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Order from Amazon ABOUT PAUL ERDS (An overview of the life of Paul Erds. This is not an excerpt from the book, My Brain Is Open: The Mathematical Journeys of Paul Erds, but a separate article prepared by its author, Bruce Schechter) FOR OVER half a century, early in the morning or in the middle of the night, mathematicians in Budapest or Berkeley, Prague or Sydney have been summoned from their multi-dimensional dreams by a knock at the door. Their unexpected guest was a short, smiling man wearing thick glasses and an old suit. In one hand he held a small suitcase containing everything he owned, in the other a shopping bag stuffed with papers. It was Paul Erds, one of the greatest mathematicians of the twentieth century, a man who lived in the space of Platonic Ideals and infinite beauty, who called no place on Earth home. Never one to waste time on formalities with work to be done, Erds would announce to his host: "My brain is open!" For the next few days, brains open, Erds and his host, with other mathematicians recruited as needed, would be off on a mathematical journey of problem, conjecture, theorem and proof. The goal of their journey was nothing less than Truth and Beauty. "If numbers aren't beautiful, I don't know what is," Erds once remarked. While the pursuit of mathematical beauty was Erds's only goal, his ideas inevitably have found practical applications. One of the small ironies of Erds's life is that, although he never owned or used a computer, mathematics that he invented is the basis for modern computer science; although he never had a secret, his mathematics is used by those who invent secret codes. Throughout his life Erds was drawn to areas of mathematics that did not require excessive technical knowledge; many problems that Erds stated can be easily understood by high school students. He was like a master chef who enjoyed demonstrating his mastery by whipping up magnificent creations from the humblest ingredients. One of Erds's important books has the beguilingly unassuming title, The Art of Counting. Before long Erds, who fueled his mathematical creativity with Benzedrine and coffee, would exhaust his hosts. Brain still wide open, he would take off to mathematical congress or visit another colleague, logging hundreds of thousands of miles on his journeys. Andrew Wiles, who recently stunned the world by his proof of the famous Fermat Conjecture--a problem that had challenged both amateur and professional mathematicians for two centuries--spent seven solitary years working in his attic office, telling no one of his efforts. Erds viewed mathematics as a joyous and collaborative activity. He wrote papers with nearly 500 different mathematicians, an unequaled record of intellectual promiscuity. Erds was the Johnny Appleseed of mathematics, who nurtured mathematics and mathematical talent all around the world. He was a frequent visitor to Budapest, the city of his birth, even during the Cold War, which helps explain the astonishing stream of world-class Hungarian mathematicians. To a large extent, the story of Erds's life is the story of mathematics in this century. Erds had a vocabulary all his own: God was the SF, or the Supreme Fascist; Joe and Sam were Joseph Stalin and Uncle Sam, two of his lifelong adversaries; children, whom he loved, were epsilons, which is how mathematicians speak of small quantities; "It's a pity Psa died at such a young age," he lamented. Psa, Erds's favorite child prodigy is alive and well, but at 17 was no longer as consumed with producing mathematical proofs and conjectures as when he was a 13-year-old epsilon. When Erds left, at the age of 83, he was attending a mathematical conference in Warsaw. "He died with his boots on, in hand-to-hand combat with one more problem," said Ron Graham, director of the information sciences research center at AT&T Laboratories, old friend and collaborator. In a world built on mathematics, mathematicians are strangely ignored. Most people would find it difficult to name a single mathematician, living or dead. Nevertheless, the world's major newspapers noted Erds's passing. The New York Times ran his obituary on the front page, introducing a whole new public to the story of this eccentric mathematical pilgrim. Erds received a state funeral and was buried in the Hungarian National Cemetery, in Budapest, amidst the heroes of Hungary's past. Several hundred mathematicians from scores of countries and representatives of the world's major mathematical societies attended. That night and the following day in a hastily arranged seminar, they reminisced about Erds's contribution to their lives and works. Paul Erds was born in Budapest on March 26, 1913, the son of two high-school mathematics teachers. His two young sisters, said to have been even smarter than Paul, died of scarlet fever while his mother was in the hospital giving birth to him. Less than two years later the Russians captured his father in an offensive and sent him to Siberia. Paul's mother, Anna, fearful of contagion, educated Paul at home until he went to high school. Even then he only attended school every other year because "Anyuka" kept changing her mind. At three he amazed visitors by multiplying three-digit numbers in his head. At four he made his first mathematical discovery, negative numbers. As a teenager Erds began to publish original mathematical results. His first love, to which he would be constant his whole life, was prime numbers. Primes are the basic atoms of the integers, numbers that can be divided only by one and themselves. Discerning the patterns, relationships and distribution of prime numbers has been an obsession of mathematicians since Euclid discovered an elegant proof that the number of primes is infinite. Paul's father showed him this proof when he was 10 and, as he recalls, "I was hooked." Questions about prime numbers are easy to ask and difficult to answer. Is there a prime number between every number and twice that number? Is there a prime between 2,314,947 and 4,629, 814, for example? The answer is yes, it is always true, but this was first proved only in 1850, by Pafnuty Lvovitch Chebyshev, the father of Russian mathematics. Chebyshev's proof was incredibly difficult and long-winded. Erds liked to imagine that God had a book in which he wrote down all the most elegant and beautiful mathematical proofs. Chebyshev's proof would definitely not be included in The Book. When he was 17 years, old Paul devised a beautiful new proof of Chebyshev's theorem, short and pithy. Mathematicians outside Hungary began to take notice of the young prodigy from Budapest. The great German mathematician, Issai Shur, dubbed him der Zauber von Budapest, the magician from Budapest. Growing up a Jew in the increasingly hostile era between the wars, Erds knew from an early age that he would one day have to leave Hungary. When he was just six years old, faced with increasing anti-Semitism, his mother suggested they convert. "You may do as you wish," said the boy, "but I will remain as I was born." When he got his doctorate, at age 21, he left Hungary to study in Manchester, England. He returned home for holidays, but after Hitler's Anschluss in 1938 he knew he could not return. He fled to the United States where he would spend the next decade, the longest semi-stationary period of his adult life. Then, as he once recalled, "my problems started with Joe and Sam." Although he desperately wanted to see his mother again--his father had died of a heart attack and much of his family had been killed in the Holocaust--he did not want to return to Hungary because of "Joe" (Joseph Stalin). In 1954, however, he was invited to a mathematical conference in Amsterdam. As an alien he would have to apply for a re-entry visa, usually a routine matter. But his extensive correspondence with mathematicians outside the United States, and especially with a number theorist in Communist China, raised the suspicions of the McCarthy era immigration officials. He was a member of the mathematics department at Notre Dame. An immigration agent came to interview Erds in his office, the last office he would ever call his own....
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