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Paul Erdös's parents had two daughters who died just days before Paul was born. This had the effect of his parents being extremely protective of Paul. He was taught mathematics by his parents, themselves both teachers of mathematics.
While Paul was at school, his father was captured by the Russian army as it attacked the Austro-Hungarian armies. Paul's father spent six years in captivity in Siberia. As soon as he was captured Paul's mother took Paul away from school and the rest of his early education took place at home.
Erdös studied for his doctorate at the University of Budapest. Around this time he discovered an elegant proof of the result, first proved by Chebyshev, that for every n there is a prime between n and 2n. Awarded a doctorate in 1934, he then took up a post-doctoral fellowship at Manchester. The situation in Hungary by the late 1930s was clearly impossible for someone of Jewish origins to return so Erdös went to the USA.
The Prime Number Theorem, namely:-
The number of primes n tends to as n/ln n,was conjectured in the 18th century, but it was not proved until 1896, when Hadamard and de la Vallée Poussin independently proved it using complex analysis. In 1949 Erdös and Atle Selberg found an elementary proof. Subsequent events are described in :-
Selberg and Erdös agreed to publish their work in back-to-back papers in the same journal, explaining the work each had done and sharing the credit. But at the last minute Selberg ... raced ahead with his proof and published first. The following year Selberg won the Fields Medal for this work. Erdös was not much concerned with the competitive aspect of mathematics and was philosophical about the episode.This result was typical of the type of mathematics Erdös worked on. He posed and solved problems that were beautiful, simple to understand, but notoriously difficult to solve.
Erdös did receive 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.
During the early 1950s U.S. senator Joseph R McCarthy whipped up strong feelings against communism in the USA. Erdös began to come under suspicion from authorities who saw imaginary problems everywhere. When asked by US immigration, as he returned after a conference in Amsterdam, what he thought of Marx, Erdös made the ill judged reply:-
I'm not competent to judge, but no doubt he was a great man.Erdös was not allowed back to the United States and spent much of the next ten years in Israel. During the 1960s he was again allowed to return but by this time he had become a traveller moving from one university to another, and from the home of one mathematician to another.
Although somewhat over the top, the following quote from  shows the high regard in which Erdös was held by his fellow mathematicians:-
Never, mathematicians say, has there been an individual like Paul Erdös. He was one of the century's greatest mathematicians, who posed and solved thorny problems in number theory and other areas and founded the field of discrete mathematics, which is the foundation of computer science. He was also one of the most prolific mathematicians in history, with more than 1,500 papers to his name. And, his friends say, he was also one of the most unusual.Erdös won many prizes including the Wolf Prize of 50 000 dollars in 1983. However he had a lifestyle that needed little money and he gave away
most of the money he earned from lecturing at mathematics conferences, donating it to help students or as prizes for solving problems he had posed.In 1976 Ulam gave this description of Erdös:-
He had been a true child prodigy, publishing his first results at the age of eighteen in number theory and in combinatorial analysis. Being Jewish he had to leave Hungary, and as it turned out, this saved his live. In 1941 he was twenty-seven years old, homesick, unhappy, and constantly worried about the fate of his mother who remained in Hungary. ... Erdös is somewhat below medium height, an extremely nervous and agitated person. ... His eyes indicated he was always thinking about mathematics, a process interrupted only by his rather pessimistic statements on world affairs, politics, or human affairs in general, which he viewed darkly. ... His peculiarities are so numerous it is impossible to describe them all. ... Now over sixty, he has more than seven hundred papers to his credit.References (16 books/articles)
References elsewhere in this archive:
Paul Erdös was the American Mathematical Society Cole Prize winner in 1951. You can see a history of the AMS Cole Prize and a list of the winners.
Other Web sites:
You can see the Erdos Number Web site at Oakland, USA
Some information about Erdös' Reciprocal Sum Constants
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