John von Neumann

"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."

"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!"

"At about that time Einstein had agreed to serve as a consultant to our group but did not want to travel to Washington. So there had to be a liaison person and I was given that opportunity. Since Einstein did not know me, there had to be someone to introduce us. It then happened that I was introduced to Einstein by John von Neumann, one of the most important mathematicians of all time, and who had also become a consultant to our group. It was a very great experience for a new Ph.D. to be introduced to Einstein by Von Neumann!"

"Von Neumann was one of the greatest geniuses that ever lived."

"[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 was also a delight to be with. His brainpower stuck out in every direction."

"Intellectual brilliance."

"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.”"

"The most outstanding and at the same time versatile mathematician in the world in the second quarter of the 20th century."

"Around 1922–23, being then professor at Marburg University, I received from Professor Erhard Schmidt, Berlin (on behalf of the Redaktion of the Mathematische Zeitschrift) a long manuscript of an author unknown to me, Johann von Neumann, with the title Die Axiomatisierung der Mengenlehre, this being his eventual doctor dissertation which appeared in the Zeitschrift only in 1928, (Vol. 27). I was asked to express my view since it seemed incomprehensible. I don’t maintain that I understood everything, but enough to see that this was an outstanding work and to recognize ex ungue leonem. While answering in this sense, I invited the young scholar to visit me (in Marburg) and discussed things with him, strongly advising him to prepare the ground for the understanding of so technical an essay by a more informal essay which should stress the new access to the problem and its fundamental consequences. He wrote such an essay under the title, Eine Axiomatisierung der Mengenlehre, and I published it in 1925 in the Journal für Mathematik (vol. 154) of which I was then Associate Editor."

"I will not attempt to describe John von Neumann's unique abilities, but only say a little about the impression he made on us. The most striking was the enormous speed with which his brain worked. One could believe he already knew beforehand everything one asked him about. A little story illustrates this. Stefan Bergman […] went around and posed a problem to people. If one approached it directly, it required some calculation and the summation of a geometric series. But if one gave it a suitable twist, the solution became immediately apparent. When von Neumann promptly gave the correct answer, Bergman said: "You are the first of those I have asked who did not sum the geometric series." "No!" answered von Neumann, "I summed it.""

"John von Neumann is a kind of legendary mind ... Many people say he's like one of the smartest humans ever."

"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."

"A more interesting activity during that time was my periodic contact with Albert Einstein, who, along with other prominent experts such as John von Neumann, served as a consultant for the High Explosive Division."

"[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."

"That von Neumann was brilliant, perhaps a good deal more than brilliant, had been clear even in childhood."

"He is regarded as one of the giants of modern mathematics."

"One of the great mathematical universalists."

"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."

"Fantastic speed."

"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."

"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."

"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."

"Johnny has a very good mind."

"I think he was a damn fast guy for figuring out what the other guy was doing and explaining it better."

"Several years ago his wife gave him a 21-volume Cambridge History set, and she is sure he memorized every name and fact in the books. “He is a major expert on all the royal family trees in Europe,” a friend said once. “He can tell you who fell in love with whom, and why, what obscure cousin this or that czar married, how many illegitimate children he had and so on.” One night during the Princeton days a world-famous expert on Byzantine history came to the Von Neumann house for a party. “Johnny and the professor got into a corner and began discussing some obscure facet,” recalls a friend who was there. “Then an argument arose over a date. Johnny insisted it was this, the professor that. So Johnny said, ‘Let’s get the book.’ They looked it up and Johnny was right. A few weeks later the professor was invited to the Von Neumann house again. He called Mrs. von Neumann and said jokingly, ‘I’ll come if Johnny promises not to discuss Byzantine history. Everybody thinks I am the world’s greatest expert in it and I want them to keep on thinking that.'”"

"I got to know von Neumann and I thought he was very quick mentally in mathematics and things."

"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."

"At the age of 6 he was able to divide two eight-digit numbers in his head. By the age of 8 he had mastered college calculus and as a trick could memorize on sight a column in a telephone book and repeat back the names, addresses and numbers. History was only a “hobby,” but by the outbreak of World War I, when he was 10, his photographic mind had absorbed most of the contents of the 46-volume works edited by the German historian Oncken with a sophistication that startled his elders."

"One of the world's great mathematicians."

"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."

"Von Neumann was a great mathematician and had the reputation at that time of being the cleverest man in the world. He was supposed to be the intellectual force driving the whole development of computers. He was a great thinker and a great entrepreneur."

"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."

"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."

"Perhaps an even greater genius than Einstein, of almost extraterrestrial brilliance."

"John von Neumann's brilliant mind blazed over lattice theory like a meteor."

"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."

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

"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."

"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."

"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.""

"People would come to him because of his great insight."

"He had always done his writing at home during the night or at dawn. His capacity for work was practically unlimited."

"He stimulated people everywhere. Von Neumann was generous intellectually, because his resources were so enormous, that he never gave away anything that he couldn't do without. He was a fountainhead of information, and he didn't hold back because there was always much more in depth than he ever exposed at one time. I'm not exaggerating. This was indeed how he was. In the few decades that followed, I have had the experience of understanding what this was like, by working as a consultant for some groups who were at a technical level so far below what I knew myself, that what they felt was worth bickering about was in fact possible [?] that one could ignore it, because one knows one has much more in depth than that and that's not an important point. Let them bicker about it, or let them think that they did something great. He was precisely that way. He was in depth, more knowledgeable than any man, and I say this having worked with Wiener for four years, and Wiener was no slouch himself. Von Neumann was a giant. He was ahead of anybody."

"Some people confess guilt to claim credit for the sin."