Quotations on Paul Erdős


My notions of historiography have been influenced by Carlyle's "On heroes and hero-worship"[...] One of our heroes is the embodiment of our virtues, although he might not appear heroic in other subcultures. I refer to Paul Erdős whose contribution to the Monthly and to Association meetings we appreciate along with his brilliant achievements in research. Erdős combines creativity and honesty with generosity and humility, extraordinary mathematical talent with exceptional human feeling. With unusual breadth in mathematics he is able, and ready, to help anyone with a question. He can always find something good to say about te mathematics of a fellow human being, even though he may despise his politics.

It seems a long time since Erdős appeared at the Swartmore meeting after Christmas of 1946, newly returned from the clothing store to which a group of friends had dragged him, attired in a brand new suit which somehow already looked slept in. There he stood, smiling gently at his friends silly concern—he didn't resent the time which might have been wasted—he had thought about a mathematical problem throughout the merchandising transaction... (R.A.Rosenbaum: History of the MAA since World War II, American Mathematical Monthly, 74(1967), Jan. 12-22.)


Erdős is somewhat below medium height, an extremely nervous and agitated person. At that time [1941] he was even more in perpetual motion than now—almost constatly jumping up and down or flapping his arms. His eyes indicated he was always thinking about mathematics, a process interrupted only by his rather pessimistic statements on world affairs, politics, or human affairs in general, which he viewed darkly. If some amusing thought occurred to him, he would jump up, flap his hands, and sit down again. (Stanislav M. Ulam: Adventures of a Mathematician)
It is an understatement to say that I have learned a lot from him, not only mathematics in the technical sense, and not even only elements of the fine art of problem solving, but also his way of pursuing knowledge: complete opennes in problems and partial results, which necessarily leads to collaboration and a wider perspective. This was especially great for students: those problems were fresh out of the oven, and you had a chance to solve one or the other with an open mind and some luck. And if you were able to solve one of his problems, your result would be made known in a matter of days all over the world. Sitting in the hotel lobby as a student, one could observe mathematics in the making, and witness the development of whole fields like finite and infinite Ramsey theory, combinatorial set theory, random graphs, or combinatorial number theory. (László Lovász, 1993)
Erdős and his collaborators have left an indelible mark on the mathematics of the 20th century. The areas of probabilistic number theory, partition calculus for infinite cardinals, extremal combinatorics, and the theory of random graphs have all practically been created by Erdős, and no-one has done more to develope and promote the use of probabilistic methods throughout mathematics.

Erdős is the mathematician par excellence: he thrives on mathematics, living in a state of continuous excitement; he raises, answers and communicates questions, picking up the problems of others and making incisive contributions to them with lightning speed.

For over sixty years now, Erdős has been the world's most celebrated problem solver and problem poser, unrivalled, king, non-pareille, ... He has been called an occidental Ramanujan, a modern-day Euler, the Mozart of mathematics. These glowing epithets accurately capture the different faces of Paul Erdős—each is correct in its own way. He has a unique talent to pose penetrating questions. It is easy to ask questions that lead nowhere, questions that are either impossibly hard or too easy. It is a completely different matter to raise, as Erdős does, innocent-looking problems whose solutions shed light on the shape of the mathematics landscape. (Béla Bollobás: Paul Erdős—Life and Work)


Rien de ce que fait Erdős n'est facile; c'est toujours extrêmement astucieux. [Nothing that Erdős does is easy; it is always extremely ingenious.] (Dieudonné)
"Szekeres Gy., open up your wise mind." This was Paul's customary invitation—or was it an order?—to listen to a proof or a problem of his. Our discussions centered around mathematics, personal gossip, and politics. It was the beginning of a desperate era in Europe. Most of us in the circle belonged to that singular ethnic group of European society which drew its cultural heritage from Heinrich Heine and Gustav Mahler, Karl Marx and Cantor, Einstein, and Freud, later to becom the principal target of Hitler's fury. (G. Szekeres)
When Uncle Paul arrives at the Budapest airport nowadays, and gets through visa formalities, a large group of young and not so young mathematicians is waiting for him. After a few steps he starts sorting out presents from the plastic bags, while asking questions about our relatives, discussing healt problems of mathematician friends we do not always know (say, from New Guinea), questions about departmental politics intermingled with remarks about the serious situation perhaps in Tanzania or giving partial results on a conjecture of Graham's. We slowly get to the car, while he is still asking questions, addressing Miki as Vera, Vera as Laci, and so on. By the time we get to his quarters, he immediately makes five phone calls, with the bags partially unpacked. The all-engulfing old atmosphere of mathematics prevails, and we are all deeply involved with the problems he has already suggested.

It is always fascinating to work with him. He has a fantastic insight, an intense curiosity, and a drive to discover all facts about the subject we are working on. Those who do not know him well, might think he is trying to make a list of all possible theorems. We have seen it many times, that answers to tiny and seemingly unimportant questions which he raised when we were just trying to finish a paper, later turned out to be pertinent to other important problems. Many of them helped to answer questions which were unsolved for years.

Alfréd Rényi, one of his best friends, once said that Paul must have a contract with the devil.
(Andras Hajnal, Vera T. Sós: Paul Erdős is Seventy)


Erdős's way of thinking was very close to the ideas of the French Enlightement. He believed deeply that all great problems facing mankind have rational solutions. In his own way, he always tried to do everything to further the truth. As a profane extension of an idea from Anatole France's novel, Revolt of the Angels, he liked to call Fate the "Supreme Fascist". (Fascism had been the determining experience of his younger years, so it is not suprising that he used it as a metaphor for Evil.) He said, more or less as a joke, that life was a game in which our opponent was the Supreme Fascist (S.F.). The S.F. gets two points if we do some thing mean and one point if we fail to do good. In this game, only the S.F. can win, but it should be our goal to keep his score low. (János Pach: Two places at once)

Erdős feels that he "should have invented" Extremal Graph Theory, back in 1938. He has failed to notice that his theorem was the root of an important and beautiful theory. 2-3 years later Turán proved his famous theorem and right after that he posed a few relevant question, thus initiating a whole new branch of graph theory. Erdős often explains his "blunder" by telling the following story.

Crookes observed that leaving a photosensitive film near the cathod-ray-tube causes damage to the film: it becomes exposed. He concluded that "Nobody should leave films near the cathod-ray-tube." Röntgen observed the same phenomenon a few years later and concluded that this can be used for filming the inside of various objects. His conclusion changed the whole Physics. (When I asked Paul, why did he think that Röntgen's discovery changed the whole Physics, he answered that Röntgen's findings had led to certain results of Curie and from that point it was only a short step to the A-bomb.) "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," Paul concludes his story. (Miklós Simonovits: Paul Erdős' Influence on Extremal Graph Theory)


I first met Erdős the day that the atomic bomb was dropped on Hiroshima. I worked in the ballistic research laboratory at that time. Among my colleagues were several world class mathematicians (one was a corporal and another was a sergeant). They were, of course, Erdős' friends and they were regular stops in his world travels.

When we heard the news about the atomic bomb a great shout went up and we rushed to the roof of the laboratory to celebrate. I was delighted because the fantasy of atomic power had come true, because the war was now over and I would be able to go back to school, and because the Japs got what was coming to them.

To my surprise Erdős, who was always so cheerful, pointed out that there was much to mourn. We had placed incredible power in the hands of people who could not understand it and who would use it only for conquest. Many civilians had been killed. The horror of Hiroshima did not erase the horror of Pearl Harbor. On the contrary the effect was additive. He pointed out that we could have demonstrated the power of the bomb on an unoccupied island.

He was very persuasive. And he has guided my thinking on many topics since that day. Sometimes in person, sometimes I just ask myself "what would Erdős think of that."

(Gustave Rabson)
From our first encounter, Erdős has been a constant inspiration to me to engage in mathematics. When later I contemplated leaving mathematics to go to the Technical University and become an engineer, Erdős said: "I'll hide and when you enter the gate of the Technical University, I will shoot you." This settled the issue. (Andrew Vázsonyi)
At that time he espoused the cause of China—not then "Red China"—and used to raise quite a bit of money by volunteering to drink small quantities of "poison" (i.e., alcoholic beverages) for so many dollars for China. (Nowadays the U.S. custom for raising money for good causes is for volunteers to walk so many miles at so much per mile, paid for by other volunteers. This at least encourages a healthier lifestyle.) (A. H. Stone: Encounters with Paul Erdős)
When I asked György Szekeres not so long ago, how and when Erdős became interested so much in number theory, his answer was: in the crib. (Vera T. Sós)
No one can state Erdős' first conjecture—I would not be surprised if it was his frist meaningful sentence, as a child. (Paulo Ribenboim: Catalan's Conjecture, Academic Press, 1994, p. 325)
Erdős was famous for anticipating the "right" results. "This is obviously true; only a proof is needed" he used to say quite often. Most of the times, his conjectures turned to be true. Some of his conjectures failed fot the more or less trivial reason that he was not always completely precise with the formulation of the problem. However, it happened only very rarely that he was essentially wrong with his conjectures. If someone proved something that was in contrast with Erdős' anticipation, he or she could really boast to have proved a really surprising result. Erdős was always honest with his conjectures. (Tamás Erdélyi)
It is clear that he has founded a unique school of mathematical research, international in scope, and highly visible to the world at large. (D. Goldfeld: The elementary proof of the prime number theorem: an historical perspective)
I knew Erdős's mother—a remarkable woman. Everybody used to ask her to help if they wanted to reach Paul. Paul traveled so much that the only way to find out where he was, was to call his mother. Whenever I had to write to Paul about something urgent, I would write to her to find out where he was traveling, and then on the basis of that information I would choose five places and write to each one of them. Paul entered into the spirit of this. He answered every one of my letters. (Interview with Arnold Ross, Notices of the AMS, 48(2001), August, 691-698.)
Things won't be the same without Uncle Paul. (Vojtech Rödl)
To find another life this century as intensely devoted to abstraction, one must reach back to Ludwig Wittgenstein (1889-1951). But whereas Wittgenstein discarded his family fortune as a form of self-torture, Mr. Erdős gave away most of his money he earned because he simply did not need it ... And where Wittgenstein was driven by near suicidal compulsions, Mr. Erdős simply constructed his life to extract the maximum amount of happiness. (The Economist, October 5th 1996, page 83.)