Mathematicians From The United States

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

"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.""

"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."

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

"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.”"

"Intellectual brilliance."

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

"[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 one of the greatest geniuses that ever lived."

"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!"

"Finally there came in the mail an invitation from the Institute for Advanced Study: Einstein. . . von Neumann. . .Weyl. . . all these great minds!"

"Johnny von Neumann was the greatest mathematician around."

"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."

"He is really a professional, isn’t he!"

"You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!"

"Our country’s greatest Jancsi."

"In speed and understanding Von Neumann was certainly phenomenal. He could understand a proof even far from his own subject very fast. I remember once in Cambridge I told him a proof of interpolation that was not quite correct. By the time we met again I had a correct proof. Von Neumann told me, “Something seems to be wrong in that proof.” And it was really not his subject. He wasn’t that interested in it, but he was quite right."

"Von Neumann was very impressive to talk with. He was very quick."

"The Alexanders gave humdinger, wonderful parties. I don't know whether they would be regarded as outlandish today, but they were certainly regarded as far out in those days. The phenomenal feature of von Neumann was that he could go to these parties and party and drink and whoop it up to the early hours of the morning, and then come in the next morning at 8:30, hold class, and give an absolutely lucid lecture. What happened is that some of the graduate students thought that the way to be like von Neumannn was to live like him, and they couldn't do it."

"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."

"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."

"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."

"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."

"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."

"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."

"[One early 1945 night,] he woke up and started talking at a speed which, even for him, was extraordinarily fast. “What we are creating now is a monster whose influence is going to change history, provided there is any history left, yet it would be impossible not to see it through, not only for the military reasons, but it would also be unethical from the point of view of the scientists not to do what they know is feasible, no matter what terrible consequences it may have. And this is only the beginning!” The concerns von Neumann voiced that night were less about nuclear weapons, and more about the growing powers of machines. “From here on, Johnny’s fascination and preoccupation with the shape of things to come never ceased,” concludes Klári’s account. For the next seven years he neglected mathematics and devoted himself to the advance of technology in all forms. “It was almost as if he knew that there was not very much time left.”"

"Strange, contradictory, and controversial person; childish and good-humored, sophisticated and savage, brilliantly clever yet with very limited, almost primitive lack of ability to handle his emotions—an enigma of nature that will have to remain unsolved."

"Von Neumann I never could quite figure out. He was just too fast for me."

"Mr. von Neumann, in spite of his youth, is a completely exceptional personality ... who has already done very productive work ... and whose future development is being watched with great expectation in many places."

"He did a tremendous amount of different things in mathematics, many of them revolutionary."

"Bennie decided to approach Johnnie on the matter and arranged to travel to Princeton’s Institute for Advanced Study, headed up at the time by Oppenheimer, where Johnnie (and lesser geniuses such as Albert Einstein) was stationed."

"Now the story doesn't end here. Before going on with it, however, I'd like to introduce you to Johnnie von Neumann, an incredible genius whose mind worked about as rapidly as the super high-speed computers he helped design."

"Genius of the highest order."

"The smartest man in the world."

"Von Neumann was capable of all sorts of remarkable things."

"[He] thought so fast that he very often anticipated what one was going to say. . . . a pleasant agreeable person . . . the amazing logic of his thought processes."

"He was incredibly perceptive."

"He was incredible - the enormous perception that he had. For me, ever since, a standard of comparison has always been von Neumann. And if I say, "He reminds me of von Neumann," that's about the best compliment I can give anyone."

"He was about as likable a chap as you could imagine. There is just one short thing about him. I was riding in a Pullman one day in the lounge car after the war and I hadn't looked about me before I sat down; I was reading something and it had my full attention. From across came von Neumann. He sat down aside me and introduced himself. Well here was the man who, in my opinion, was the most able mathematician in the country in many ways and he felt that he needed to introduce himself to me. That's a type of modesty one can't help liking."

"The manuscripts for both parts of the present volume were unfinished; indeed, they were both, in a sense, first drafts. There is one compensation in this: one can see von Neumann's powerful mind at work."

"Von Neumann was a very great mathematician. He made many important contributions in a wide range of fields."

"The crucial point: in Dr. von Neumann the Institute has perhaps the cleverest man in the world, and the really deciding factor in the end should, I am sure, be what he wants to do."

"The greatest polymath of the 20th century."

"In a Silliman lecture ... John von Neumann, who was dying at the time, wrote some of the most splendid sentences he wrote in all his life ... He pointed out that there were good grounds merely in terms of electrical analysis to show that the mind, the brain itself, could not be working on a digital system. It did not have enough accuracy; or ... it did not have enough memory. ... And he wrote some classical sentences saying there is a statistical language in the brain ... different from any other statistical language that we use... this is what we have to discover. ...I think we shall make some progress along the lines of looking for what kind of statistical language would work."