$7 million is payoff for answering world's hardest math problems

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http://www.techserver.com/noframes/story/0,2294,500208167-500291071-501581109-0,00.html

The Associated Press

PARIS (May 25, 2000 1:41 a.m. EDT http://www.nandotimes.com) - If
square-root signs and algebraic theorems never looked appealing
before, consider this: A group of the world's top mathematicians is
offering $7 million for solutions to some of the world's hardest
equations.

After puzzling for years over seven unsolved math problems, a
U.S.-based mathematics foundation put the "Millennium Prize Problems"
challenge to the world via the Internet on Wednesday.

Experts say solving the problems could lead to breakthroughs in
encryption and aerospace - and open areas of mathematics as yet
unimagined.

The Clay Mathematics Institute posted the problems on its Web site,
http://www.claymath.org at the same time it unveiled the contest in
Paris at its annual meeting.

"The seven mathematical problems stand out as great unresolved
problems of the 20th century," said Andrew Wiles, a Princeton
University math professor known for cracking a 350-year-old conjecture
known as "Fermat's Last Theorem" in 1995.

"We hope that by attaching prizes to them, it will incite and inspire
future generations of mathematicians," said Wiles, 45, who told a news
conference that he first came across Fermat's puzzle in a comic book
at the age of 10.

The group has posted a $1 million prize for each of the seven
problems.

Few expect a winner to come forward anytime soon.

"There's no time limit," said Arthur Jaffe, a Harvard University math
professor and president of the Clay institute, a private, nonprofit
foundation based in Cambridge, Mass.

According to contest rules, solutions must be published in a renowned
math journal and undergo a two-year waiting period to allow time for
independent review. If the mathematics community accepts the solution,
the Clay institute will then open its own review before awarding any
money.

Mathematicians are quick to note that a few decades, or even a
century, is not a long wait to unravel the world's toughest puzzles.

The list of problems - like the choice of Paris for launching the
group's challenge - was inspired by a list presented 100 years ago by
German mathematician David Hilbert to the International Congress of
Mathematicians meeting in Paris.

Hilbert's list of 23 equations - of which three remain unsolved -
served as a road map for 20th century math and led to modern-day
breakthroughs in medicine, technology and safety.

Members of the Clay institute say their list is a worthy successor.

It includes the following equations, named for the mathematicians who
postulated them: the Riemann Hypothesis, the Poincare Conjecture, the
Hodge Conjecture, the Birch and Swinnerton-Dyer Conjecture,
Navier-Stokes Equations, the Yang-Mills Theory and the P versus NP
Problem.

The Riemann Hypothesis - the oldest and best-known of the seven -
dates to 1859 and was included on Hilbert's list in 1900.

If solved, it could revolutionize encryption, which is used to secure
information sent through a forum like the Internet. Consumer credit
card numbers, medical records, financial records and Internet shopping
could be made safer from Cyber-snoops as a result, experts say.

Cracking the Navier-Stokes Equations - which deal with turbulence,
hydrodynamics and fluid flow - could help build better airplanes and
ships.

Mathematicians from outside the Clay institute say the foundation may
never have to part with its millions.

However, the million-dollar challenge is sure to tempt bright young
minds, said Keith Devlin, dean of science at St. Mary's College in
Moraga, Calif., and author of several popular math books.

Even if the seven equations, which Devlin calls the "Mount Everest" of
math problems, remain unsolved, the research could produce important
side effects.

"Only a few people actually manage to reach the summit of Mount
Everest," said Devlin. "But millions benefit from the survival
equipment developed in pursuit of the lofty goal. So, too, with the
big problems of mathematics."

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