Polymaths

"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."

"Von Neumann was a giant in the breadth of his knowledge."

"Considered the smartest man alive."

"His quickness was quite remarkable."

"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."

"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."

"No other mathematician in this century has had as deep and lasting an influence on the course of civilization."

"There is also no objection to a mathematician’s doing physics, provided he is qualified. The prime example was von Neumann—when he did physics, he talked, thought, and calculated like a physicist (but faster). He understood all branches of physics (including elementary particles as they were known then), and chemistry and astronomy, and he had a talent for introducing those and only those mathematical ideas that were relevant to the physics at hand."

"Nevertheless, it was generally agreed that von Neumann was the leading mathematical mind in the world at that time."

"If someone gave a problem and von Neumann did not give an immediate solution, then it was an unsolvable problem."

"He was a multifaceted genius."

"I think I had some feeling that their minds [von Neumann and Weyl] were so far ahead of mine that it was difficult to follow their thoughts."

"I met him, but in a sense, he didn’t meet me. We were introduced at a game theory conference in 1955, two years before he died. I said, “Hello, Professor von Neumann,” and he was very cordial, but I don’t think he remembered me afterwards unless he was even more extraordinary than everybody says. I was a young person and he was a great star."

"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."

"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."

"John von Neumann was an enormous personality."

"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."

"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."

"Under the force of Courant's plea, Trowbridge reconsidered Hilbert's request; and in the fall of 1926 von Neumann came to Göttingen as a Rockefeller Fellow. The young mathematicians there recognized that he was obviously a prodigy, but some were suspicious of what they saw as a certain “glibness” about him. They also found his mathematics “too abstract” for their taste. “We were wrong about that,” confessed Friedrichs, part of whose later work was to be strongly influenced by the work of von Neumann."

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

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

"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.”"

"Evidence enough has been given for von Neumann’s genius and eminence in pure and applied mathematics."

"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."

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

"The goys have proven the following theorem…"

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

"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."

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

"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."

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

"All the mathematicians I have talked to have said that von Neumann had the quickest mind they ever knew."

"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."

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

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

"If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other."

"When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system."

"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."

"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?"

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

"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."

"One of the world's great mathematicians."

"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."

"Princeton was the place which had all these names—Einstein, Weyl, von Neumann—who were great figures at the time."

"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 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."

"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."

"Nobody doubts that von Neumann was brilliant; everybody admits that."

"Remarkable mathematician."

"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."