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[Ben]:Yet another possible solution to the Riemann hypothesis No discussion found
Prof has made a career out of solving puzzle
Purdue mathematician may have the answer to $1 million question.

By Barb Berggoetz
barb.berggoetz@indystar.com
June 28, 2004

As a young French boy new to America in the 1940s, Louis de Branges de Bourcia would spend hours unscrambling letters in cryptograms in The Philadelphia Inquirer.

He conquered a book of 300 algebra problems one summer in his early teens. For a year, he labored over one complex math problem given to him by the former president of DuPont Co..

But those stories pale in comparison to the Purdue University professor's nearly 20-year pursuit of the Riemann hypothesis, a problem concerning the nature of prime numbers that has stymied mathematicians since 1859.

At age 72, de Branges recently claimed to have proven the hypothesis -- considered by many to be the greatest unsolved problem in math.

If his theory is published and proven accurate by experts in the field, de Branges is in line to get $1 million from the Clay Mathematics Institute. In 2000, the Cambridge, Mass.-based institute offered $7 million in prize money to solve seven long-standing, classic math problems, with $1 million going to each person who succeeded first.

But money isn't what has driven de Branges to devote a large chunk of his life to solving the Riemann hypothesis.

"I've been doing it because I think it needs to be done. Money is certainly not the motivation for my work," said de Branges, speaking from his small apartment outside of Paris where he has spent summers with his wife since 1989, never far from his research.

"I've put a lot of time and effort into this, especially when I travel to France," said de Branges, a distinguished professor of math at Purdue, where he's been an instructor and researcher since 1962. "I've worked in isolation this whole career of mine. It's been hard, especially in the final stages."

He's spent countless hours pursuing the solution.

"I would actually be sitting, doing mathematics eight hours a day, in addition to teaching," he said. "But I couldn't keep that up."

De Branges knows much work remains to convince colleagues he's right. His theory must be accepted by a scientific journal. After a two-year waiting period, a panel of experts appointed by the Clay Institute will examine the 124-page document that de Branges wrote to prove his theory before he can collect the $1 million, said Jim Carlson, institute president.

The highly complex theory involves the nature of prime numbers -- those numbers divisible only by one and themselves.

Experts say solving the problem is important to understanding a basic building block in mathematics. "Primes are to numbers like atoms are to chemistry," said Carlson.

Primes are used, for example, every time a purchase is made over the Internet. Credit card numbers are encrypted based on prime numbers for security reasons.

Frank Lester, an Indiana University mathematics educator, said many people are discouraged from trying to solve the Riemann hypothesis because it's "too tough a nut to crack."

Nobel Prize winner John Nash Jr., whose struggle with schizophrenia was the basis of the movie "A Beautiful Mind," worked on Riemann, Lester noted.

Mathematician Bernhard Riemann published the theory in 1859 about how prime numbers are distributed among other numbers, but he couldn't prove it. The Riemann theory would show how the sequence of prime numbers -- 2, 5, 7, 11, etc. -- deviates from the expected sequence.

"It's one of those holy grails for mathematicians," said Bart Ng, math professor at Indiana University-Purdue University Indianapolis. "A lot of math, in number theory, is at the heart of cryptology."

This is not de Branges' first attempt to solve the hypothesis.

While fellow mathematicians praise his devotion to solving complex math problems, some also look at his latest 124-page answer as another in what's becoming a series of attempts.

"At this point, I'm just skeptical," said Andrew Odlyzko, mathematics professor at the University of Minnesota, who has worked on the Riemann hypothesis and looked at de Branges' previous answers.

Although he hasn't read the most recent proof on de Branges' Web site, Odlyzko said he's not inclined to look at this version unless other experts signal this one is different.

But de Branges has had previous successes and is considered a top mathematician worldwide. About 20 years ago, he proved another long-standing math problem after several misfires.

"He's a very innovative and somewhat unconventional fellow," said Ng. "It's very risky to put your entire career on attempting to solve a problem that defies the efforts of so many."

De Branges, who wants to teach a course on the Riemann theory in the fall if enough students sign up, knew he was taking a risk. He thought he'd be done 10 years ago. But the Cornell University graduate thinks he has it right now.

"You don't know how much time and work it's going to require and whether you'll live long enough to finish."
  2004-06-28
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Yet another possible solution to the Riemann hypothesis
 
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