Paul Erdős also Pál Erdős, in English Paul Erdos or Paul Erdös, (March 26, 1913 – September 20, 1996) was an immensely prolific and famously eccentric Hungarian mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory.
He was born in Budapest, Hungary as Erdős Pál. (Erdős is pronounced as IPA /ɛrdøːʃ/, similar to "Air-dersh" if you say the second syllable non-rhotically.) His parents were non-practising Jews. The Budapest Jewish community of that day produced at least five remarkable thinkers besides Erdős: Eugene Wigner, the physicist and engineer; Edward Teller, the physicist and politician; Leó Szilárd, the chemist, physicist and politician; John von Neumann, the mathematician and polymath; and Georg Lukács, the philosopher. Erdős showed early promise as a child prodigy, and soon became regarded as a mathematical genius by his peers.
Although he was famous and the recipient of many awards, worldly goods meant little to him; and as a philanthropist, he donated most of the money he got from awards or other sources to people in need and various worthy causes. He spent most of his life as a "vagabond," travelling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce "my brain is open," staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom he (Erdős) should visit next. His working style has been humorously compared to traversing a linked list.
As his colleague Alfréd Rényi said, “a mathematician is a machine for turning coffee into theorems,” and Erdős drank plenty of it. After 1971 he also took amphetamines, despite the concern of his friends, who bet him $500 that he could not stop taking amphetamines for a month. Erdős won the bet, but complained that mathematics had been set back by a month. He complained, "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." The bet won, he promptly resumed his habit.
He had his own idiosyncratic vocabulary: he spoke of "The Book," an imaginary book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in The Book." He himself doubted the existence of God, whom he called the "Supreme Fascist" (SF), but accused the SF of hiding his socks, Hungarian passport, and the best equations. When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from The Book!". Other idiosyncratic elements of Erdős' vocabulary include: children were referred to as "epsilons"; women were "bosses"; men were "slaves"; people who stopped doing math had "died"; people who died had "left"; alcoholic drinks were "poison"; music was "noise"; and, to give a mathematical lecture was "to preach." Also, all countries which he thought failed to provide freedom to individuals as long as they did no harm to anyone else were classified as Imperialism and given a name that began with a lowercase letter. For example, the U.S. was "samland" (after Uncle Sam), the Soviet Union was "joedom" (after Joseph Stalin), and Israel was referred to as "israel." For his epitaph he suggested the saying "Finally I am becoming stupider no more" (Hungarian: "Végre nem butulok tovább").
Erdős was one of the most prolific publishers of papers in mathematical history, second only to Leonhard Euler. He wrote around 1,500 mathematical articles in his lifetime, mostly with co-authors, all of them nontrivial. He had about 500 collaborators, and made mathematical collaboration a social activity in a way that changed the way many mathematicians worked.
Of his contributions, the development of Ramsey theory, and the application of the probabilistic method, stand out. Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory.
Among his frequent collaborators were Yousef Alavi, Béla Bollobás, Stefan Burr, Fan Chung, Ralph Faudree, Ron Graham, András Gyárfás, András Hajnal, Eric Milner, János Pach, Carl Pomerance, Richard Rado (one of the co-authors of the famous Erdős–Ko–Rado theorem), Alfréd Rényi, Vojtech Rődl, C. C. Rousseau, Andras Sárközy, Dick Schelp, Miklós Simonovits, Vera Sós, Joel Spencer, Endre Szemerédi, Paul Turán and Peter Winkler.
Because of his prolific output, friends created the Erdős number as a humorous tribute; Erdős alone was assigned the Erdős number of 0 (for being himself), while his immediate collaborators could claim an Erdős number of 1, their collaborators received Erdős number of 2, and so on. Some have estimated that 90% of the world's active mathematicians have an Erdős number smaller than 10 (not surprising in the light of the small world phenomenon). It is jokingly said that Baseball Hall of Famer Hank Aaron has an Erdős number of 1 because they both autographed the same baseball when Emory University awarded them honorary degrees on the same day.
- Erdős–Borwein constant
- Prime number theorem
- Erdős conjectures
- Erdős–Gyárfás conjecture
- Erdős–Ko–Rado theorem
- Erdős–Ginzburg–Ziv theorem
- Erdos–Szekeres theorem
- Paul Hoffman. The man who loved only numbers. Hyperion, 1998. ISBN 0786863625
- Bruce Schechter. My brain is open. Touchstone, 2000. ISBN 0684859807 (biography)
- O'Connor, John J., and Edmund F. Robertson. "Paul Erdős". MacTutor History of Mathematics archive.
- Paul Erdős at the Mathematics Genealogy Project
- N is a Number: a portrait of Paul Erdős
- Jerry Grossman at Oakland University. The Erdös Number Project
- The Man Who Loved Only Numbers - Royal Society Public Lecture by Paul Hoffman (RealVideo)de:Paul Erdős
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