Riemann hypothesis proved?

Louis de Branges de Bourcia, the Edward C. Elliott Distinguished Professor of Mathematics at Purdue's School of Science, this week posted a 23-page paper detailing his attempts at a proof. Usually, mathematicians announce such breakthroughs at conferences or in scientific journals. Finding a solution to the Riemann hypothesis, however, carries a $1 million prize, so he decided to publish early.

"I invite other mathematicians to examine my efforts," de Branges said in a prepared statement. "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 hypothesis concerns the distribution of prime numbers. A prime number is divisible only by itself and one. Prime numbers are necessary for, among other tasks, encryption.

Earlier this month, a group confirmed that it has found the largest prime number known about to date. The new number, expressed as 2 to the 24,036,583th power minus 1, has 7,235,733 decimal digits.

Like many other math problems, immediate commercial applications for a proof of the Riemann hypothesis are unlikely, but uses decades from now are a definite possibility.

The origins of the hypothesis date back to 1859, when mathematician Bernhard Riemann came up with a theory about how prime numbers were distributed, but he died in 1866, before he could conclusively prove it.

Since then, the problem has attracted a cult following. John Nash, the Nobel Prize-winning mathematician whose life was chronicled in the book and movie "A Beautiful Mind," attempted to solve it. In 2001, the Clay Mathematics Institute in Cambridge, Mass., offered a $1 million purse for proving it.

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.