Mathematicians From Hungary

""Johnny," as all his friends called him, was the only scientist of the era to whom the word "genius" was almost universally applied. He had an uncanny ability to handle complex mathematical calculations in seconds. When he was six years old he could divide one eight-digit number into another, entirely in his head."

"Then, of course, there was Neumann, who always knew everything anyhow."

"Weyl had a very tremendous respect for him, and I could see in this advanced, seminar when Weyl didn't know the answer he would say, "Neumann, how does that go?" We all realized this was a great mathematician."

"His effectiveness was largely due to his ever-present mental manipulatory quickness. He could literally "think on his feet," and much of his best work may have received its initial impulse in just this way. He had a prodigious memory, and legend has it that he knew all the facts and dates from many volumes of standard histories by heart."

"He was also a great reader of books on history throughout his life, and in both science and history his retentive memory was most remarkable."

"It was also well remembered about 25 years later by one of his colleagues here at the time, M. Plancherel, who mentioned it to me then as an example of the extraordinary ability H. Weyl had, shared only by J. von Neumann among the mathematicians he had known, to get into a new subject and bring an important contribution to it within a few months."

"Von Neumann was considered the leading mathematician in the United States."

"Great mathematician."

"He would seize on the fuzzy notions of others and, by dint of his prodigious mental powers, leap five blocks ahead of the pack. “You would tell him something garbled, and he’d say, ‘Oh, you mean the following,’ and it would come back beautifully stated,” said his onetime protégé, the Harvard mathematician Raoul Bott."

"Von Neumann is a great scientific hero to me because it seemed… he seemed to have something. And of course it may be envy rather than admiration, but it's good to envy someone like von Neumann."

"Mathematics is not a pompous activity, least of all in the hands of extraordinarily fast and penetrating minds like Johnny von Neumann."

"There was something endearing and personal about Johnny von Neumann. He was the cleverest man I ever knew, without exception. And he was a genius, in the sense that a genius is a man who has two great ideas. When he died in 1957 it was a great tragedy to us all."

"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."

"The greatest polymath of the 20th century."

"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."

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

"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."

"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."

"He was a superb lecturer. Superb."

"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 incredibly perceptive."

"[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."

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

"The smartest man in the world."

"Genius of the highest order."

"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."

"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."

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

"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."

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

"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."

"[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.”"

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

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

"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."

"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."

"Perhaps an even greater genius than Einstein, of almost extraterrestrial brilliance."

"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."

"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."

"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 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 got to know von Neumann and I thought he was very quick mentally in mathematics and things."

"I think he was a damn fast guy for figuring out what the other guy was doing and explaining it better."

"Johnny has a very good mind."

"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."

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

"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."

"Our country’s greatest Jancsi."

"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!"

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