Mathematicians From Hungary

"Young men like Heisenberg himself, Dirac, Wolfgang Paul and John von Neumann were making new discoveries almost every day. This feverish atmosphere is not one in which I function well."

"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."

"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."

"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."

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

"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."

"I spent the rest of 1936 preparing for my trip to the United States, where von Neumann, with whom I had enjoyed friendly relations at least since 1930, had arranged for me to spend the second semester (from January through May, 1937) at the Institute for Advanced Study in Princeton."

"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."

"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."

"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."

"The relationship with Weyl was so close that the 22-year-old student von Neumann finished his lecture on axiomatics in February 1925 when Weyl had to take a health-related leave. In doing so, Weyl reported to the Swiss School Council that von Neumann, alongside Hilbert, was "the most expert among present mathematicians" in this field and that he himself in his lecture had "presented the subject in that form which had emerged from the unpublished investigations of Mr. Neumann.""

"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."

"For Wigner, von Neumann and thinking were synonymous."

"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."

"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."

"I think the choice of von Neumann is clear by the criteria of getting the best mathematical talent in the world."

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

"No one that he had to compete with. But he nevertheless was a terrifically competitive person."

"Johnny was probably the most brilliant star in this constellation of scientists."

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

"I never could keep up with him."

"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."

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

"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."

"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."

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

"His quickness was quite remarkable."

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

"Universal mind."

"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."

"Incredible rapidity."

"Considered the smartest man alive."

"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."

"John von Neumann was one whose talents reached so widely, I could talk to him about the puzzles of the geometry around what we today call a black hole."

"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."

"The two mathematicians now or recently active in America who have adopted a similar point of view are—and I believe not by coincidence—two of the greatest forces in modern mathematics, namely, Hermann Weyl and John von Neumann."

"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."

"He understood mathematical problems not only in their initial aspect, but in their full complexity."

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

"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."

"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."

"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."

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

"He had a real knack for calculatin."

"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."

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