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

Computers are like humans - they do everything except think.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

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.

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

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.

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.