Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Godel's achievement.

Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.

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

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

The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.

Young man, in mathematics you don't understand things. You just get used to them.

I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.