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.

Computers are like humans - they do everything except think.

Truth is much too complicated to allow anything but approximations.

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

It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.

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