Mathematicians From Hungary

"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."

"Johnny von Neumann was the greatest mathematician around."

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

"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!"

"Von Neumann was one of the greatest geniuses that ever lived."

"[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 also a delight to be with. His brainpower stuck out in every direction."

"Intellectual brilliance."

"I think that, as , a very clever young Israeli mathematician, once said, "I am an opportunist. I do what I can do." If there is anything in number theory that I can do, I certainly do it. But you see some of the problems in number theory are enormously difficult and many of these classic problems are very, very hard to make any progress in."

"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."

"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."

"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."

"Let n be an integer."

"The first sign of senility is that a man forgets his theorems, the second sign is that he forgets to zip up, the third sign is that he forgets to zip down."

"A mathematician is a machine for turning coffee into theorems."

"God may not play dice with the universe, but something strange is going on with the prime numbers."

"SF means Supreme Fascist — this would show that God is bad. I don't claim that this is correct, or that God exists, but it is just sort of half a joke. … As a joke I said, "What is the purpose of Life?" "Proof and conjecture, and keep the SF's score low." Now, the game with the SF is defined as follows: If you do something bad the SF gets at least two points. If you don't do something good which you could have done, the SF gets at least one point. And if nothing — if you are okay, then no one gets any point. And the aim is to keep the SF's score low."

"This one's from the Book!"

"We'll continue tomorrow — if I live."

"Végre nem butulok tovább"

"It is not enough to be in the right place at the right time. You should also have an open mind at the right time."

"If numbers aren't beautiful, I don't know what is."

"My brain is open!"

"Some French socialist said that private property was theft … I say that private property is a nuisance."

"The SF created us to enjoy our suffering. … The sooner we die, the sooner we defy His plans."

"Television is something the Russians invented to destroy American education."

"Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack."

"Another roof, another proof."

"I'm not competent to judge. But no doubt he was a great man."