LONDON (April 25) - For nearly 100 years, mathematicians have been stumped by one of the math world's most difficult problems, a conjecture by French scientist Henri Poincare about the properties of three-dimensional space.
Now, a British math whiz claims to have solved the problem.
His work - and the unconventional way he's presented it on the Internet - have both been challenged by other mathematicians.
But Martin Dunwoody's efforts have also been praised - by the leader of a respected U.S.-based mathematics foundation that has offered $1 million to anyone who can solve it.
''This is the first serious effort on any of our seven problems,'' said Arthur Jaffe, president of the Clay Mathematics Institute, a nonprofit group founded two years ago to identify the world's seven toughest math problems and offer $1 million for their solutions.
''I get thousands of communications from people who say they've solved one of the problems,'' Jaffe said. ''They come by phone, fax, e-mail and letter all the time. Generally, it takes about a tenth of a second to know what to do with them.''
One thing is certain - whether Dunwoody, a professor at Southampton University, turns out to be right, his efforts have generated a lot of public interest in a field many consider difficult and boring.
''The hits on our Internet site have skyrocketed since early April,'' when Dunwoody's solution began appearing on his university's website, Jaffe said.
The school's math and public relations departments also have been bombarded with phone calls ever since the 64-year-old professor began publicizing and revising his answer on the Internet, while refusing to give interviews.
To understand all the hoopla, it is helpful to look back on the genius of Poincare and the conjecture, or question, that he raised in 1904.
A professor of astronomy who made fundamental contributions regarding the motions of the planets, Poincare went on to found the field of topology, a branch of geometry, and even competed with Albert Einstein in the study of relativity.
The math mystery he raised regards the properties of three-dimensional space.
Before Poincare, mathematicians fully understood two-dimensional space, such as the Earth's surface, and could list all the possible shapes of two-dimensional surfaces and use mathematical calculations to distinguish between them.
Poincare made strides in understanding three-dimensional spaces - the kind, for instance, that an airplane flies through, made up of north-south, east-west and up-down measurements.
His question, or conjecture, was whether the two-dimensional calculations could be easily modified to answer similar questions about three-dimensional spaces.
He was pretty sure the answer was yes but couldn't prove it mathematically. Nearly 100 years later, math whizzes remain stuck.
Even more frustrating, the mathematics of two-dimensional spaces were conquered by two Germans in the 1800s, and all other dimensions of four or higher were proven mathematically by American and British experts in the last 40 years.
That leaves three dimensions as the remaining problem.
Barely six pages long, and only an outline, Dunwoody's solution - complete with formulas and diagrams - has been praised and challenged in England.
''This is the first good shot at this problem in years,'' said Professor Ian Stewart of the University of Warwick, one of Britain's most respected mathematicians. ''It looks like a competent attempt.''
But Colin Rourke, another University of Warwick mathematician, disagreed. When he raised a problem in the solution, Dunwoody admitted on his Web site that it could be difficult to overcome.
''He's acknowledged the gap in his solution that I pointed out,'' Rourke said in a telephone interview. ''He doesn't have cast-iron proof.''
Even if Dunwoody continues to refine his answer and eventually is proven correct, it could be a long time before it's official.
First, he must get it published in a mathematics journal, then undergo a two-year waiting period of international review.
Once the math community has accepted the solution, the Clay Mathematics Institute in Cambridge, Mass., must conduct its own review. Only if that proves successful will he be rewarded.
Jaffe said Dunwoody took an unusual step in posting his solution in preliminary form on the Internet, then revising it there.
People familiar with Dunwoody describe him as a confident mathematician with a good record on research, but not a high flyer known for solving big problems. The university, where he specializes in topology and geometric group theory, said it doesn't even know how long he has been working on Poincare's Conjecture.
That leaves people wondering whether he is willing to go to the lengths of Professor Andrew Wiles, the British number theorist who drew widespread acclaim by solving Fermat's Last Theorem in the early 1990s.
Wiles of Princeton University devoted his life to the theorem, a conundrum that had baffled experts for centuries.
Pierre de Fermat, a French judge who studied math in his spare time, came up with the complex equation in the 17th century.
Wiles began work on his 100-page calculation in 1986. For seven years he worked in isolation, often in his attic, worried others might copy his strategy.
In 1993, Wiles revealed his proof to the world. Later, a flaw emerged in his logic, and Fermat's Last Theorem remained unproven.
In the end, it wasn't until 1995 that a new insight allowed Wiles to fix his proof and achieve his life's ambition.
AP-NY-04-25-02 1617EDT
Copyright 2002 The Associated Press. The information contained in the AP news report may not be published, broadcast, rewritten or otherwise distributed without the prior written authority of The Associated Press. All active hyperlinks have been inserted by AOL.
Posted by Cartman (Member # 256) on :
This stuff is way over my head, but from what I am able to understand I can tell it's an impressive accomplishment.
Posted by Krenim (Member # 22) on :
Take that, ya lousy dimension!
Posted by YrdMehc (Member # 417) on :
Gee, I found the copyrighting more interesting.....
Posted by The Apocalypse (Member # 633) on :
I was expecting the Asians, mostly the Chinese to find something mathematically extrodinary(sp?) before the others. Oh well, you can't always count on the ones who look and are smart, you have to go with the other foreign smart people, and I haven't the slightest idea what I'm blabbing on about... Posted by PsyLiam (Member # 73) on :
Oh yes, Prof Stephen Hawkings is famous for being a bit rubbish at mathematics and stuff, isn't he?
Posted by Cartman (Member # 256) on :
Hawkings?
Posted by Sol System (Member # 30) on :
quote: Oh well, you can't always count on the ones who look and are smart, you have to go with the other foreign smart people
Words to live by.
If you have some sort of severe mental problem.
Posted by PsyLiam (Member # 73) on :
Profesor Stephen Hawking is clever enough to qualify as a plural, yes.
Posted by Mucus (Member # 24) on :
Profesor? Posted by TSN (Member # 31) on :
I recommend spelling his name "Steven" in your next post...
Posted by Sol System (Member # 30) on :
![[Confused]](confused.gif)
![[Wink]](wink.gif)
![[Smile]](smile.gif)