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The legendary mathematician

Chủ đề trong 'Anh (English Club)' bởi username, 10/11/2001.

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    Have you ever heard of the legendary mathematician Paul Erdos, who had no nationality but wandered around the world, inspiring the mathematical world, whose work in Mathematics beats any other mathematicians ? He died 3 years ago, leaving the remaining world poorer and poorer.
    It is my regret that I can never meet him in my life, but I have a Moroccan friend who fortunately met him twice in Strasbourg, who told me his generosity and warmth.

    Paul Erdảs dies at 83
    Bâla BollobĂs


    Paul Erdảs, mathematician, died on September 20, 1996, in Warsaw, aged 83. He was born on March 26, 1913, in Budapest.
    Paul Erdảs was one of the most brilliant and probably the most remarkable of mathematicians of this century. Through his prodigious output and many collaborators, he greatly influenced many branches of mathematics and was the prime mover in the rapid growth of combinatorics. He never had a `proper' teaching job, but constantly travelled around the world, in search of new challenges. Considering material possessions a nuisance, he lived for over sixty years out of half-full suitcases, which he never learned to pack. His discarded suit was rejected by Oxfam. He was the quintessential mathematician: although he was interested in history, medicine and politics, he was totally dedicated to mathematics. He wrote about 1500 papers, about five times as many as other prolific mathematicians, and had close to 500 collaborators. His enormous output even inspired a limerick:

    A conjecture both deep and profound
    Is whether the circle is round.
    In a paper of Erdảs,
    Written in Kurdish,
    A counterexample is found.

    According to a wit, on a long train journey he would write a joint paper with the conductor.
    Erdảs was born into an intellectual Hungarian-Jewish family in Budapest amidst tragic circumstances: when his mother returned home from the hospital she found that her two daughters had died of scarlet fever. Soon after the outbreak of the First World War, Erdảs's father was taken prisoner by the Russians and returned home from Siberia only six years later. The young Erdảs was brought up by his mother, a teacher of mathematics like his father, and he remained devoted to her throughout his life.

    He was a child prodigy: as a small boy, he amused people by asking them how old they were and telling them how many seconds they had lived. Erdảs was educated mostly at home, by his father, until 1930, when he entered the Pâter PĂzmĂny University in Budapest, where he was soon at the centre of a small group of outstanding young Jewish mathematicians. As a second year undergraduate, he practically completed his doctorate under Leopold Fejâr. His main result was a simple proof of an extension of Bertrand's Postulate, first proved by the Russian mathematician Chebyshev, that there is always at least one prime number between any positive integer and its double. For Erdảs, 1934 was a momentous year: not only did he graduate from the university, but he also received his doctorate, and got a fellowship to join the remarkable group of mathematicians that was brought together by Louis Mordell in Manchester. He also met Richard Rado and Harold Davenport, who became his great friends and collaborators.

    In 1938 Erdảs sailed for the United States, where he was to stay for the next decade. During his first year, at the Institute for Advanced Study in Princeton, he wrote ground-breaking papers with Wintner and Kac, which founded probabilistic number theory, with TurĂn he proved great results in approximation theory, and he solved the then outstanding problem in dimension theory. When his Fellowship at the Institute was not renewed, he started his peregrinations, with longer stays at the University of Pennsylvania, Notre Dame, Purdue and Stanford. The great mathematical event of 1949 was an elementary proof of the Prime Number Theorem, given by Atle Selberg and Erdảs. The result, which predicts the distribution of primes with some accuracy, was first proved in 1896 by sophisticated methods, and it had been thought that no elementary proof could be given.

    In 1954 he fell foul of the McCarthy era: despite being refused a reentry visa, he left the United States and, as a result, for the next nine years he was not allowed to return to America. Israel came to his aid with a job for three months at the Hebrew University of Jerusalem. Although officially he became a resident of Israel, he refused its citizenship and kept his Hungarian passport, claiming that he was a citizen of the world. Although in 1963 he was allowed to return to America, and from then on spent most of his time there, he could never forgive the American government. From 1964 on, his mother, who was then aged 84, accompanied him on his travels. This was a golden period for Erdảs, who never recovered from her death in 1971.

    In over six decades of furious activity, he wrote fundamental papers on number theory, real analysis, geometry, probability theory, complex analysis, approximation theory, set theory and combinatorics, among other areas. His first great love was number theory, while in his later years he worked mostly in combinatorics. In 1966, with Selfridge, he solved a notorious problem in number theory that had been open for over 100 years, namely that the product of consecutive positive integers (like 4ã5ã6ã7ã8) is never an exact square, cube or any higher power. With Rado and Hajnal, he founded partition calculus, a branch of set theory, which is a detailed study of the relative sizes of large infinite sets. Nevertheless, he will be best remembered for his contributions to combinatorics, an area of mathematics fundamental to computer science. He founded extremal graph theory, his theorem with Stone being of prime importance, and with Rânyi he started probabilistic graph theory. He advocated the use of elementary methods, in ad***ion to techniques requiring vast preparation, and decades before it became commonly accepted, he had showed the power of random methods in mathematics. He showed that simply stated problems often lead to exciting phenomena, and left behind hundreds of exciting problems whose solutions will influence combinatorics for many years to come.

    ***ual pleasure revolted him; even an accidental touch by anyone made him feel uncomfortable. He never married or had a family, although he was very good with children. As a truly unworldly figure, he lived for mathematics and relied on his friends to look after him; in his later years he particularly liked to be in Budapest, Memphis and Kalamazoo where, in ad***ion to his mathematical friends, he found good medical care. He hated to be alone, and almost never was; he loved to attend conferences and enjoyed the attention of mathematicians. His main aim in life was ``to do mathematics: to prove and conjecture''.

    A favourite saying of his was that ``every human activity, good or bad, must come to an end, except mathematics.'' He died as he wished to, before his powers were greatly diminished: while attending a conference, he was killed by a massive heart attack.

    Source: http://www.ams.org/new-in-math/erdosobit.html

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