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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 124-page paper detailing his attempt at a proof on his university Web page. 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 whoever accomplishes it first – has encouraged de Branges to announce his work as soon as it was completed.
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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 Lip#z, head of Purdue's mathematics department, said that de Branges' claim should be taken seriously.
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Riemann Hypothesis "Proof" Much Ado About Nothing
A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.
The Riemann hypothesis asserts that all interesting solutions of the equation
z(s) = 0
lie on a straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.