John von Neumann

Truth is much too complicated to allow anything but approximations.

John von Neumann (28 December 1903 – 8 February 1957) was a Hungarian-American-German-Jewish mathematician and computer scientist, generally regarded as one of the foremost mathematicians of the 20th century.

Quotes

In mathematics you don't understand things. You just get used to them.

You wake me up early in the morning to tell me that I'm right? Please wait until I'm wrong.

• I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is ... governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.
  • "The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago

• 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

• 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.
  • "The Role of Mathematics in the Sciences and in Society" (1954) an address to Princeton alumni, published in John von Neumann : Collected Works (1963) edited by A. H. Taub ; also quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by R. Schmalz

• 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

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

• 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

• If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.
  • As quoted in Proportions, Prices, and Planning (1970) by András Bródy

• If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
  • Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.

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; also in The Pólya Picture Album (1987), p. 154

External links

• Profile at University of St Andrews
• von Neumann's contribution to economics — International Social Science Review
• Oral history interview with Alice R. Burks and Arthur W. Burks at Charles Babbage Institute
• Oral history interview with Nicholas C. Metropolis, at Charles Babbage Institute
• Von Neumann vs. Dirac — at Stanford Encyclopedia of Philosophy
• John von Neumann Postdoctoral Fellowship – Sandia National Laboratories
• Von Neumann's Universe, audio talk by George Dyson
• John von Neumann's 100th Birthday, article by Stephen Wolfram
• Annotated bibliography for John von Neumann from the Alsos Digital Library for Nuclear Issues
• Budapest Tech Polytechnical Institution – John von Neumann Faculty of Informatics
• John von Neumann speaking at the dedication of the NORD (2 December 1954) — audio recording
• The American Presidency Project
• John Von Neumann Memorial at Find A Grave