Reminiscences of Paul Erdös (1913-1996) Melvin Henriksen Harvey Mudd College

Humanistic Mathematics Network Journal Issue 15 Article 7 7-1-1997 Reminiscences of Paul Erdös (1913-1996) Melvin Henriksen Harvey Mudd College Follow this and additional works at: http://scholarship.claremont.edu/hmnj Part of the Mathematics Commons Recommended Citation Henriksen, Melvin (1997) "Reminiscences of Paul Erdös (1913-1996)," Humanistic Mathematics Network Journal: Iss. 15, Article 7. Available at: http://scholarship.claremont.edu/hmnj/vol1/iss15/7 This Article is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted for inclusion in Humanistic Mathematics Network Journal by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Reminiscences of Paul Erdos (1913 01996) Melvin Henriksen HalVey MuddCollege Claremont CA 91711 [email protected] Reprinted from theMathematicalAssociation of America website: htlp:llwww.maa. orgJfeatureslerdos.html I met Paul Erdos shortly after his 40th birthday inApril and perhaps because two older sisters died of scarlet 1953 a t Purdue University in West Lafayette, Indiana. fever shortly before he was born, his parents shielded Hewas already a living legend becau se of his substan him almost comp letely from the everyday problems tial contributions to the theory of nu mbers, the theory of life. For example, he never had to tie his own shoe of sets, what is now called discrete mathematics, as laces un til he was 14 years old, and never buttered we ll as to many other areas of mathematics. (For ex his own toast un til he was 21 years old in Cambridge, ample, although he had little interest in topology, his England . In return for the freedom to concentrate al name appears in most topology texts as the first per most exclusively on intellectual pursuits, he paid the son to give an exam ple of totally disconnected topo price ofno t learni ng the social skills tha t are expected logical space that is no t zero-dimensional.) I was a 26 of all of us and usually acquired in childhood . year old instructor in my first year at Purd ue. Many of my colleagues knew him well. He had been a visit He became intern ationally famous at the age of 20 ing research associate at Purdue for a coup le of yea rs when he got a simple proof of a theo rem that was origi during World War II, and had visited so many uni nally conjectured by Bertrand and later proved by versities and atten ded so many conferences that he Tchebychev: For every positive integer n, there is a was well known to most of the others. Those that were primebetween n and 2n.Tchebychev's proof was qui te active in research admired his ma thematical accom hard! Erdos completed the requirements for the Ph.D. plishments, while others on the facu lty were amused at the University of Bud apest about a year later, but by his eccentricities. What I remember most clearly is had no chance of getting a position in Hungary be his announcement to everyone that "death begins at cause he was a Jew living und er a right wing dicta 40". torship allied with Nazi Germany. He spent some time at Cambridge University in 1935. There, his life as a I am not qualified to write a biography of Erd os, but wande ring mathematician began. In fact, he had vis some background seems necessa ry. There is an excel ited Cambridge three times the year before. He liked lently written and accurate obituary of him by Gina traveling and had no trouble working while doing so. Kolata in the Sept. 21, 1996 issu e of the New York He liked people, and excep t for those who could not Times, beginning on page 1. An interview conducted tolerate his ignoran ce of the social graces, they liked in 1979 which reveals much of his personality ap him. He tried his best to be pleasant to everyone an d peared in the volume Mathematical People edited by was generous in giving cred it and respect to his col D.J. Albers an d G.L. Alexanderson (Birkhauser 1985). laborators. The MathematicalAssociation ofAmerica (MAA) sells two videos of Erdos, and Ronald Graham, a long time I do not know when he first came to the United States, collabora tor, has edited together with [arik Nesetril but he spent the yea rs of World War II here, two of two volumes on his mathematical work and life. (Both them at Purdue. Nor can I give a list of the many uni volumes have been published by Springer-Verlag and versities he visited for any substantial length of time. were available in January 1997. They include a de By the time I met him, he had written joint papers tailed biographical article by Bella Bollobas.) with many mathematicians most of who m had estab lished research reputations before working w it h Erdos was born in Budapest in 1913 of p arents who Erdos. The only Erd os collaborator who worked with were Jewish intellectuals. His brilliance was evident him unwillingly was Atle Selbe rg. In the late 1940s, by the time he was three years old . For thi s reason, both of them, working independently, had obtained Humanistic Mathematics NetworkJournal #15 13 "elementary" proofs (meaning: proofs that did not use sphere. complex analysis) of the prime number theorem. The theorem states that the number of primes less than or At that time, Leonard Gillman and I were trying to equal to (a positive real number) x is asymptotically study the structure of the residue class field s of rings equal to x/Iogfr ). This had been conjectured by Gauss of real-valued continuous fun ctions on a topological and Legendre based on empirical data, butit had only space modulo maximal ideals. We had learned quite been proved many years later, by two French math a bit about them, but had run into serious set-theo ematicians, Jacques Hadamard and Ch arles de la retic difficulties. Erdos had little interest in abstract Vallee Poussin (also working independently). Both algebra or topology, but was a master of set-theoretic proofs depended heavily on complex analysis. What constructions. Without bothering him with our moti Selberg and Erdos did in their "elementary" proofs vation for asking them, we asked him a series of ques was to avoid using complex analysis (the proofs were tions abou t set theory, which he managed to answer in no sense "easy"). In those pre-email days, the fast while we could not. est courier of mathematical news was Paul Erdos. He told anyone who would listen that Selberg and he had He was no t terribly interested when we supplied him dev ised an elementary proof of the prime number with the motivation, and I have often said tha t Erdo s theorem. never understood our paper; all he did was the hard part. This paper by Erdos,Gillman and Henriksenwas Almost every number theorist knew of Erdos, while published in the Annals of Mathema tics in 1955. With few had heard of the young Norwegian Selberg. So out any of us realizing it in advance, itbecame one of when the news traveled back to Selberg, it appeared the pioneering papers in nonstandard analysis, and that Erdos had claimed all the credit for himself. The was often credited to Erdos, et al. ensuing bitterness was not healed by the two of them Erdos got an offer allowing him to stay indefinitely at writing a joint paper. Selberg later published another Notre Dame on the same generous basis. His friends elementary proof on his own,and went on to a bril urged him to accept. "Paul", we said "how much liant mathematical career, eventuallybecoming a per longer can you keep up a life of being a traveling manent member of the Institute for Advanced Study mathematician?" (Little did we suspect that the an in Princeton, the Valhalla for mathematicians. Erdos swer was going to tum out to be "more than 40 years.") had been a visitor there earlier, but was not offered a Erdos thanked Ross, but turned him d own. As it member ship. Exactly whathappened is controversial turned out, he would not have been at Notre Dame to this day, and reading the articl e by Bollobas will the next year whatever his answer had been. shed more light on this matter than this short sum mary can. The cold war was in full swing, the United States was in the grip of paranoia about communism, and many Erdos spent the academic year 1953-54 at the Univer regarded unc onventional behavior as evidence of dis sity of Notre Dame in South Bend, Indiana. Arnold loyalt y. Erdos had never applied for citizenship any Ross, the chairman of the Mathematics Depa rtment, where he lived, and had acquired Hungarian citizen had arranged for him to teach only one (advanced) ship only by accident of birth. He belonged to no po course, and supplied an assistant who could take over litical party, but had a fierce belief in the freedom of his class if he had the urge to travel to talk with a col ind ividuals as long as they did no harm to anyone laborator. Erdos had rejected organiz ed religion as a else. All countries who failed to follow this were clas young man, an d had be en persecuted in Roman sified as imp erialist and given a name that began with Catholic Hungary. So we teased him about working a small letter.

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