Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed… — 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
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
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore. — John von Neumann Copy Share
There is no point in being precise if you do not even know what you are talking about. — John von Neumann Copy Share
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
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
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
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
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
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
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. — John von Neumann Copy Share
By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it… — John von Neumann Copy Share
I think that it is a relatively good approximation to truth which is much too complicated to allow anything but approximations, that mathematical ideas… — John Von Neumann Copy Share
The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any… — John Von Neumann Copy Share
