N is a Number
A Portrait of Paul Erdös |

Erdös' genius was for the problem that requires little mathematical experience to state and only ingenuity to solve. He cared little for the applications of his ideas... He never had a "proper" teaching job, but constantly traveled around the world, in search of new challenges. Considering material possessions a nuisance, he lived for over 60 years out of half-full suitcases, which he never learned to pack. His discarded suit was rejected by Oxfam. He succumbed to the seduction of every beautiful problem he encountered. A mathemetician of unique style and vision, Erdös will remain on the short list of those whose work defines the mathematics of our century. Erdös' interests covered a multitude of branches of mathematics. Foremost among them are number theory, finite and transfinite combinatorics, classical analysis (especially by the theory of interpolation), and discrete geometry, but his work extends to many other fields, including probability theory, topology, group theory, complex functions, and more. He became the most prolific mathematician of his generation, writing or co-authoring 1,000 papers and still publishing one a week in his seventies. His research spanned many areas, but it was in number theory that he was considered a genius. He set problems that were often easy to state but extremely tricky to solve and which involved the relationships between numbers. He liked to say that if one could think of a problem in mathematics that was unsolved and more than 100 years old, it was probably a problem in number theory. Paul Erdös was well known even outside mathematical circles for his singular dedication to mathematics, which resulted in his living as a "mathematical pilgrim" for much of his life. He was known as a poser and solver of problems, but his problems often seemed to lead to deep theories, which were then explored by others. By his trips and by his collaboration with other mathematicians, Erdös stimulated an enormous amount of mathematical activity. His contributions to number theory and to combinatorics were immense. If the Martians had made contact with earth during the lifetime of Paul Erdös he would have made a good choice as this planet's ambassador. The aliens would have appreciated his unearthly intelligence. He spoke the universe's common tongue, the theory of numbers, with fluency and wit. Importantly, Mr. Erdös would never have missed the trappings of this world. He had no children, no wife, no house, no credit card, no job, no change of shoes, indeed nothing but a suitcase containing a few clothes and some notebooks. Neither was he fussy about food, as long as he had coffee. In more than six decades of astonishing activity, Erdös made fundamental contributions to number theory, probability theory, real and complex analysis, geometry, approximation theory, set theory and, especially, combinatorics. Perhaps his genius shone brightest in number theory and combinatorics. He practically created the areas of probabilistic number theory, partition calculus for infinite cardinals, extremal graph theory and the theory of random graphs..."Another roof, another proof" was his legendary motto, and from his twenties he hardly ever slept in the same bed for seven consecutive nights...But it was as a source of problems that Erdös was in a class of his own: in the entire history of mathematics there is nobody remotely like him. He has left behind hundreds of attractive problems that are easy to state but that usually turn out to have pinpointed the heart of the matter...Paul Erdös lived as he wanted to: he "proved and conjectured" to the great benefit of mathematics. He kept up the flood of exciting results well into his seventies, and remained phenomenally productive until the day he died. He would bring the mathematical news, pose problems, inspire the locals with his brilliant ideas, and depart in a few days, leaving behind his exhausted hosts to work out the details of their joint work. His open mind, his ability to see the unexpected, and his willingness to wrestle with complications without the help of well-established tools made him a welcome guest wherever he went...Perhaps his greatest contribution to mathematics was that he realized and demonstrated (decades before it came to be accepted) the importance of seemingly contradictory properties, such as efficient networks with few connections. These methods are of paramount importance in computer science, though Erdös himself never touched a computer. | |

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