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

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.

Truth is much too complicated to allow anything but approximations.

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.

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.