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

Just as houses are made of stones, so is science made of facts.

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.

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.