Paul Erdos

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Paul Erdös (1913-1996) was an immensely prolific mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, and number theory.

Paul Erdös (pronounced "Erd-ish") was born in Budapest, Hungary into a non-practicing Jewish family. The Budapest Jewish community of that day produced at least four remarkable thinkers besides Erdos: Eugene Wigner, the physicist and engineer; Edward Teller, the physicist and politico; Leo Szilard, the chemist, physicist and politico; and Johnny Von Neumann, the mathematician and Renaissance man.

Erdös was an only child, having lost his only siblings (two sisters aged three and five) to scarlet fever just days before he was born. Both his parents taught mathematics, and Erdös, by the age of four, had independently observed several established properties of prime numbers.

In 1914, Erdös's father Lajos was captured by the Russian army in its attack on the Austro-Hungarian alliance. He spent six years in captivity in Siberia. Erdös's mother Anna, excessively protective after the loss of her husband and two daughters, kept Paul away from school for much of his early years but hired a tutor to teach him at home. In 1920, Lajos Erdös returned from captivity and continued the education of his son in mathematics and English.

Despite the restrictions on Jews entering universities in Hungary, Erdös was accepted in 1930, having won a national examination. In 1934, he was awarded his doctorate. Anxious about rising anti-semitism in Hungary during the 1930s, he took a post-doctoral fellowship at Manchester. In 1938, he took his first American position at Princeton, though he did not get tenure because the administration of Princeton deemed him "uncouth and unconventional". Around this time Erdös began his habit of travelling from campus to campus which was to define his professional career.

All accounts report Erdös to have been a naïve, almost childlike character. An awkward incident occurred in 1941 when Erdös and another mathematician became involved in a heated discussion about a point of mathematical theory, and failed to notice they were too near a military communication facility on Long Island. They were arrested for trespassing and on suspicion of spying, and Erdös unfortunately earned an FBI record.

The contributions which Erdös made to mathematics were numerous and broad. However, basically Erdös was a solver of problems, not a builder of theories. The problems which attracted him most were problems in combinatorics, graph theory, and number theory. He did not just want to solve problems, however, he wanted to solve them in an elegant and elementary way. To Erdös the proof had to provide insight into why the result was true, not just provide a complicated sequence of steps which would constitute a formal proof yet somehow fail to provide any understanding.

Professionally, Erdös is best known as a solver of problems, particularly those regarded as exceptionally challenging. His characteristic style was to solve complicated problems in an elegant and visionary manner. Erdös received the Cole Prize of the American Mathematical Society in 1951 for his many papers on the theory of numbers, and in particular for the paper "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem", published in the Proceedings of the National Academy of Sciences in 1949.

In the early 1950's Erdös's FBI record brought him to the attention of the McCarthy Investigations, and Erdös suddenly found he could not obtain a visa to the United States. Consequently, he spent much of the next ten years in Israel. During the early 1960s he made numerous requests to be allowed to return to the United States and a visa was finally granted in November 1963.

For the next thirty years Erdös "officially" held posts at a number of universities in Israel, the US and Great Britain, but in reality he was a permanent nomad of no fixed agenda or location, wandering to all major universities as he saw fit. His working habits became characterised by working obsessively long hours, sleeping at most 4-5 hours a night and relying on the heavy use of amphetamines to maintain his activity levels. Once a friend challenged him to give up his drug use for a month; he complied, but later complained bitterly that mathematics was held up for a month.

His prestige and genius usually guaranteed him a warm welcome at any universities, and he inevitably completed a paper with any mathematician who could present a topic that appealed to him. As a result, he may be the most collaborative mathematician ever, with nearly 1,500 jointly published papers. The community of mathematicians who worked with him created the (tongue in cheek) Erdös number in his honor.

Erdös was a constant source of witty aphorisms: "Another roof, another proof", "A mathematician is a machine for turning coffee into theorems", "You don't have to believe in God, but you should believe in The Book" (refering to The Book which he felt contained the most succinct, elegant and illuminating proofs for all mathematical statements). Erdös used the word "to leave" for people who died, and the word "to die" for people who stopped doing mathematics.

Erdös went on to receive many awards including the Wolf Prize of 50 000 dollars in 1983. He lived simply, and gave most of it to help favored students or as prizes for solving problems he had posed. He died in Warsaw on September 20 1996.