John von Neumann

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Truth is much too complicated to allow anything but approximations.

John von Neumann (28 December 19038 February 1957) Hungarian-American-German-Jewish Catholic mathematician and computer scientist.


  • "Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number– there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."
    • On mistaking pseudorandom number generators for being truly "random" — this quote is often erroneously interpreted to mean that von Neumann was against the use of pseudorandom numbers, when in reality he was cautioning about misunderstanding their true nature while advocating their use. From "Various techniques used in connection with random digits" by John von Neumann in Monte Carlo Method (1951) edited by A.S. Householder, G.E. Forsythe, and H.H. Germond
  • 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.
    • As quoted in "The Mathematician" in The World of Mathematics (1956), by James Roy Newman.
  • You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.
    • Suggesting to Claude Shannon a name for his new uncertainty function, as quoted in Scientific American Vol. 225 , (1971), p. 180
  • Young man, in mathematics you don't understand things. You just get used to them.
    • Reply to Felix T. Smith who had said "I'm afraid I don't understand the method of characteristics." —as quoted in The Dancing Wu Li Masters: An Overview of the New Physics (1984) by Gary Zukav footnote in page 208.
  • Truth is much too complicated to allow anything but approximations.
    • As quoted in Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (1991) by Manfred Schroder
  • A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.
    • As quoted in Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993) by R. Schmalz.
  • 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.


  • It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.
  • There's no sense in being precise when you don't even know what you're talking about.
  • The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.
  • 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.
  • You insist that there is something that a machine can't do. If you will tell me precisely what it is that a machine cannot do, then I can always make a machine which will do just that.
  • With the Russians it is not a question of whether but of when. [...] If you say why not bomb them tomorrow, I say why not today? If you say today at 5 o'clock, I say why not one o'clock?

Quotes about von Neumann

  • There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

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