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

You wake me up early in the morning to tell me I am right? Please wait until I am wrong.

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.

It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.

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.

There's no sense in being precise when you don't even know what you're talking about.

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.