Paul Erdos (March 26, 1913 – September 20, 1996) was an immensely prolific and famously eccentric 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 (pronounced "Air-dersh", SAMPA /errd9:S/), into a non-practicing Jewish family. 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 Renaissance man, 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, 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. Worldly goods meant little to him, and he gave away most of the money he got from awards or other sources to people in need and various worthy causes.
He once famously said "A mathematician is a machine for converting coffee into theorems", and he 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. He won the bet, but complained that mathematics had been set back for 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 (although he was an atheist and playfully referred to God as the "Supreme Fascist"). Children were referred to as "epsilons", women were "bosses", men "slaves". People who stopped doing math had "died"; people who died had "left". To give a mathematical lecture was "to preach". His self-suggested epitaph was "Finally I am becoming stupider no more".
Erdős was one of the most prolific publishers of papers in mathematical history. He wrote around 1500 mathematical articles in his lifetime, mostly co-authored with other people. He had about 500 collaborators, and made mathematical collaboration a social activity in a way that changed the way many mathematicians worked.
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, collaborators once removed received Erdős number of 2, and so on. Some have estimated that 90% of the world's active mathematicians have an Erdös number smaller than 10. 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 the University of Georgia awarded them honorary degrees on the same day.
Among his frequent collaborators were Yousef Alavi, Bela Bollobas, 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.