Mathematicians From Hungary

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

"Brilliant mathematician."

"A great mathematician in his or any era."

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

"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.’’"

"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."

"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."

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

"Incredible rapidity."

"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."

"John von Neumann was an enormous personality."

"One of the world's great mathematicians."

"I was absolutely fascinated with von Neumann; I still am."

"It will not be sufficient to know that the enemy has only fifty possible tricks and that we can counter every one of them, but we must be able to counter them almost at the very instant they occur."

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

"Some people confess guilt to claim credit for the sin."

"Keeping up with him was... impossible. The feeling was you were on a tricycle chasing a racing car."

"I was fascinated by whatever von Neumann did."

"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."

"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."

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

"If you say why not bomb them tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?"

"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."

"There probably is a God. Many things are easier to explain if there is than if there isn't."

"As a writer of mathematics von Neumann was clear, but not clean; he was powerful but not elegant. He seemed to love fussy detail, needless repetition, and notation so explicit as to be confusing. To maintain a logically valid but perfectly transparent and unimportant distinction, in one paper he introduced an extension of the usual functional notation: along with the standard \phi(x) he dealt also with something denoted by \phi((x)). The hair that was split to get there had to be split again a little later, and there was \phi(((x))), and, ultimately, \phi((((x)))). Equations such as"

"Genius of the highest order."

"The smartest man in the world."

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

"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."

"If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other."

"One famous story concerns a complicated expression that a young scientist at the Aberdeen Proving Ground needed to evaluate. He spent ten minutes on the first special case; the second computation took an hour of paper and pencil work; for the third he had to resort to a desk calculator, and even so took half a day. When Johnny came to town, the young man showed him the formula and asked him what to do. Johnny was glad to tackle it. "Let's see what happens for the first few cases. If we put n = 1, we get..." -- and he looked into space and mumbled for a minute. Knowing the answer, the young questioner put in "2.31?" Johnny gave him a funny look and said "Now if n = 2, ...", and once again voiced some of his thoughts as he worked. The young man, prepared, could of course follow what Johnny was doing, and, a few seconds before Johnny finished, he interrupted again, in a hesitant tone of voice: "7.49?" This time Johnny frowned, and hurried on: "If n = 3, then...". The same thing happened as before - Johnny muttered for several minutes, the young man eavesdropped, and, just before Johnny finished, the young man exclaimed: "11.06!" That was too much for Johnny. It couldn't be! No unknown beginner could outdo him! He was upset and he sulked till the practical joker confessed."

"I became Johnny’s assistant. How was it? Scary. The most spectacular thing about Johnny was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast."

"Throughout the world mathematicians and others had marvelled at the lightning speed with which von Neumann analyzed and solved complex problems."

"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."

"You wake me up early in the morning to tell me that I'm right? Please wait until I'm wrong."

"He was a superb lecturer. Superb."

"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."

"With four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

"Most of the legends, from childhood on, tell about his phenomenal speed in absorbing ideas and solving problems. At the age of 6 he could divide two eight-digit numbers in his head; by 8 he had mastered the calculus; by 12 he had read and understood Borel’s Théorie des Fonctions."

"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."