Academics From Hungary

""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."

"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."

"Remarkable mathematician."

"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."

"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."

"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.”"

"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."

"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."

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

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

"He was a multifaceted genius."

"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."

"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."

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

"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."

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

"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."

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

"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."

"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."

"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."

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

"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)."

"The smartest person I've ever met."

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

"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."

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

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

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

"Hungarian mathematician Paul Erdős, although an atheist, spoke of an imaginary book, in which God has written down all the most beautiful mathematical proofs. When Erdős wanted to express particular appreciation of a proof, he would exclaim "This one's from the Book!". This viewpoint expresses the idea that mathematics, as the intrinsically true foundation on which the laws of our universe are built, is a natural candidate for what has been personified as God by different religious mystics."

"Nothing bothered Erdős more than political strictures which did not allow for complete freedom of expression and the ability to travel freely. … Always traveling with a single shabby suitcase which doubled as a briefcase, he had little need or interest in the material world."

"Twenty hours of work a day was not unusual. Upon arriving at a meeting, he would announce, in his thick Hungarian accent, "my brain is open." At parties, he would often stand alone oblivious to all else, deep in thought pondering some difficult argument."

"He loved to play silly tricks to amuse children and to make sly jokes and thumb his nose at authority. But most of all, Erdős loved those who loved numbers, mathematicians."

"Want to meet Erdos?" mathematicians would ask. "Just stay here and wait. He'll show up."

"He was the Bob Hope of mathematics, a kind of vaudeville performer who told the same jokes and the same stories a thousand times. … When he was scheduled to give yet another talk, no matter how tired he was, as soon as he was introduced to an audience, the adrenaline (or maybe amphetamine) would release into his system and he would bound onto the stage, full of energy, and do his routine for the 1001st time."

"A conjecture both deep and profound Is whether a circle is round. In a paper of Erdős Written in Kurdish A counterexample is found."

"In the early 1960s, when I was a student at University College London … Erdős came to visit us for a year. After collecting his first month's salary he was accosted by a beggar on Euston station, asking for the price of a cup of tea. Erdős removed a small amount from the pay packet to cover his own frugal needs and gave the remainder to the beggar."

"Paul Erdős (1913–1996) was once told that a friend of his had shot and killed his wife. Without blinking an eye, Erdős said, "Well, she was probably interrupting him when he was trying to prove a theorem.""

"As a mathematician Erdös is what in other fields is called a "natural". If a problem can be stated in terms he can understand, though it may belong to a field with which he is not familiar, he is as likely as, or even more likely than, the experts to find a solution."

"In the late 1980s Erdős heard of a promising high school student named Glen Whitney who wanted to study mathematics at Harvard but was a little short the tuition. Erdős arranged to see him and, convinced of the young man's talent, lent him $1,000. He asked Whitney to pay him back only when it would not cause financial strain. A decade later Graham heard from Whitney, who at last had the money to repay Erdős. "Did Erdős expect me to pay interest?" Whitney wondered. "What should I do?" he asked Graham. Graham talked to Erdős. "Tell him," Erdős said, "to do with the $1,000 what I did.""

"His language had a special vocabulary — not just "the SF" [God] and "epsilon" [child] but also "bosses" (women), "slaves" (men), "captured" (married), "liberated" (divorced), "recaptured" (remarried), "noise" (music), "poison" (alcohol), "preaching" (giving a mathematics lecture), "Sam" (the United States), and "Joe" (the Soviet Union). When he said someone had "died," Erdős meant that the person had stopped doing mathematics. When he said someone had "left," the person had died."

"In a never-ending search for good mathematical problems and fresh mathematical talent, Erdős crisscrossed four continents at a frenzied pace, moving from one university or research center to the next. His modus operandi was to show up on the doorstep of a fellow mathematician, declare, "My brain is open," work with his host for a day or two, until he was bored or his host was run down, and then move on to another home. Erdős's motto was not "Other cities, other maidens" but "Another roof, another proof." He did mathematics in more than 25 different countries, completing important proofs in remote places and sometimes publishing them in equally obscure journals."

"He wrote or co-authored 1,475 academic papers, many of them monumental, and all of them substantial. It wasn't just the quantity of work that was impressive but the quality: "There is an old saying," said Erdős. "Non numerantur, sed ponderantur (They are not counted but weighed)."

"The SF is the Supreme Fascist, the Number-One Guy Up There, God, who was always tormenting Erdős by hiding his glasses, stealing his Hungarian passport, or, worse yet, keeping to Himself the elegant solutions to all sorts of intriguing mathematical problems."

"This book is dedicated to Paul Erdos, who not only possessed the art of asking the right question, but of asking it of the right person."

"Probably the greatest mathematician of the twentieth century, Paul Erdős … was so eccentric that he made Einstein look normal. He was 11 before he ever tied his shoes, 21 before he ever buttered toast, and died without ever boiling an egg. Erdős lived on the road, traveling from conference to conference, owning nothing but math notebooks and a suitcase or two. His life consisted of math, nothing else."

"He was an absolutely wonderful man. He was interested in everything. You felt right away that you are not dealing with one of your colleagues or an average guy. He was a genius, his thoughts were all over the place. I've met very smart people. I have never met a genius before. … He basically disregarded any disciplined approach to anything."

"One of my greatest regrets is that I didn't know him when he was a million times faster than most people. When I knew him he was only hundreds of times faster."

"Paul Erdős is the consummate problem solver: his hallmark is the succinct and clever argument, often leading to a solution from "the book". He loves areas of mathematics which do not require an excessive amount of technical knowledge but give scope for ingenuity and surprise. The mathematics of Paul Erdős is the mathematics of beauty and insight."

"Erdős knows about more problems than anybody else, and he not only knows about various problems and conjectures, but he also knows the tastes of various mathematicians. So if I get a letter from him giving me three of his conjectures and two of his problems, then it's sure that these are exactly the kind of conjectures and problems I'm interested in, and these are exactly the kind of questions I may be able to answer. Of course, this applies not only to me, but to everybody else. So Erdős has an amazing ability to match problems with people. Which is why so many mathematicians benefit from his presence. Every letter is likely to inspire you to do some work, or every phone call will give you some problems you are interested in."