Articles

# Paul Erdös

1913-1996

'Paul Erdös was regarded by fellow mathematicians as the most brilliant, if eccentric, mind in his field.' So begins the obituary in The Times on September 25 1996.

Paul Erdös was one of this century's most prolific mathematicans. He wrote or co-authored over 1000 papers and was publishing one a week in his seventies. He travelled constantly and compulsively and collaborated with so many mathematicians that the phenomenon of an 'Erdös number' became part of mathematical folklore. To have an Erdös number 1, a mathematician must have published a joint paper with Erdös. To have an Erdös number of 2, you must have published a joint paper with someone with an Erdös number of 1. And so on. It is estimated that four and a half thousand mathematicians have an Erdös number of 2. Only one mathematician could claim an Erdös number of zero: Erdös himself.

Erdös Pàl (to use the Hungarian form of his name) was born into a Hungarian-Jewish family in Budapest. His mathematical talent was already apparent at the age of three, when he used to amuse guests by multiplying three-digit numbers in his head. At the age of 20 he discovered a new and very neat proof of a famous result of the Russian mathematician Chebyshev: for every n there is a prime number between n and 2n. After obtaining his doctorate from the University of Budapest he went to Manchester in 1934 on a post-doctoral fellowship. It soon became obvious that to return to Hungary would be suicide, and Erdös left for the United States. Most members of his family who remained in Hungary were killed during the war.

In 1949 Erdös and Atle Selberg produced a brilliant elementary proof of the Prime Number Theorem, which describes the distribution of prime numbers. Selberg rushed the proof into print and was subsequently awarded a Fields Medal (the mathematical equivalent of a Nobel Prize). Never concerned about personal prestige, Erdös was philosophical about the episode.

Erdös had no fixed home, and lived out of a suitcase for most of his adult life. He needed no library, no laboratory, no equipment to do his job: only the company of like minds. He would arrive in a town and present himself to the most prominent local mathematician with the announcement 'My brain is open.' For the next few days he would exhaust his host with intense mathematical conversation, then move on. Typically, such an encounter would produce a joint research paper.

Erdös was constantly posing and solving problems across a wide spectrum of mathematics: geometry, number theory, combinatorics and graph theory. He was a walking encyclopaedia of mathematics. He had little need for money, and was eagerly sought as a guest of honour by conference organizers and Mathematics Departments. When he turned 80 in 1993, he was invited to 80th Birthday Conferences until he was well past 81. He died on 20 September 1996 in a hotel room in Warsaw, where he was attending yet another conference and working on yet another problem.