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Last Updated: Thursday, 10 June, 2004, 13:56 GMT 14:56 UK
Greatest maths problem 'solved'
By Dr David Whitehouse
BBC News Online science editor

Prime numbers, BBC
Each one a prime
A mathematician at Purdue University in the US claims to have proved the Riemann Hypothesis - called the greatest unsolved problem in maths.

The hypothesis concerns prime numbers and has stumped the world's mathematicians for more than 150 years.

Now, Professor Louis De Branges de Bourcia has posted a 23-page paper on the internet detailing his attempt at a proof.

There is a $1m prize for whoever solves the hypothesis.

Cult following

"I invite other mathematicians to examine my efforts," says de Branges.

"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.

It has defeated mathematicians since 1859 when Bernhard Riemann published a conjecture about how prime numbers were distributed amongst other numbers.

Since then the problem has 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.

Reputation demands

Such is the importance, and difficulty, of the problem that in 2001, the Clay Mathematics Institute in Cambridge, Massachusetts, US, offered a $1m purse to whoever proves it first.

De Branges solved another 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."

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