Difficult problems Quotes by John von Neumann

Truth is much too complicated to allow anything but approximations.

— John von Neumann

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

— John von Neumann

It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful…

— John von Neumann

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

— John von Neumann

There is no point in being precise if you do not even know what you are talking about.

— John von Neumann

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

— John von Neumann

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

— John von Neumann

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than…

— John von Neumann

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical…

— John von Neumann

Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will…

— John von Neumann

If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.

— John Von Neumann

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

— John von Neumann