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… — John von Neumann Copy Share Image
Truth is much too complicated to allow anything but approximations. — John von Neumann Copy Share Image
Problems are often stated in vague terms... because it is quite uncertain what the problems really are. — John von Neumann Copy Share Image
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 Copy Share Image
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore. — John von Neumann Copy Share Image
There is no point in being precise if you do not even know what you are talking about. — John von Neumann Copy Share Image
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 Copy Share Image
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 Copy Share Image
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 Copy Share Image
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 Copy Share Image
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 Copy Share Image
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 Copy Share Image
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. — John von Neumann Copy Share Image
