de Branges de Bourcia '49 may have solved Riemann Hypothesis

Now a mathematician who has been working on the challenge for 20 years is putting his latest proposed proof on the Internet.

Purdue University Professor Louis de Branges de Bourcia has offered proofs before, only to withdraw them. By one account, the National Science Foundation has given him more than $450,000 over the years to work on the Riemann Hypothesis. This time around, de Branges has posted the proof online even before submitting it to peer-reviewed publications — in hopes of eventually claiming the $1 million from the Clay Mathematics Institute.

"I invite other mathematicians to examine my efforts," de Branges said today in a news release from Purdue. "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."

Back in 1984, de Branges delivered a proof for the Bieberbach Conjecture, another longstanding puzzle in the math world, so his colleagues tend to take him seriously. "It will obviously take time to verify his work," said Leonard Lipshitz, head of Purdue's mathematics department, "but I hope that anyone with the necessary background will read his paper so that a useful discussion of its merits can follow."

What's the big deal about the Riemann Hypothesis? The challenge dates back to 1859, when German mathematician Georg Friedrich Bernhard Riemann published a conjecture about how prime numbers were distributed among other numbers. Riemann could never prove the conjecture for all numbers, nor could anyone else since then — although a distributed-computing project called ZetaGrid has shown it to be true for the first 100 billion solutions.

The details are strewn with zetas, sigmas, pis and phis — the math Greek only a geek could love. But the bottom line is that an airtight, elegant proof of the Riemann Hypothesis could well shed new light on the "music of the primes."

Mathematicians have always been fascinated by prime numbers — integers that are cleanly divisible only by themselves and the number 1. More practically, prime numbers form the foundation for the cryptographic systems that keep online purchases secure. So any progress on primes would prick up the ears of very smart people around the world.

To learn more about the Riemann Hypothesis, click through this Web portal on the problem at the University of Exeter. I particularly recommend the applet on this Web page, which helps you visualize what Riemann was talking about.