Downloaded from rsbm.royalsocietypublishing.org on April 4, 2013 Paul Erdõs. 26 March 1913 −− 20 September 1996 : Elected For.Mem.R.S. 1989 A. Baker and B. Bollobás Biogr. Mems Fell. R. Soc. 1999 45, doi: 10.1098/rsbm.1999.0011, published 1 November 1999 Receive free email alerts when new articles cite this article - sign up in the box at the top right-hand Email alerting service corner of the article or click here To subscribe to Biogr. Mems Fell. R. Soc. go to: http://rsbm.royalsocietypublishing.org/subscriptions Downloaded from rsbm.royalsocietypublishing.org on April 4, 2013 PAUL ERDOS 26 March 1913 — 20 September 1996 Biog. Mems Fell. R. Soc. Lond. 45, 147–164 (1999) Downloaded from rsbm.royalsocietypublishing.org on April 4, 2013 Downloaded from rsbm.royalsocietypublishing.org on April 4, 2013 PAUL ERDOS 26 March 1913 — 20 September 1996 Elected For.Mem.R.S. 1989 B A. B, F.R.S.*, B. B† *Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, UK †Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA, and Trinity College, Cambridge CB2 1TQ, UK In the first part of the twentieth century, Hungary produced an unusually large number of world-class mathematicians. They included, most notably, L. Fejér, A. Haar, F. and M. Riesz, J. von Neumann, G. Pólya, G. Szego , P. Turán and perhaps, above all, the subject of this memoir, Pál (Paul) Erdos. As Ernst Straus put it, Erdos was ‘the crown prince of problem solvers and the undisputed monarch of problem posers’. Erdos was born in Hungary but left his native land when he was 21; from then on he lived in England, the USA, Canada, Israel and many other countries but frequently visited Hungary and had many Hungarian friends. Although he never had a ‘proper’ academic job, through his prodigious output, his host of co-authors, his constant travels and his amazing body of unsolved problems, he has greatly influenced mathematics today. He proved fundamental results in number theory, combinatorics, probability and approximation theory, as well as in set theory, elementary geometry and topology, and real and complex analysis. He was instrumental in the birth of probabilistic number theory and was the main advocate of the use of probabilistic methods in mathematics in general. He was also one of the originators of modern graph theory. He had an exceptional ability for joint work and many of his best results were obtained in collaboration; he wrote altogether about 1500 papers, perhaps five times as many as other prolific mathematicians, and he had about 500 collaborators. Erdos was slightly built, with a somewhat nervous disposition and angular movements. His total dedication to his subject was rare even among mathematicians. He simplified his life as much as possible and lived for his work. He never married and travelled almost all the time, in an age when travel was not the vogue as it is now. He never had a cheque book or credit card, he never learned to drive, and he was happy to travel for years on end with two half-empty 149 © 1999 The Royal Society Downloaded from rsbm.royalsocietypublishing.org on April 4, 2013 150 Biographical Memoirs suitcases. Erdos paraphrased Pierre Joseph Proudhon’s saying ‘La propriété, c’est le vol’ to ‘Property is a nuisance’, and he fully lived up to his belief. For a while he travelled with a small transistor radio but later he abandoned even that. With his motto, ‘another roof, another proof’, he would arrive on the doorstep of a mathematical friend, bringing news of discoveries and problems. Declaring ‘his brain open’, he would plunge into discussions about the work of his hosts and, after a few days of furious activity of ‘proving and conjecturing’, he would take off for another place, leaving his exhausted hosts to work out the details and to write up the papers. In addition to producing an immense body of results, Erdos contributed to mathematics in three important ways: he championed elementary and probabilistic methods and turned them into powerful tools; and, above all, he gave the mathematical world hundreds of exciting problems. Although he never had any formal research students, he nevertheless created a great international school of mathematics and his legacy will be of fundamental importance for many years to come. E ’ Childhood, 1913–30 Paul Erdos was born into an intellectual Hungarian-Jewish family on 26 March 1913, in Budapest, amid tragic circumstances; when his mother returned home from the hospital with the little Paul, she found that her two daughters had died of scarlet fever. Both his parents were teachers of mathematics and physics; his father was born Louis (Lajos) Engländer (1879–1942) but changed his name to the Hungarian Erdos (‘of the forest’, a fairly common name in Hungary), and his mother was born Anna Wilhelm (1880–1972) who, by family tradition, was a descendent of the renowned scholar and teacher Rabbi Judah Loew ben Bezalel of Prague. Paul was only a year and a half old when World War I broke out; the first great offensive by the Austro-Hungarian armies quickly turned into a disaster for the invaders and many Hungarians were taken prisoner by the Russians. Among them was Lajos Erdos, who returned home from his prisoner-of-war camp in Siberia six years later. In the absence of his father, the young Erdos was brought up by his mother and a German Fräulein; understandably, throughout her life, Erdos’s mother felt excessively protective towards her son and there was always an unusually strong bond between them. In 1919, at the end of the war, the Hungarian government could not accept the harsh demands of the victorious Entente and, in the turmoil that followed, a Dictatorship of the Proletariat was proclaimed. Practically the entire economy and cultural life were placed under state supervision and everything was run by Revolutionary Soviets. Erdos’s mother was a member of the Soviet running her school; the Dictatorship collapsed after four and a half months and, in the ensuing counter-revolutionary terror, she was dismissed from her job and could never teach again. It is not surprising that this traumatic experience shaped Erdos’s political outlook and throughout his life he remained sympathetic towards the left in every shape or form. Erdos was a child prodigy; at the age of three he could multiply three-digit numbers, and at the age of four he discovered negative numbers on his own. At the fashionable spa to which his mother took him, he would ask the guests how old they were and tell them how many Downloaded from rsbm.royalsocietypublishing.org on April 4, 2013 Paul Erdo s 151 seconds they had lived. His mother was so worried that he would catch diseases at school that for many of his school years he was educated at home, mostly by his father, who taught him not only mathematics and physics, but English as well. As his father never really spoke English, having learned it from books, the young Erdos acquired a somewhat idiosyncratic pronunciation. Besides German and English, he learned French, Latin and Ancient Greek; later in life he picked up a smattering of Hebrew. Erdos spent two brief periods in school: first in the Tavaszmezo Gymnasium and then in the St Stephen Gymnasium, where his father taught for a while. In addition to his parents, an important influence in nurturing and developing his interest in mathematics was the journal Középiskolai Matematikai és Fizikai Lapok. This was founded by the young teacher Dániel Arany in 1893 as a mathematical monthly for high schools; it specializes in publishing problems of various levels of difficulty. Model solutions to the problems appear subsequently and the photographs of the best solvers are published in the final issue of the year. The readers are encouraged to generalize and strengthen the results and thus the journal provides an exciting introduction to mathematical research. Erdos and many of his later friends were avid readers and cut their mathematical teeth on the challenging problems. A photograph of Erdos appeared in each of his high school years; moreover, a model solution published under the names of Paul Erdos and Paul Turán (1910– 76) was his ‘first joint paper’. Turán met Erdos only some years later and he went on to become one of his closest collaborators and best friends. University, 1930–34 In 1930, at the age of 17, Paul Erdos entered the Pázmány Péter Tudományegyetem, the science university of Budapest founded in 1635, and soon became the focal point of a small group of extremely talented mathematicians, all studying mathematics and physics. The group included Turán, Dezso Lázár, György Szekeres, Eszter Klein, László Alpár, Márta Svéd and others: they discussed mathematics not only at the university but also at regular meetings in the afternoons and evenings, and went for day-long excursions in the mountains near Buda and the parks of Budapest. One of their favourite meeting places was a well-known landmark of Budapest, the Statue of Anonymus, the chronicler of Béla III (1173–96). It was during this period that Erdos started to develop his own special language: he called a child an epsilon, a woman a boss, a man a slave; Sam (or better still, sam) was the USA and Joe (or joe) was the Soviet Union, and so on. In his words, a slave could be captured and later liberated, one could drink a little poison and listen to noise, and a mathematician could preach, usually to the converted. In the course of his regular studies at the university, Erdos learned most from Lipót (Leopold) Fejér (1880–1959), one of the founders of harmonic analysis, and Dénes (Dennis) König (1884–1944), the author of the first book on graph theory (König 1936).