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John Von Neumann

Birthdate: 28. December 1903
Date of death: 8. February 1957

John von Neumann was a Hungarian-American mathematician, physicist, and computer scientist. He made major contributions to a number of fields, including mathematics , physics , economics , computing , and statistics.

Generally regarded as the foremost mathematician of his time and said to be "the last representative of the great mathematicians" like Euler, Gauss, Poincaré or Hilbert, he was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer. He published over 150 papers in his life: about 60 in pure mathematics, 20 in physics, and 60 in applied mathematics, the remainder being on special mathematical subjects or non-mathematical ones. His last work, an unfinished manuscript written while in the hospital, was later published in book form as The Computer and the Brain.

His analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated, "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932."

During World War II he worked on the Manhattan Project, developing the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. After the war, he served on the General Advisory Committee of the United States Atomic Energy Commission, and later as one of its commissioners. He was a consultant to a number of organizations, including the United States Air Force, the Army's Ballistic Research Laboratory, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory. Along with theoretical physicist Edward Teller, mathematician Stanislaw Ulam, and others, he worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

„If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.“

—  John Von Neumann

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.

„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.“

—  John Von Neumann

"The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago
Context: 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.

„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.“

—  John Von Neumann

Suggesting to Claude Shannon a name for his new uncertainty function, as quoted in Scientific American Vol. 225 No. 3, (1971), p. 180.
Context: 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.

„Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.“

—  John Von Neumann

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 <!-- National Bureau of Standards Applied Mathematics Series, 12 (Washington, D.C.: U.S. Government Printing Office, 1951): 36-38. -->
Context: 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.

„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.“

—  John Von Neumann

"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 <!-- Macmillan, New York -->; also quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by R. Schmalz
Context: 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.

„Young man, in mathematics you don't understand things. You just get used to them.“

—  John Von Neumann

Reply, according to Dr. Felix T. Smith of Stanford Research Institute, to a physicist friend 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 (1979) by Gary Zukav, Bantam Books, p. 208, footnote.

„If you say why not bomb them tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?“

—  John Von Neumann

As quoted in "The Passing of a Great Mind" by Clay Blair, Jr., in LIFE Magazine (25 February 1957), p. 96

„You don't have to be responsible for the world that you're in.“

—  John Von Neumann

Advice given by von Neumann to Richard Feynman as quoted in "Los Alamos from Below" in Surely You're Joking, Mr. Feynman! (1985).

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„The goys have proven the following theorem…“

—  John Von Neumann

Statement at the start of a classroom lecture, as quoted in 1,911 Best Things Anyone Ever Said (1988) by Robert Byrne.

„There probably is a God. Many things are easier to explain if there is than if there isn't.“

—  John Von Neumann

As quoted in John Von Neumann : The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence and Much More (1992) by Norman Macrae, p. 379

„With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.“

—  John Von Neumann

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 http://dx.doi.org/10.1038/427297a

„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.“

—  John Von Neumann

As quoted "John von Neumann (1903 - 1957)" by Eugene Wigner, in Year book of the American Philosophical Society (1958); later in Symmetries and Reflections : Scientific Essays of Eugene P. Wigner (1967), p. 261

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