Polymaths

"Many mathematicians have suffered in fact by comparing themselves with von Neumann."

"Universal mind."

"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."

"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."

"It is indeed supremely difficult to effectively refute the claim that John von Neumann is likely the most intelligent person who has ever lived."

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

"His quickness was quite remarkable."

"The extensive work Mathematische Begründung der Quantentheorie also testifies to the extraordinary talent of the author in the appropriation and assimilation of a large area of material."

"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."

"Other smart people commonly said that John von Neumann was the smartest person they had ever known. Although I worked with him for only five years—1952-57, and even then on just an occasional basis—I came to know him well enough to feel the same way. His accomplishments generally confirmed this view."

"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."

"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."

"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."

"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."

"Incredible rapidity."

"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."

"Von Neumann was extremely intelligent, and curious about everything. He looked like a cherub and sometimes acted like one; my three and 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."

"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."

"I feel that Weyl and von Neumann were the greatest mathematicians that I have known."

"Many people have wondered how Johnny von Neumann could think so fast and so effectively. How he could find so many original solutions, in areas where most people did not even notice the problems. I think I know a part of the answer, perhaps an important part, Johnny von Neumann enjoyed thinking. 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 a suspicion that he enjoyed practically nothing else. This explains a lot, because what you like, you do well. And he liked thinking, not just in mathematics. He liked thinking in the clear and complete manner of mathematicians, in every field; in mathematics, in physics, in the business world - his father was a banker - and in many other fields. 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. This also explains his effectiveness in connection with computing machines, because computing machines apply logical processes to fields: not only mathematics, but to others as yet untouched by the logical process. And it is very significant that this revolution, the revolution of the electronic brains, was practically initiated by Johnny von Neumann. I cannot think of Johnny now without remembering a very tragic circumstance when he was dying of cancer. His brain was affected. I visited him frequently and he was trying to do what he always tried to do. And he was trying to argue with me as he used to and it wasn't functioning anymore. And I think that he suffered from this loss more than I have seen any human to suffer in any other circumstance."

"I never could keep up with him."

"[Addressing Banesh Hoffmann] He also thought very fast."

"I'm sure that von Neumann threw off lots of ideas, as he went about, that led to Ph.D. theses."

"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."

"Johnny was the most versatile and brilliant scientist I have ever known. His mind operated at speeds that suggested neural superconductivity."

"I believe that if a mentally superhuman race ever develops, its members will resemble Johnny von Neumann."

"That deep, practically monomaniacal devotion to the thinking process is what set Johnny von Neumann apart from everyone else I have ever known."

"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."

"When Ratz saw how intelligent Jancsi was, he began giving him private lessons. . . . [Ratz] felt so privileged to tutor a phenomenon like Jancsi that he refused any money for it. His compensation was more subtle: the brush with a special kind of mind; the privilege of training that mind in a discipline that both of them loved."

"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."

"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."

"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."

"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."

"His memory and unlimited scope of universal interests was amazing. At that time we probably did not attach any further significance to this, nor did we evaluate or even could have evaluated the incredible multiplicity and diversification of the innumerable subjects so discussed. But later, perhaps decades later, many of these subjects reappeared in his scientific work (directly, or in the background), and he had no difficulty in recovering these or related ideas from his memory as they became relevant in specific instances."

"The first thing that people recall about John von Neumann is his phenomenal speed of thought. He didn’t have to remember things; he computed them. If he was asked a question and didn’t know the answer, he would think for three seconds and produce a response. Yet, fast thinking was not his most outstanding characteristic. He was also very deep. It is the breadth of his scientific heritage that amazes me the most."

"I think that in terms of mathematical intelligence, he was virtually unparalleled."

"Brilliant mathematician."

"John von Neumann was one of the greatest mathematicians of the 20th century."

"A great mathematician in his or any era."

"Von Neumann was exceptionally widely known among mathematicians, and there are plenty of anecdotes related to him. I think that as a student, I heard from my professor A. Rényi the saying: ‘‘Other mathematicians prove what they can, Neumann what he wants.’’"

"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."

"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."

"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."

"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."

"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."

"Johnny was a most unusual person, a marvellously quick thinker, and was recognized as such in high school."