Sourced

• 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 No. 3, (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.

• You don't have to be responsible for the world that you're in.
  • Advice given by von Neumann to Richard Feynman as quoted in "Los Alamos from Below" in Surely You're Joking, Mr. Feynman! (1985)

• The goys have proven the following theorem...
  • Statement at the start of a classroom lecture, as quoted in 1,911 Best Things Anyone Ever Said (1988) by Robert Byrne

• 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.
  • As quoted in Single Variable Calculus (1994) by James Stewart.
  • As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman.

• With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
  • Attributed to von Neumann by Enrico Fermi, as quoted by Freeman Dyson in "A meeting with Enrico Fermi" in Nature 427 (22 January 2004) p. 297

• You wake me up early in the morning to tell me that I'm right? Please wait until I'm wrong.
  • As quoted by Jacob Bronowski in The Ascent of Man TV series

Quotes about von Neumann

• The only student of mine I was ever intimidated by. He was so quick. 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.
  • George Pólya, in How to Solve It (1957) 2nd edition, p.xv