The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.

The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.

Problems are often stated in vague terms... because it is quite uncertain what the problems really are.

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

Life is a process which may be abstracted from other media.

If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.