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The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.

John von Neumann

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John von Neumann
Age: 53 †
Born: 1903
Born: December 28
Died: 1957
Died: February 8
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John Von Neumann
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More quotes by John von Neumann

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Life is a process which may be abstracted from other media.
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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.
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I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.
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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.
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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.
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You wake me up early in the morning to tell me I am right? Please wait until I am wrong.
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There's no sense in being precise when you don't even know what you're talking about.
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All stable processes we shall predict. All unstable processes we shall control.
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There probably is a God. Many things are easier to explain if there is than if there isn't.
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Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.
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If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
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I am thinking about something much more important than bombs. I am thinking about computers.
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Science, as well as technology, will in the near and in the farther future increasingly turn from problems of intensity, substance, and energy, to problems of structure, organization, information, and control.
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Truth is much too complicated to allow anything but approximations.
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If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.
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You don't have to be responsible for the world that you're in.
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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
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When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.
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If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
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Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.
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