Mathematicians From The United States

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

"I never could keep up with him."

"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 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."

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

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

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

"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."

"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."

"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 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."

"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.’’"

"Brilliant mathematician."

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

"He was a superb lecturer. Superb."

"His contributions to physics, mathematics, computer science, and economics rank him as one of the all-time intellectual giants of each field."

"If any one person in the previous century personified the word polymath, it was von Neumann."

"One of the century’s most esteemed scientists."

"Neumann was undoubtedly a genius. This meant among other things that be was able to learn a new subject in an incredibly short time. Before designing the computer, he took two weeks off to learn electronics, thus became able to supervise the construction of the hardware."

"I was a graduate student—he was one of the great mathematicians of the world."

"The smartest person I've ever met."

"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)."

"But when you were in real thinking trouble, you would go to von Neumann and nobody else."

"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."

"Comparing this work with the habilitation thesis, one recognizes in how outstanding and promising a manner the highly gifted young researcher combines the ability for far-reaching abstraction with a powerful sense for constructive work and also for the advancement of concrete problems."

"The author, who through his previous mathematical achievements has already placed himself in the forefront of German mathematicians, is only 23 years old and completed his studies in chemistry at the Eidgenössisches Polytechnikum in Zurich with the diploma examination. He combines penetrating abstract acumen with an astonishing speed in the productive assimilation of large bodies of scientific knowledge. This is undoubtedly an altogether extraordinary talent, which justifies unlimited hopes."

"A man so smart that he saw through himself."

"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."

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

"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."

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

"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."

"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."

"He was a multifaceted genius."

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

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

"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."

"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."

"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.”"

"Von Neumann was a calculating prodigy as well. He could divide two eight-digit numbers in his head with little effort. Cuthbert Hurd of IBM told me of von Neumann’s uncanny ability to create and revise computer programs (as long as fifty lines of assembly-language code!) in his head."

"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."

"Remarkable mathematician."

"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."

""Johnny" von Neumann, as he was always known among scientists, achieved fame first of all as a pure mathematician. I am not qualified to describe his contributions to pure mathematics, which usually related to the most recent, and most abstruse, branches of the subject at the time, but they certainly placed him among the leaders of modern mathematics. In the 1920s, he was interested in the development of quantum mechanics, then in rapid growth, which caused difficulty to many because of the bold use of new mathematical techniques. Von Neumann contributed greatly to making this new subject "respectable"; he pointed out the precise mathematical significance of the new developments and, at the same time, helped greatly to clarify the physical content of the new ideas. He was, in fact, quicker than many physicists in grasping the changes that were then taking place in physics Later he was a frequent visitor to the Atomic Weapons Project at Los Alamos. Here his particular quality of combining powerful mathematical insight with a very practical interest in the problems became familiar to all those associated with the project. He was never satisfied with showing that a problem could be solved on paper, but he took a personal interest in its quantitative application and in its practical realization. His many contributions, particularly to the hydrodynamics of shock waves and detonation waves, which are important both in the design of atomic weapons and in an understanding of their effects, were vital to the success of the project. For a man to whom complicated mathematics presented no difficulty, he could explain his conclusions to the uninitiated with amazing lucidity. After a talk with him one always came away with a feeling that the problem was really simple and transparent. About the same time, he became interested in the application of computing techniques to mathematical problems, and this led him to design the computer now in operation at Princeton and to planning out its applications both to practical problems and to abstract problems in nonlinear equations. He was the antithesis of the conventional image of the "long-haired" mathematics don. Always well-groomed, he had as lively views on international politics and practical affairs as on mathematical problems. His book on the Theory of Games, "including the theory of bluffing at poker," which has proved fruitful for many applications going beyond the field of games of chance and skill, is another example of the happy combination of his command of mathematics with an interest in practical matters. For the last few years, he was a member of the Atomic Energy Commission, and it is worth recording that in a field beset with much controversy, he retained the universal respect and confidence of those who did not agree with his views on policy as well as those who did."

"If doing physics meant proving theorems, you’d be a great physicist."

"Von Neumann's reputation and fame have grown steadily since his death. His fantastic brain, and the breadth of his interests and undertakings, have become almost legendary."

"In my life I have met men even greater than Johnny, but none as brilliant. He shone not only in mathematics but was also fluently multilingual and particularly well-versed in history. One of his most remarkable abilities I soon came to note was his power of absolute recall."

"Morgenstern was once asked how a scholar outside the mainstream of economic thinking could make a contribution as original, innovative, and decisive as Johnny's. He replied that Johnny had an extraordinary capacity for picking the brains of a person whom he engaged in casual conversations. Once he saw from these that there was a problem of sufficient mathematical interest to warrant his spending time on it, he homed on to that subject like a guided missile."

"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."