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John von Neumann

Hungarian and American mathematician and physicist (1903–1957) From Wikiquote, the free quote compendium

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John von Neumann (28 December 1903 – 8 February 1957) was a Hungarian-American-Jewish mathematician, physicist, inventor, computer scientist, and polymath. He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, set theory, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.

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Quotes

  • 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. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up. It would be easy to give examples, to trace specific evolutions into the baroque and the very high baroque... 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
  • For progress there is no cure.... The only safety possible is relative, and it lies in an intelligent exercise of day-to-day judgement.
    • "Can we survive Technology?" 1950.[1]
  • 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
  • The total subject of mathematics is clearly too broad for any one of us. I do not think that any mathematician since Gauss has covered it fully and uniformly, even Hilbert did not, and all of us are of considerably lesser width (quite apart from the question of depth) than Hilbert. It would therefore, be quite unrealistic not to admit, that any address I could possibly give would not be biased towards some areas in mathematics in which I have had some experience, to the detriment of others which may be equally or more important. To be specific, I could not avoid a bias towards those parts of analysis, logics, and certain border areas of the applications of mathematics to other sciences in which I have worked. If your Committee feels that an address which is affected by such imperfections still fits into the program of the Congress, and if the very generous confidence in my ability to deliver continues, I shall be glad to undertake it.
    • Letter to H. D. Kloosterman (April 10, 1953), unpublished, John von Neumann Archive, Library of Congress, Washington, D.C., as quoted by Miklós Rédei, 1999. "Unsolved Problems in Mathematics": J. von Neumann's Address to the International Congress of Mathematicians, Amsterdam, September 2-9, 1954 in Mathematical Intelligencer, 21(4), 7–12.
  • 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
  • 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.
    • "Method in the Physical Sciences", in The Unity of Knowledge (1955), ed. L. G. Leary (Doubleday & Co., New York), p. 157
  • 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
  • When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.
    • As quoted in John von Neumann, 1903-1957 (1958) by John C. Oxtoby and B. J. Pettis, p. 128
  • 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.
    • 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
  • 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, 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.
  • 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.
  • 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.
    • ‍'‍...Several versions of [computer] background wiring and their corresponding source [programming] languages were under discussion, each having a vocabulary between 50 and 100 [CPU] instruction types. Their implementation and testing began in 1948. They were still only on paper at the end of 1947, when the Association for Computing Machinery was founded and held its first national meeting at Aberdeen Proving Ground. The attendance at that meeting was 300; the program consisted of about a dozen papers. We had succeeded in obtaining John von Neumann as keynote speaker. He discussed the need for, and likely impact of, electronic computing. He mentioned the "new programming method" for ENIAC and explained that its seemingly small vocabulary was in fact ample: that future computers, then in the design stage, would get along on a dozen instruction types, and this was known to be adequate for expressing all of mathematics....Von Neumann went on to say that one need not be surprised at this small number, since about 1,000 words were known to be adequate for most situations of real life, and mathematics was only a small part of life, and a very simple part at that. This caused some hilarity in the audience, which provoked von Neumann to say: "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."‍'‍
  • There probably is a God. Many things are easier to explain if there is than if there isn't.
    • 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
  • 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?
    • As quoted in "The Passing of a Great Mind" by Clay Blair, Jr., in LIFE Magazine (25 February 1957), p. 96
  • Some people confess guilt to claim credit for the sin.
    • As quoted in John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (2016) by Norman Macrae, p. 352 in response to Oppenheimer's 'destroyer of worlds' quote.
  • It will not be sufficient to know that the enemy has only fifty possible tricks and that we can counter every one of them, but we must be able to counter them almost at the very instant they occur.
    • As quoted in Defense in Atomic War by John von Neumann. Paper delivered at a symposium in honor of Dr. R. H. Kent, December 7, 1955, The Scientific Bases of Weapons, Journ. Am. Ordnance Assoc., 21–23, 1955.

Mathematical Foundations of Quantum Mechanics (1932)

Main article: Mathematical Foundations of Quantum Mechanics
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Quotes about von Neumann

Sorted alphabetically by author or source
  • One of the world's great mathematicians.
  • I think I had some feeling that there minds [von Neumann and Weyl] were so far ahead of mine that it was difficult to follow their thoughts.
  • If one applies an appropriately broad view of physics one must say that von Neumann had a quite outstanding insight into the problems of physics. Because he has done first-rate work, and he was the man who succeeded in giving a correct mathematical formulation of quantum mechanics, and this was the major theory in physics in the first half of the century.
  • Von Neumann was considered to be the most brilliant of the young mathematicians.
  • I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man.
    • Hans Bethe, as quoted in LIFE Magazine (1957), pp. 89–104
  • He had the kind of mind that if you go in to see him with an idea, inside of five minutes he's five blocks ahead of you and sees exactly where it's going. His mind was just so fast and so accurate that there was no keeping up with him. There was nobody on earth, as far as I'm concerned, who was in his category.
    • Julian Bigelow, as quoted in Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study (1988) by Edward Regis, pp. 103–104
  • What Von Neumann contributed as far as the engineering was concerned, was simply the enormous confidence everybody had that a machine so simple, and with no more doodads on it could knock dead, so to speak, an enormous amount of the computation that needed to be done in this world for the next few decades. He never came over and said to make a circuit of this, but he did know so much more of the deeper aspects of mathematics and the practical aspects of computation than any of the rest of us. What he did essentially, was to serve as this unshakable confidence that said: "Go ahead, nothing else matters, get it running at this speed and this capability, and the rest of it is just a lot of nonsense."
  • John von Neumann's brilliant mind blazed over lattice theory like a meteor.
  • I went in and started telling him about my thesis. He listened for about ten minutes and asked me a couple of questions, and then he started telling me about my thesis. What you have really done is this, and probably this is true, and you could have done it in a somewhat simpler way, and so on. He was a really remarkable man. He listened to me talk about this rather obscure subject and in ten minutes he knew more about it than I did. He was extremely quick. I think he may have wasted a certain amount of time, by the way, because he was so willing to listen to second- or third-rate people and think about their problems. I saw him do that on many occasions.
    • David Blackwell, as quoted in Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993) by Rosemary Schmalz, p. 213
    • quoted DeGroot, Morris H. "A conversation with David Blackwell." Statistical Science 1.1 (1986): 40–53.
  • After the last visitor had departed Von Neumann would retire to his second-floor study to work on the paper which he knew would be his last contribution to science. It was an attempt to formulate a concept shedding new light on the workings of the human brain. He believed that if such a concept could be stated with certainty, it would also be applicable to electronic computers and would permit man to make a major step forward in using these 'automata'. In principle, he reasoned, there was no reason why some day a machine might not be built which not only could perform most of the functions of the human brain but could actually reproduce itself, i.e., create more supermachines like it. He proposed to present this paper at Yale, where he had been invited to give the 1956 Silliman Lectures.
    • Clay Blair Jr., in Passing of a Great Mind: John von Neumann, a Brilliant, Jovial Mathematician, was a Prodigious Servant of Science and his Country (25 February 1957)
  • Probably the greatest mathematician of the century.
    • Stanley A. Blumberg, in Energy and Conflict: The Life and Times of Edward Teller (1976), p. 130
  • "Johnny," as all his friends called him, was the only scientist of the era to whom the word "genius" was almost universally applied. He had an uncanny ability to handle complex mathematical calculations in seconds. When he was six years old he could divide one eight-digit number into another, entirely in his head.
    • Stanley A. Blumberg, in Energy and Conflict: The Life and Times of Edward Teller (1976), p. 137
  • Then, of course, there was Neumann, who always knew everything anyhow.
  • Weyl had a very tremendous respect for him, and I could see in this advanced, seminar when Weyl didn't know the answer he would say, "Neumann, how does that go?" We all realized this was a great mathematician.
  • His effectiveness was largely due to his ever-present mental manipulatory quickness. He could literally "think on his feet," and much of his best work may have received its initial impulse in just this way. He had a prodigious memory, and legend has it that he knew all the facts and dates from many volumes of standard histories by heart.
  • He was also a great reader of books on history throughout his life, and in both science and history his retentive memory was most remarkable.
  • Von Neumann was considered the leading mathematician in the United States.
    • Max Born, in My Life: Recollections of a Nobel Laureate, pp. 236–237
  • He would seize on the fuzzy notions of others and, by dint of his prodigious mental powers, leap five blocks ahead of the pack. “You would tell him something garbled, and he’d say, ‘Oh, you mean the following,’ and it would come back beautifully stated,” said his onetime protégé, the Harvard mathematician Raoul Bott.
  • Von Neumann is a great scientific hero to me because it seemed… he seemed to have something. And of course it may be envy rather than admiration, but it's good to envy someone like von Neumann.
  • Mathematics is not a pompous activity, least of all in the hands of extraordinarily fast and penetrating minds like Johnny von Neumann.
  • There was something endearing and personal about Johnny von Neumann. He was the cleverest man I ever knew, without exception. And he was a genius, in the sense that a genius is a man who has two great ideas. When he died in 1957 it was a great tragedy to us all.
  • In a Silliman lecture ... John von Neumann, who was dying at the time, wrote some of the most splendid sentences he wrote in all his life ... He pointed out that there were good grounds merely in terms of electrical analysis to show that the mind, the brain itself, could not be working on a digital system. It did not have enough accuracy; or ... it did not have enough memory. ... And he wrote some classical sentences saying there is a statistical language in the brain ... different from any other statistical language that we use... this is what we have to discover. ...I think we shall make some progress along the lines of looking for what kind of statistical language would work.
    • Jacob Bronowski, The Origins of Knowledge and Imagination (1978); referring to von Neumann's, The Computer and the Brain (1958)
  • Von Neumann was a very great mathematician. He made many important contributions in a wide range of fields.
    • Arthur Burks, in Theory of Self-Reproducing Automata (1966) by John von Neumann, p. 2
  • The manuscripts for both parts of the present volume were unfinished; indeed, they were both, in a sense, first drafts. There is one compensation in this: one can see von Neumann's powerful mind at work.
    • Arthur Burks, in Theory of Self-Reproducing Automata (1966) by John von Neumann, p. 19
  • He was about as likable a chap as you could imagine. There is just one short thing about him. I was riding in a Pullman one day in the lounge car after the war and I hadn't looked about me before I sat down; I was reading something and it had my full attention. From across came von Neumann. He sat down aside me and introduced himself. Well here was the man who, in my opinion, was the most able mathematician in the country in many ways and he felt that he needed to introduce himself to me. That's a type of modesty one can't help liking.
  • He was incredible - the enormous perception that he had. For me, ever since, a standard of comparison has always been von Neumann. And if I say, "He reminds me of von Neumann," that's about the best compliment I can give anyone.
  • [He] thought so fast that he very often anticipated what one was going to say. . . . a pleasant agreeable person . . . the amazing logic of his thought processes.
    • Jule Gregory Charney, 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. 317
  • Von Neumann was capable of all sorts of remarkable things.
  • Now the story doesn't end here. Before going on with it, however, I'd like to introduce you to Johnnie von Neumann, an incredible genius whose mind worked about as rapidly as the super high-speed computers he helped design.
    • Samuel T. Cohen, in Confessions of the Father of the Neutron Bomb (2006), pp. 61–62
  • Bennie decided to approach Johnnie on the matter and arranged to travel to Princeton’s Institute for Advanced Study, headed up at the time by Oppenheimer, where Johnnie (and lesser geniuses such as Albert Einstein) was stationed.
  • He did a tremendous amount of different things in mathematics, many of them revolutionary.
    • John Horton Conway, as quoted in Candid Science V: Conversations with Famous Scientists (2005) by Istvan Hargittai and Balazs Hargittai, p. 17
  • Mr. von Neumann, in spite of his youth, is a completely exceptional personality ... who has already done very productive work ... and whose future development is being watched with great expectation in many places.
  • Von Neumann I never could quite figure out. He was just too fast for me.
    • Joseph F. Daly, in an interview with William Aspray, July 10, 1984[10]
  • Strange, contradictory, and controversial person; childish and good-humored, sophisticated and savage, brilliantly clever yet with very limited, almost primitive lack of ability to handle his emotions—an enigma of nature that will have to remain unsolved.
  • [One early 1945 night,] he woke up and started talking at a speed which, even for him, was extraordinarily fast. “What we are creating now is a monster whose influence is going to change history, provided there is any history left, yet it would be impossible not to see it through, not only for the military reasons, but it would also be unethical from the point of view of the scientists not to do what they know is feasible, no matter what terrible consequences it may have. And this is only the beginning!” The concerns von Neumann voiced that night were less about nuclear weapons, and more about the growing powers of machines. “From here on, Johnny’s fascination and preoccupation with the shape of things to come never ceased,” concludes Klári’s account. For the next seven years he neglected mathematics and devoted himself to the advance of technology in all forms. “It was almost as if he knew that there was not very much time left.”
  • He had always done his writing at home during the night or at dawn. His capacity for work was practically unlimited.
  • People would come to him because of his great insight.
    • George Dantzig, as quoted in More Mathematical People: Contemporary Conversations (1990), p. 76
  • In von Neumann’s generation his ability to absorb and digest an enormous amount of extremely diverse material in a short time was exceptional; and in a profession where quick minds are somewhat commonplace, his amazing rapidity was proverbial.
  • May have been the last representative of a once-flourishing and numerous group, the great mathematicians who were equally at home in pure and applied mathematics and who throughout their careers maintained a steady production in both directions.
  • However, as noted earlier, one of his central objectives—as a mathematician—was to publish the generalized proof of the fixed point theorem. Was the economics merely a convenient vehicle for an essentially mathematical exercise for von Neumann? Genius that he was, perhaps that is all that he wanted to do at that time. Later, after meeting Oscar Morgenstern, he returns to economics, but only through their joint interest in the theory of games.
    • Mohammed Dore, in John von Neumann and Modern Economics (1989), p. 86
  • I remember a talk that Von Neumann gave at Princeton around 1950, describing the glorious future which he then saw for his computers. Most of the people that he hired for his computer project in the early days were meteorologists. Meteorology was the big thing on his horizon. He said, as soon as we have good computers, we shall be able to divide the phenomena of meteorology cleanly into two categories, the stable and the unstable. The unstable phenomena are those which are upset by small disturbances, the stable phenomena are those which are resilient to small disturbances. He said, as soon as we have some large computers working, the problems of meteorology will be solved. All processes that are stable we shall predict. All processes that are unstable we shall control. He imagined that we needed only to identify the points in space and time at which unstable processes originated, and then a few airplanes carrying smoke generators could fly to those points and introduce the appropriate small disturbances to make the unstable processes flip into the desired directions. A central committee of computer experts and meteorologists would tell the airplanes where to go in order to make sure that no rain would fall on the Fourth of July picnic. This was John von Neumann's dream. This, and the hydrogen bomb, were the main practical benefits which he saw arising from the development of computers.
    • Freeman Dyson, in an account of a 1950 talk by von Neumann, in Infinite in All Directions (1988); the statement "All stable processes we shall predict. All unstable processes we shall control" is sometimes attributed to von Neumann directly, but may be a paraphrase.
  • Von Neumann compensated for these superhuman abilities with an earthy sense of humor and tireless social life, and tried, with mixed success, to blend in on a normal human scale.
    • George Dyson, in Turing's Cathedral: The Origins of the Digital Universe (2012), p. 47
  • The Alexanders gave humdinger, wonderful parties. I don't know whether they would be regarded as outlandish today, but they were certainly regarded as far out in those days. The phenomenal feature of von Neumann was that he could go to these parties and party and drink and whoop it up to the early hours of the morning, and then come in the next morning at 8:30, hold class, and give an absolutely lucid lecture. What happened is that some of the graduate students thought that the way to be like von Neumannn was to live like him, and they couldn't do it.
  • Von Neumann was very impressive to talk with. He was very quick.
    • Paul Erdős, in Mathematical People: Profiles and Interviews (1985), p. 89
  • In speed and understanding Von Neumann was certainly phenomenal. He could understand a proof even far from his own subject very fast. I remember once in Cambridge I told him a proof of interpolation that was not quite correct. By the time we met again I had a correct proof. Von Neumann told me, “Something seems to be wrong in that proof.” And it was really not his subject. He wasn’t that interested in it, but he was quite right.
    • Paul Erdős, in Mathematical People: Profiles and Interviews (1985), p. 89
  • You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!
  • He is really a professional, isn’t he!
  • Dr. von Neumann is one of the very few men about whom I have not heard a single critical remark. It is astonishing that so much equanimity and so much intelligence could be concentrated in a man of not extraordinary appearance.
    • Laura Fermi, as quoted in John Von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 29
  • Johnny von Neumann was the greatest mathematician around.
  • Finally there came in the mail an invitation from the Institute for Advanced Study: Einstein. . . von Neumann. . .Weyl. . . all these great minds!
  • [Addressing Albert Tucker] The story goes that von Neumann's parents had all been lawyers and they sort of hoped that Johnny would be a good, lawyer. When he was sixteen or so they sort of tolerated his fiddling around with chemistry and mathematics. Finally they found out he wanted to be a mathematician, or chemist, or some mixture. They were very upset. Well, their attitude was that it wasn't too bad if he was going to pe a good one. So they inquired around who the best mathematician in his part of the world was, and it turned out to be Siegel. They had lots of money, and they arranged for Siegel to talk to Johnny. Afterwards they asked him, "Well, do you think he has any potential?" He said, "He knows more mathematics than I do now."
  • Von Neumann would engage in any subject you wanted to discuss and within five minutes be right at the heart of the issue, even when he started off by saying, “I can discuss that not prejudiced by any facts.”
  • John von Neumann is a kind of legendary mind ... Many people say he's like one of the smartest humans ever.
    • Lex Fridman, in Demis Hassabis: Future of AI, Simulating Reality, Physics and Video Games | Lex Fridman Podcast #475
  • I never ceased to be fascinated by electronic computers, and I feel that I have been privileged in having been initiated so marvellously by the Master himself. His mathematical achievements are far too subtle and technical for me to understand or to describe, but I can attest to the strength of his brain because I once saw him, for a bet, drink sixteen martinis in a row and then be still on his feet and quite lucid, though somewhat pessimistic in his utterances.
  • IQ tests for geniuses have not yet been constructed, because one cannot expect the IQ-specialists to be geniuses, but one must suspect that the scale continues upwards to giddy heights of ability. Most of those who have known the mathematician John von Neumann have felt as slow and stupid in his presence as the dunce with the top of the form.
    • Dennis Gabor, in The Mature Society; A View of the Future By the Winner of the 1971 Nobel Prize for Physics, p. 73
  • [On Rayleigh–Taylor instability] So, Fermi said, "Let me make a model; I'll have a broad tongue which moves into the dense material; I'll have a narrow tongue that moves away from it, and I'll just solve this numerically." So, he did some of that, but he wasn't quite satisfied with the solution. One afternoon around 4:50 p.m., John von Neumann came by and saw what Fermi had on the blackboard and asked what he was doing. So, [[Enrico Fermi|Enrico] told him, and John von Neumann said, "That's very interesting." He came back about 15 minutes later and gave him the answer. Fermi leaned against his doorpost and told me, "You know, that man makes me feel I know no mathematics at all."
  • Well, I was so flattered to be mentioned in a footnote by John von Neumann that it didn't occur to me that he hadn't actually credited us with what we were doing.
  • The fact, however, remains that a lot of wonderful people never received the prize. Just take a few examples from among Hungarian physicists. Von Neumann never received the prize and neither did Szilard.
    • Vitaly Ginzburg, as quoted in Candid Science VI: More Conversations with Famous Scientists (2006) by István Hargittai and Magdolna Hargittai, p. 811
  • That von Neumann was brilliant, perhaps a good deal more than brilliant, had been clear even in childhood.
    • Jim Glenn, in Scientific Genius: The Twenty Greatest Minds (1996), p. 130
  • He is regarded as one of the giants of modern mathematics.
  • While still very young, von Neumann showed tremendous intellectual and linguistic ability, and he once told the author that at six he and his father often joked with each other in classical Greek.
  • One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes. Another time, I watched him lecture on some material written in German about twenty years earlier. In this performance von Neumann even used exactly the same letters and symbols he had in the original.
  • I guess one of [Veblen's] greatest mathematical accomplishments was finding Johnny von Neumann and bringing him to Princeton University. At least I suppose that was his greatest achievement among many achievements.
  • Whenever you'd go into his office, having spent the last week working on something, and say, "Johnny, I've got an idea," and start to write, you'd get maybe the first half-a-line down before he'd say, "Yes, let me have the chalk." Then he'd get up there, and for the rest of the hour he would be putting it down in the way it ought to be done.
  • He had another quality which I always thought was unbelievable. He and I worked at trying to prove something about bounds on eigen values one time without .any success. One day I saw in Math Reviews a statement that Kolmogorov or somebody had proved a theorem, and I said, "This is what so and so proved." He said, "Sure, this is how it goes." And he went to the blackboard and he proved it. Somehow, just knowing that it was true, and not just a conjecture of ours, made it possible for him to see the proof. I don't know how or why or what.
  • At just about the time you could run your eye down the page, he would be turning it.
  • I always remember one time, Bochner, von Neumann, and I were in a room, I guess Johnny's room in the Institute. Bochner was presenting material to us, and he got stuck. He hemmed and hawed for a while, and he said "If you'll wait a minute, I know where the book is that has the proof of this. I'll run upstairs and get it." Johnny said, "Don't do that, I don't know what book it's in, but I 'II prove it for you." And he did.
  • It is the hallmark of a great mathematician that his output is prodigious and von Neumann was indeed a great mathematician.
  • In a 1948 Princeton talk, replying to a frequent affirmation that it's impossible to build a machine that can replace the human mind, von Neumann said: 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.
    • Edwin Thompson Jaynes, Probability Theory: The Logic of Science (2003); referring to the 1948 Princeton talk he attended to.
  • Most of the legends, from childhood on, tell about his phenomenal speed in absorbing ideas and solving problems. At the age of 6 he could divide two eight-digit numbers in his head; by 8 he had mastered the calculus; by 12 he had read and understood Borel’s Théorie des Fonctions.
    • Paul Halmos, in The legend of John von Neumann. The American Mathematical Monthly, 80(4), 382–394
  • The speed with which von Neumann could think was awe-inspiring.
    • Paul Halmos, in The legend of John von Neumann. The American Mathematical Monthly, 80(4), 382–394
  • When his electronic computer was ready for its first preliminary test, someone suggested a relatively simple problem involving powers of 2. (It was something of this kind: what is the smallest power of 2 with the property that its decimal digit fourth from the right is 7? This is a completely trivial problem for a present-day computer: it takes only a fraction of a second of machine time.) The machine and Johnny started at the same time, and Johnny finished first.
    • Paul Halmos, in The legend of John von Neumann. The American Mathematical Monthly, 80(4), 382–394
  • One famous story concerns a complicated expression that a young scientist at the Aberdeen Proving Ground needed to evaluate. He spent ten minutes on the first special case; the second computation took an hour of paper and pencil work; for the third he had to resort to a desk calculator, and even so took half a day. When Johnny came to town, the young man showed him the formula and asked him what to do. Johnny was glad to tackle it. "Let's see what happens for the first few cases. If we put n = 1, we get..." -- and he looked into space and mumbled for a minute. Knowing the answer, the young questioner put in "2.31?" Johnny gave him a funny look and said "Now if n = 2, ...", and once again voiced some of his thoughts as he worked. The young man, prepared, could of course follow what Johnny was doing, and, a few seconds before Johnny finished, he interrupted again, in a hesitant tone of voice: "7.49?" This time Johnny frowned, and hurried on: "If n = 3, then...". The same thing happened as before - Johnny muttered for several minutes, the young man eavesdropped, and, just before Johnny finished, the young man exclaimed: "11.06!" That was too much for Johnny. It couldn't be! No unknown beginner could outdo him! He was upset and he sulked till the practical joker confessed.
    • Paul Halmos, in The legend of John von Neumann. The American Mathematical Monthly, 80(4), 382–394
  • As a writer of mathematics von Neumann was clear, but not clean; he was powerful but not elegant. He seemed to love fussy detail, needless repetition, and notation so explicit as to be confusing. To maintain a logically valid but perfectly transparent and unimportant distinction, in one paper he introduced an extension of the usual functional notation: along with the standard he dealt also with something denoted by . The hair that was split to get there had to be split again a little later, and there was , and, ultimately, . Equations such as

have to be peeled before they can be digested; some irreverent students referred to this paper as von Neumann's onion.

    • Paul Halmos, in The legend of John von Neumann. The American Mathematical Monthly, 80(4), 382–394
  • The most spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast.
  • Keeping up with him was... impossible. The feeling was you were on a tricycle chasing a racing car.
  • Great.
    • Richard Hamming, as quoted in Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993) by Rosemary Schmalz, p. 157
  • Von Neumann was a true genius, the only one I’ve ever known. I’ve met Einstein and Oppenheimer and Teller and—who’s the mad genius from MIT? I don’t mean McCulloch, but a mathematician. Any-way, a whole bunch of those other guys. Von Neumann was the only genius I ever met. The others were supersmart .... And great prima donnas. But von Neumann’s mind was all-encompassing. He could solve problems in any domain. . . . And his mind was always working, always restless. He walked into my living room one night and a half dozen people were already having cocktails, and he disappeared into a corner and stood with his back to us, hands behind him, and after about two minutes turned to me and said, “About two thirds of a liter a week, Leon.” And I had to think about it for three or four minutes, and finally I said, “Yeah, Johnny, that’s just about right.” He’d walked up to the nine-gallon tropical fish aquarium that stood on a table in the corner, had noted the temperature of the water, had made an estimate of the surface area, had seen the gap that existed between the overhead light and the glass to keep the fish from jumping out, made an estimate of the particular escape velocity of the water molecules, integrated and found out how much added water was needed each week for that aquarium. And he was right within a few percent. That’s the kind of thing he did all the time. Another thing that he isn’t known well for was his sense of humor. He really enjoyed dirty limericks. And though we never said anything to each other deliberately, it sort of evolved that whenever we came together, whether it was an hour or a month later, the name of the game was to see who could rush up the fastest and unload the largest number of new limericks. It turned out to be a delightful game. He had oodles of them; I was hard put to keep up with him. His memory was just beyond conception, a photograph for everything he ever learned or saw. Lightning calculator and head screwed on to boot—he put all of those together with a huge creative talent.
    • Leon Harmon, as quoted in Machines Who Think: A Personal Inquiry into the History and Prospects of Artificial Intelligence (2004) by Pamela McCorduck, pp. 81–82
  • Fantastic mind.
    • Demis Hassabis, in Demis Hassabis: Future of AI, Simulating Reality, Physics and Video Games | Lex Fridman Podcast #475
  • His extraordinariness lay in his mental abilities. These were so dazzling that some of his admiring colleagues were at a loss to describe them in ordinary human terms.
    • Steve J. Heims, in John Von Neumann and Norbert Wiener: From Mathematics to the Technologies of Life and Death (1980), p. 26
  • [Addressing Albert Tucker] He thought very fast, yes, and he was extraordinarily subtle. He was most impressive. You've heard the story of Robertson driving van Neumann to somewhere. Von Neumann asked him what he was working on, and Robertson said such and such an equation. By the time they got to the end of the ride von Neumann had solved the equation in his head. Had you heard that?
  • As a mathematician, Steinhaus’s main strengths were his intelligence and an unerring instinct and taste in the choice of problems. In this respect he reminded me of John von Neumann, a mathematician whom he greatly liked and admired.
    • Mark Kac, in Enigmas of Chance: An Autobiography (1985), p. 51
  • Unquestionably the nearest thing to a genius I have ever encountered.
    • Nicholas Kaldor, as quoted in John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 250
  • There were several times in my life that I’ve, one way or another, got that feeling, my gosh, here is a tremendous mathematician; for instance, Weil, von Neumann, Serre, Milnor, Atiyah. Well, those are obvious names.
    • Irving Kaplansky, as quoted in More Mathematical People: Contemporary Conversations (1990), p. 128
  • Certainly the greatest mathematician of that time.
    • John G. Kemeny, in Mathematical People: Profiles and Interviews (1985), pp. 163–164
  • It must have been a shattering experience to have grown up with von Neumann however bright one is.
    • Thomas Kuhn, 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. 72
  • He was the most remarkable man. I’m always utterly surprised that his name is not common, household. It is a name that should be known to every American—in fact, every person in the world, just as the name of Einstein is. I am always utterly surprised how come he’s almost totally unknown. In fact, did you know – you did know, all right, you are an unusually well informed person. All people who had met him and interacted with him realized that his brain was more powerful than anyone’s they have ever encountered. I remember Hans Bethe even said, only half in jest, that von Neumann’s brain was a new development of the human brain. Only a slight exaggeration.
  • People today have a hard time to imagine how brilliant von Neumann was. If you talked to him, after three words, he took over. He understood in an instant what the problem was and had ideas. Everybody wanted to talk to him.
  • To gain a measure of von Neumann’s achievements, consider that had he lived a normal span of years, he would certainly have been a recipient of a Nobel Prize in economics. And if there were Nobel Prizes in computer science and mathematics, he would have been honored by these, too. So the writer of these letters should be thought of as a triple Nobel laureate or, possibly, a ​3 1⁄2-fold winner, for his work in physics, in particular, quantum mechanics.
  • Von Neumann was addicted to thinking, and in particular to thinking about mathematics.
    • Peter Lax, in Remembering John von Neumann (1990), p. 6
  • "Most mathematicians prove what they can, von Neumann proves what he wants." Once in a discussion about the rapid growth of mathematics in modern times, von Neumann was heard to remark that whereas thirty years ago a mathematician could grasp all of mathematics, that is impossible today. Someone asked him: "What percentage of all mathematics might a person aspire to understand today?" Von Neumann went into one of his five-second thinking trances, and said: "About 28 percent."
    • Peter Lax, in Remembering John von Neumann (1990)
  • Most scintillating intellect of this century.
  • Eleven-year-old Johnny taught him [Wigner] set-theory math during Sunday afternoon walks.
    • Norman Macrae, in John Von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992) by Norman Macrae, p. 24
  • Wigner and others recall that Ratz’s recognition of Johnny’s mathematical talents was instant.
    • Norman Macrae, in John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 69
  • Mrs. Szego recalled that her husband came home with tears in his eyes from his first encounter with the young prodigy.
    • Norman Macrae, in John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 70
  • Von Neumann got very excited when J. M. put production functions on the board and jumped up, wagging his finger at the blackboard, saying (approx): “But surely you want inequalities, not equations there?” Jascha said that it became difficult to carry the seminar to conclusion because von Neumann was on his feet, wandering around the table, etc., while making rapid and audible progress on the linear programming theory of production. “The rapidity with which he made the connection and developed it,” said Arrow, “is in line with many anecdotes of von Neumann’s mental speed.”
    • Norman Macrae, in John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 252
  • On what was probably August 7, 1944, Goldstine took Johnny to see the ENIAC at Philadelphia. Before this visit Eckert told Goldstine he would be able to “tell whether von Neumann was really a genius by his first question. If this was about the logical structure of the machine, he would believe in von Neumann, otherwise not. Of course this was von Neumann’s first query.”
    • Norman Macrae, in John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 281
  • While all the other computer makers were generally heading in the same direction, von Neumann’s genius clarified and described the paths better than anyone else.
    • Norman Macrae, in John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 287
  • All three of these men—Strauss, Quarles, and Gardner—thought that America’s technology for war could best be advanced by the man whom they regarded as America’s quickest-thinking scientific genius.
    • Norman Macrae, in John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (1992), p. 347
  • He was building his computer. He was not just a person who told other guys to build a computer. He was always about details, "How are you going to do this? Which kind of gadget are you going to use for memory?" He was extraordinarily precise in these matters. At the same time he had written a book on the foundation of quantum mechanics, which I read with terror but great interest. He had written this book about games theory, which looked then extremely promising but of course was just the beginning. He had done this work about logic. I mean, in a way Von Neumann was the person who had performed the miracle. He was for me the model above all models.
  • He was becoming more concerned with defense than with science. But it seemed that he was living proof that one could do science without really belonging to a “guild.” In fact, he was under extreme pressure at Princeton. From there, he left for Washington and was not planning to return. Luckily, von Neumann had realized that, by having failed to claim admission to any guild, I was leading a very dangerous life. A foundation executive told me much later that von Neumann had specifically asked him to watch after me, and to help in case of trouble.
    • Benoît Mandelbrot, quoted in Barcellos, Anthony, and A. Barcellos. "Interview of BB Mandelbrot." Mathematical People: Profiles and Interviews (2008): 213-234.
  • Johnny von Neumann was the genius.
    • Harris Mayer, as quoted in Turing's Cathedral: The Origins of the Digital Universe (2012), p. 10
  • Johnny von Neumann was very, very good and very quick and very sharp. He just was a universalist. He was not a mathematician.
  • Johnny von Neumann who was very, very quick—I mean, you have no idea how quickly he would infer things and extrapolate them. Well, he was fantastic.
  • He knew so much about physics and philosophy and even things like history. He was very, very sharp. He worked all the time.
  • His talents were so obvious and his cooperative spirit so stimulating that he garnered the interest of many of us.
  • Later, Tucker told me that he had gone to von Neumann and said, ‘This seems like very interesting work, but I can’t evaluate it. I don’t know whether it should really be called mathematics.’ Von Neumann replied, ‘Well, if it isn’t now, it will be someday—let’s encourage it.’ So I got my Ph.D.”
  • He worked with tremendous energy and fantastic speed.
    • Oskar Morgenstern, in John Von Neumann: Mathematician, Amram Nowak and Patricia Powell, Mathematical Association of America, 1966.
  • I remember that there was a feeling of excitement and interest both in Hilbert’s lecture and in the lecture of von Neumann on the foundations of set theory — a feeling that one now finally was coming to grips with both the axiomatic foundation of mathematics and with the reasons for the applications of mathematics in the natural sciences.
  • Another frequent visitor was John von Neumann, a brilliant mathematician, whom I knew from Germany. Although he was Hungarian, he did not have the extreme superficial politeness of many Hungarians. He liked good living and a good story. His mathematics was of the purest and most abstract kind, but he also understood physics and had written a book about quantum mechanics. He was extremely fast in solving practical problems, and contributed many useful ideas to the work of Los Alamos.
  • Remarkable mathematician.
    • Roger Penrose, in Shadows Of The Mind: A Search For The Missing Science Of Consciousness (1994), p. 317
  • 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.
  • In 1956 Good Housekeeping magazine ran an article on Klara von Neumann and her husband with the improbable title, “Married to a Man Who Believes the Mind Can Move the World.” One of the stranger examples of 1950s women’s magazine journalism, it is a dogged attempt to humanize a not entirely promising subject. “What’s it like to suspect your husband of being the smartest man on earth?” the article asks. “When Klara von Neumann, a slender brunette of Washington, D.C., glances at her husband, a plump, cheerful man who was born in Hungary fifty-two years ago, the thought sometimes occurs to her that she may be married to the best brain in the world.”
  • It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived.
  • All the mathematicians I have talked to have said that von Neumann had the quickest mind they ever knew.
    • Constance Reid, as quoted in Mathematical People: Profiles and Interviews, p. 275
  • Apart from my thesis, though, I cannot overlook the great influence on all of us of the sparkling lectures in real analysis given by Professor John von Neumann, a young man who had also come from Germany during this period. How well I remember his hurried arrivals in the classroom, a mere second late but wasting no time. With spectacular fluency he instantly made the hour come alive. No notes were ever needed, for his complete control and mastery of his subject and his lightning-fast blackboard-equations quickly reflected to us some of the greatness of his precocious mind. His audience will remember his beautifully complexioned cheeks that often radiated a cherubic smile, and his bright piercing brown eyes that seemed to glow with great vitality.
    • Malcolm Robertson[34]
  • No other mathematician in this century has had as deep and lasting an influence on the course of civilization.
  • At this half-century birthday party I have two purposes. The first is to free the dynamic input/output paradigin from gratuitous misinterpretations. The second is to say something about the genius of John von Neumann, contrasting the fertility of his contributions to economics with that of past great mathematicians and non-economist celebrities. While memories are still green, we should preserve for the historical record some of the legends about this great genius.
    • Paul Samuelson, in John von Neumann and Modern Economics (1989), p. 100
  • Evidence enough has been given for von Neumann’s genius and eminence in pure and applied mathematics.
    • Paul Samuelson, in John von Neumann and Modern Economics (1989), p. 120
  • We economists are grateful for von Neumann’s genius. It is not for us to calculate whether he was a Gauss, or a Poincaré, or a Hilbert. He was the incomparable Johnny von Neumann. He darted briefly into our domain and it has never been the same since.
    • Paul Samuelson, in John von Neumann and Modern Economics (1989), p. 121
  • I remember having listened to Fermi’s discussions on hydrodynamics with von Neumann. (These took the strange form of competitions before Fermi’s office blackboard as each tried to solve the problem under study first; von Neumann, with his unmatched lightning-fast analytical skill, usually won).
  • The smartest person I've ever met.
    • Claude Shannon, as quoted in A Mind at Play: How Claude Shannon Invented the Information Age (2017) by Jimmy Soni and Rob Goodman, p. 76
  • I was a graduate student—he was one of the great mathematicians of the world.
    • Claude Shannon, as quoted in A Mind at Play: How Claude Shannon Invented the Information Age (2017) by Jimmy Soni and Rob Goodman, p. 76
  • Bethe, Fermi, and von Neumann could often be found sitting together in a quiet room inside the throbbing heart of the Theoretical Division, challenging each other to solve complex integral equations related to pressure waves. Sometimes Oppenheimer would join them. Von Neumann usually left these other three brilliant physicists in the dust.
    • David N. Schwartz, in The Last Man Who Knew Everything: The Life and Times of Enrico Fermi, Father of the Nuclear Age, p. 300
  • But when you were in real thinking trouble, you would go to von Neumann and nobody else.
  • A great mathematician in his or any era.
  • A memory which seemed to operate with even more speed than his machines enabled him to bring up, from his vast and well-indexed mental filing system, stories appropriate to whatever occasion.
  • He was one of the most attractive people I’ve ever known, attractive in the sense that he knew so much and could reason in front of people and show them what was going on so well, it was really quite wonderful. He also had a good sense of humor. ... He was wonderful, and I was really crushed when I found out that he had cancer.
  • Two were in their early twenties: Eugene Wigner, who became a great theoretical physicist, and Johnny von Neumann, whose brilliance as a mathematician is internationally acknowledged.
    • Edward Teller, in Memoirs: A Twentieth-Century Journey in Science and Politics (2001), p. 37
  • Johnny von Neumann was so valuable, not only as a mathematician but in virtually every field, that he was welcome to work with us even for very short periods. He was allowed to come and go freely.
    • Edward Teller, in Memoirs: A Twentieth-Century Journey in Science and Politics (2001), p. 174
  • Johnny was the most versatile and brilliant scientist I have ever known. His mind operated at speeds that suggested neural superconductivity.
    • Edward Teller, in Memoirs: A Twentieth-Century Journey in Science and Politics (2001), p. 254
  • I believe that if a mentally superhuman race ever develops, its members will resemble Johnny von Neumann.
    • Edward Teller, in Memoirs: A Twentieth-Century Journey in Science and Politics (2001), p. 410
  • That deep, practically monomaniacal devotion to the thinking process is what set Johnny von Neumann apart from everyone else I have ever known.
    • Edward Teller, in ''Memoirs: A Twentieth-Century Journey in Science and Politics (2001), p. 410
  • I have come to suspect that to most people thinking is painful. Some of us are addicted to thinking. Some of us find it a necessity. Johnny enjoyed it. I even have the suspicion that he enjoyed practically nothing else.
  • He could and did talk to my 3-year-old son on his own terms, and I sometimes wondered whether his relation to the rest of us were a little bit similar.
  • I'm sure that von Neumann threw off lots of ideas, as he went about, that led to Ph.D. theses.
  • I feel that Weyl and von Neumann were the greatest mathematicians that I have known.
  • Von Neumann was so terribly quick in lecturing that people had to slow him up by asking questions. It was understood in his classes. That people would ask questions to slow him up. I think he was quite aware of that and was grateful for this help from the audience. Von Neumann had a way of taking an idea that he had and explaining it very quickly and very clearly.
  • I think the choice of von Neumann is clear by the criteria of getting the best mathematical talent in the world.
  • No one that he had to compete with. But he nevertheless was a terrifically competitive person.
  • Then in 1927, Zawirski told me a congress of mathematicians was to take place in Lwów and foreign scholars had been invited. He added that a youthful and extremely brilliant mathematician named John von Neumann was to give a lecture.
  • Kuratowski also described von Neumann’s results and his personality. He told me how in a Berlin taxicab von Neumann had explained in a few sentences much more than he, Kuratowski, would have gotten by correspondence or conversation with other mathematicians about questions of set theory, measure theory, and real variables.
  • He always demonstrated his fantastic and to some extent prophetic range of interests in mathematics and its applications and at the same time an objectivity which I admired enormously.
  • As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self-confidence.
  • For Wigner, von Neumann and thinking were synonymous.
  • Quite aware that the criteria of value in mathematical work are, to some extent, purely aesthetic, he once expressed an apprehension that the values put on abstract scientific achievement in our present civilization might diminish: "The interests of humanity might change, the present curiosities in science may cease, and entirely different things may occupy the human mind in the future." One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.
  • Johnny was probably the most brilliant star in this constellation of scientists.
  • I remember that in 1927, when he came to Lwów (in Poland) to attend a congress of mathematicians, his work in foundations of mathematics and set theory was already famous. This was already mentioned to us, a group of students, as an example of the work of a youthful genius.
  • Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature.
    • Léon Van Hove, in Von Neumann’s contributions to quantum theory (May 1, 1958)
  • Universal mind.
    • Heinz von Foerster, in Understanding Understanding: Essays on Cybernetics and Cognition (2002), p. 150
  • John von Neumann became one of the world’s greatest mathematicians and went on to father the digital computer, a device that is revolutionizing all walks of life.
    • Theodore Von Kármán, in The Wind and Beyond: Theodore von Karman, Pioneer in Aviation and Pathfinder in Space (1967), p. 107
  • Especially as it brought me back in association with John von Neumann, whose great skill in mathematics I had first observed in Europe when he was a boy of seventeen.
    • Theodore Von Kármán, in The Wind and Beyond: Theodore von Karman, Pioneer in Aviation and Pathfinder in Space (1967), p. 229
  • Great mathematician.
    • Theodore Von Kármán, in The Wind and Beyond: Theodore von Karman, Pioneer in Aviation and Pathfinder in Space (1967), p. 301
  • Throughout much of his career, he led a double life: as an intellectual leader in the ivory tower of pure mathematics and as a man of action, in constant demand as an advisor, consultant and decision-maker to what is sometimes called the military-industrial complex of the United States. My own belief is that these two aspects of his double life, his wide-ranging activities as well as his strictly intellectual pursuits, were motivated by two profound convictions. The first was the overriding responsibility that each of us has to make full use of whatever intellectual capabilities we were endowed with. He had the scientist's passion for learning and discovery for its own sake and the genius's ego-driven concern for the significance and durability of his own contributions. The second was the critical importance of an environment of political freedom for the pursuit of the first, and for the welfare of mankind in general.
    I'm convinced, in fact, that all his involvements with the halls of power were driven by his sense of the fragility of that freedom. By the beginning of the 1930s, if not even earlier, he became convinced that the lights of civilization would be snuffed out all over Europe by the spread of totalitarianism from the right: Nazism and Fascism. So he made an unequivocal commitment to his home in the new world and to fight to preserve and reestablish freedom from that new beachhead.
    In the 1940s and 1950s, he was equally convinced that the threat to civilization now came from totalitarianism on the left, that is, Soviet Communism, and his commitment was just as unequivocal to fighting it with whatever weapons lay at hand, scientific and economic as well as military. It was a matter of utter indifference to him, I believe, whether the threat came from the right or from the left. What motivated both his intense involvement in the issues of the day and his uncompromisingly hardline attitude was his belief in the overriding importance of political freedom, his strong sense of its continuing fragility, and his conviction that it was in the United States, and the passionate defense of the United States, that its best hope lay.
    • Marina von Neumann Whitman, Introduction to John Von Neumann: Selected Letters, History of Mathematics, Vol. 27, ed. Miklos Redei (2005), pp. 15–16
  • Many mathematicians have suffered in fact by comparing themselves with von Neumann.
  • But John von Neumann had a marvelous interest in history. He had read the Cambridge Medieval History, [the] Cambridge Ancient History, and he had a phenomenal memory, so he could recite whole paragraphs from the Cambridge Ancient History and tell me about the Council of Nicea, for instance. But to become a member of the Atomic Energy Commission, I'm sure he was very useful, but it was so far removed from making use of this marvelous scientific imagination of his that I keep wondering if we made the best use of him.
  • Von Neumann and Fermi, in particular, were enormously helpful. Both had the most stunning ability to listen to a recital of current problems for only an hour or two and then provide comments or calculations that would show the way to overcoming the problems. They also enriched the life of the lab by giving colloquium talks on almost every visit.
  • Neumann is one of the two or three top mathematicians in the world, is totally without national or race prejudice, and has an enormously great gift for inspiring younger men and getting them to do research.
  • I have known a great many intelligent people in my life. I knew Max Planck, Max von Laue, and Werner Heisenberg. Paul Dirac was my brother-in-law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. And I have known many of the brightest younger scientists. But none of them had a mind as quick and acute as Jancsi von Neumann. I have often remarked this in the presence of those men, and no one ever disputed me.
    • Eugene Wigner, as quoted in The Recollections of Eugene P. Wigner: as told to Andrew Szanton (1992), p. 58
  • He understood mathematical problems not only in their initial aspect, but in their full complexity.
    • Eugene Wigner, as quoted in The Recollections of Eugene P. Wigner: as told to Andrew Szanton (1992), p. 58
  • Johnny was a most unusual person, a marvellously quick thinker, and was recognized as such in high school.
    • Eugene Wigner, as quoted in The Collected Works Of Eugene Paul Wigner (1992), p. 3
  • Nobody knows all science, not even von Neumann did. But as for mathematics, he contributed to every part of it except number theory and topology. That is, I think, something unique.
  • A deep sense of humor and an unusual ability for telling stories and jokes endeared Johnny even to casual acquaintances. He could be blunt when necessary, but was never pompous. A mind of von Neumann's inexorable logic had to understand and accept much that most of us do not want to accept and do not even wish to understand. This fact colored many of von Neumann's moral judgments. … Only scientific intellectual dishonesty and misappropriation of scientific results could rouse his indignation and ire — but these did — and did almost equally whether he himself, or someone else, was wronged.
    • Eugene Wigner, in "John von Neumann (1903 - 1957)" in Year book of the American Philosophical Society (1958); later in Symmetries and Reflections : Scientific Essays of Eugene P. Wigner (1967), p. 261
  • The accuracy of his logic was, perhaps, the most decisive character of his mind. One had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch. "If one listens to von Neumann, one understands how the human mind should work," was the verdict of one of our perceptive colleagues... "If he analyzed a problem, it was not necessary to discuss it any further. It was clear what had to be done," said the present chairman of the U. S. Atomic Energy Commission.
    • "John von Neumann (1903 - 1957)" by Eugene Wigner, in Year book of the American Philosophical Society (1958)
  • Perhaps one could find a body of phenomena which would make our concept-building ability less of a single stark fact by studying the concept-forming ability of animals. Perhaps the consciousness of animals is more shadowy than ours and perhaps their perceptions are always dreamlike. On the opposite side, whenever I talked with the sharpest intellect whom I have known -- with von Neumann -- I always had the impression that only he was fully awake, that I was halfway in a dream.
    • Eugene Wigner, "Two kinds of reality." Philosophical Reflections and Syntheses. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. 33-47.
  • “You have a good memory?” asked Kuhn. “Not like von Neumann’s,” replied Wigner.
    • Eugene Wigner, 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. 72
  • Our teachers were just enormously good, but the mathematics teacher was fantastic. He gave private classes to Johnny von Neumann. He gave him private classes because he realized that this would be a great mathematician.
  • From talking to many people who knew him, I think I’ve gradually built up a decent picture of John von Neumann as a man. He would have been fun to meet. He knew a lot, was very quick, always impressed people, and was lively, social and funny.
  • Von Neumann was extremely intelligent, and curious about everything. He looked like a cherub and sometimes acted like one; my threeand five-year-old daughters delighted in climbing on him when he came to call at the house. He was very powerful and productive in pure science and mathematics and at the same time had a remarkably strong streak of practicality. He was one of the earliest pioneers in the design and construction of large electronic computers, he developed a strong interest in the technology of nuclear and other weapons, and he made a number of elegant inventions in each of these fields. This combination of scientific ability and practicality gave him a credibility with military officers, engineers, industrialists, and scientists that no one else could match. He was the clearly dominant advisory figure in nuclear missilery at the time, and everyone took his statements about what could and should be done very seriously.
    • Herbert F. York, in Race to Oblivion: A Participant's View of the Arms Race (1970), p. 85
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  1. ↑ https://geosci.uchicago.edu/~kite/doc/von_Neumann_1955.pdf
  2. ↑ https://web.math.princeton.edu/oral-history/c1.pdf
  3. ↑ https://web.math.princeton.edu/oral-history/c2.pdf
  4. ↑ https://www.si.edu/media/NMAH/NMAH-AC0196_bige710120.pdf
  5. ↑ https://archive.org/details/interviews_with_prof_felix_bloch_-_symmetry_seeker
  6. ↑ https://archive.org/details/interviews_with_prof_felix_bloch_-_symmetry_seeker
  7. ↑ https://web.math.princeton.edu/oral-history/c4.pdf
  8. ↑ https://archive.org/details/interviews_with_prof_s_chandrasekhar_-_symmetry_seeker/page/n3/mode/1up
  9. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/geoffrey-chews-interview/
  10. ↑ https://web.math.princeton.edu/oral-history/c7.pdf
  11. ↑ https://web.math.princeton.edu/oral-history/c9.pdf
  12. ↑ https://web.math.princeton.edu/oral-history/c10.pdf
  13. ↑ https://www.webofstories.com/play/murray.gell-mann/31/
  14. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  15. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  16. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  17. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  18. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  19. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  20. ↑ https://web.math.princeton.edu/oral-history/c14.pdf
  21. ↑ https://en.m.wikipedia.org/wiki/John_von_Neumann
  22. ↑ https://web.math.princeton.edu/oral-history/c17.pdf
  23. ↑ https://web.math.princeton.edu/oral-history/c17.pdf
  24. ↑ https://web.math.princeton.edu/oral-history/c19.pdf
  25. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/george-kistiakowskys-interview/
  26. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/peter-laxs-interview/
  27. ↑ https://superintelligence.fandom.com/wiki/John_von_Neumann_(quotes_and_anecdotes)
  28. ↑ https://superintelligence.fandom.com/wiki/John_von_Neumann_(quotes_and_anecdotes)
  29. ↑ https://web.math.princeton.edu/oral-history/c8.pdf
  30. ↑ https://web.math.princeton.edu/oral-history/c8.pdf
  31. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/nicholas-metropolis-interview/
  32. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/nicholas-metropolis-interview/
  33. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/nicholas-metropolis-interview/
  34. ↑ https://web.math.princeton.edu/oral-history/c24.pdf
  35. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/ted-taylors-interview-part-1/
  36. ↑ https://ahf.nuclearmuseum.org/voices/oral-histories/ted-taylors-interview-part-1/
  37. ↑ https://web.math.princeton.edu/oral-history/c19.pdf
  38. ↑ https://archive.org/details/interviews_with_prof_s_chandrasekhar_-_symmetry_seeker/page/n3/mode/1up
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