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WEST LAFAYETTE, Ind. - A Purdue University mathematician claims to have proven the Riemann hypothesis, often dubbed the greatest unsolved problem in mathematics.

Louis De Branges de Bourcia, or de Branges (de BRONZH) as he prefers to be called, has posted a 23-page paper detailing his attempt at a proof on his university Web page at http://www.math.purdue.edu/~branges/ . While mathematicians ordinarily announce their work at formal conferences or in scientific journals, the spirited competition to prove the hypothesis - which carries a $1 million prize for whomever accomplishes it first - has encouraged de Branges to announce his work as soon as it was completed.

"I invite other mathematicians to examine my efforts," said de Branges, who is the Edward C. Elliott Distinguished Professor of Mathematics in Purdue's School of Science. "While I will eventually submit my proof for formal publication, due to the circumstances I felt it necessary to post the work on the Internet immediately."

The Riemann hypothesis is a highly complex theory about the nature of prime numbers - those numbers divisible only by 1 and themselves - that has stymied mathematicians since 1859. In that year, Bernhard Riemann published a conjecture about how prime numbers were distributed among other numbers. He labored over his own theory until his death in 1866, but was ultimately unable to prove it.

The problem attracted a cult following among mathematicians, but after nearly 150 years no one has ever definitively proven Riemann's theory to be either true or false. Although a definitive solution would not have any immediate industrial application, in 2001 the Clay Mathematics Institute in Cambridge, Mass., offered a $1 million purse to whomever proves it first.

At least two books for popular audiences have appeared recently that describe the efforts of mathematicians to solve the puzzle. One of the books, Karl Sabbagh's "Dr. Riemann's Zeros," provides an extensive profile of de Branges and offers one of the mathematician's earlier, incomplete attempts at a proof as an appendix.

De Branges is perhaps best known for solving another trenchant problem in mathematics, the Bieberbach conjecture, about 20 years ago. Since then, he has occupied himself to a large extent with the Riemann hypothesis and has attempted its proof several times. His latest efforts have neither been peer reviewed nor accepted for publication, but Leonard Lipshitz, head of Purdue's mathematics department, said that de Branges' claim should be taken seriously.

"De Branges' work deserves attention from the mathematics community," he said. "It will obviously take time to verify his work, but I hope that anyone with the necessary background will read his paper so that a useful discussion of its merits can follow."

Source: Eurekalert & others

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