If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

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.

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.

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

Chance ... must be something more than the name we give to our ignorance.

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

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