Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[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.

Thought is only a flash between two long nights, but this flash is everything.

Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science.