"As we know, there are known knowns. There are things we know we know. We also know there are known unknowns. That is to say we know there are some things we do not know. But there are also unknown unknowns - the ones we don't know we don't know."
"If you wish to foresee the future of mathematics our answer is brief and definitive - it is excellent."
"The sciences do not try to enclose nature in a straitjacket, but rather to devise concepts and discern patterns of relationships such that the experimental scientists can enlarge, modify, or change them as he wishes."
"In mathematics you don't understand things. You just get used to them."
"One expects a mathematician to know mathematics, but I am always surprised and delighted when I meet one who knows something else as well."