Elusive Proof, Elusive Prover: A New Mathematical Mystery

New York Times ^ | August 15, 2006 | DENNIS OVERBYE

[neverdem]

Grisha Perelman, where are you?

Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world’s mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought.

“It’s really a great moment in mathematics,” said Bruce Kleiner of Yale, who has spent the last three years helping to explicate Dr. Perelman’s work. “It could have happened 100 years from now, or never.”

In a speech at a conference in Beijing this summer, Shing-Tung Yau of Harvard said the understanding of three-dimensional space brought about by Poincaré’s conjecture could be one of the major pillars of math in the 21st century.

Quoting Poincaré himself, Dr.Yau said, “Thought is only a flash in the middle of a long night, but the flash that means everything.”

But at the moment of his putative triumph, Dr. Perelman is nowhere in sight. He is an odds-on favorite to win a Fields Medal, math’s version of the Nobel Prize, when the International Mathematics Union convenes in Madrid next Tuesday. But there is no indication whether he will show up.

Also left hanging...

[Blue_Ridge_Mtn_Geek]

mouth, anus

And the mouth and anus are not two holes, but two ends of one hole, the alimentary canal.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = =
True, and so if you are correct about the Eustachian tubes (and ignoring the lungs and sinus cavity which may or may not add to the count), there is indeed only "one hole" in the topological sense. And, if I am correct about those 'holes in our ears' there are, how many? Still four in that case, I think. "But I could be wrong".

[Lonely Bull]

I have detected a flaw in Dr. Perelman's work. You have 100 years to prove me wrong.

Look over there--you forgot to carry the 1.

[Blue_Ridge_Mtn_Geek]

"The ear drum covers the entire passage -- that's why your ears pop when your airline flight comes in for a landing. The air in the outer ear cannot quickly equalize pressure with that in the middle ear. The ear drum separates the outer and middle ear canals."

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Is the fit "tight" but not "secure", sometimes temporarily obstructed by excretions? Else, are our ear drums broken whenever we experience a "pop" like that, or is a wider opening through which the pressure is equalized being created through the fluid and mucous which also sometimes occupies that passage? I notice that my ears have to "pop" when my sinuses are congested, but they don't when I'm breathing freely.

[lmr]

This is all fascinating. All Mathematics can be explained through nature in relation to pi. Duh...

[lmr]

That is not a mathematical question. Perhaps, an E=Mc squared figures into that, but it is a question of science. Is matter particles of light? Or better yet, are particles of light matter? Einstein theorized one in the same...

[stands2reason]

I like pictorials.

Have you ever seen a one sided figure?

[Blue_Ridge_Mtn_Geek]

It should be noted that this proof may yet have a hole [no pun intended!], and if so it may take some time to discover it. There are precedents, e.g., Wiles agonizing extra year of work to plug the hole found after his initial announcement of a solution of the "Fermat Theorem" (for which he won a Clay Prize since that is one of the Millenium Seven):

http://en.wikipedia.org/wiki/Fermat's_last_theorem
(sorry, the syntax is correct, but the link generator must have a bug - - cut and paste the entire URL into your browser if you want to check out the reference)

"The story of the proof is almost as remarkable as the mystery of the theorem itself. Wiles spent seven years working out nearly all the details by himself and with utter secrecy (except for a final review stage for which he enlisted the help of his Princeton colleague, Nick Katz). When he announced his proof over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21-23 1993, he amazed his audience with the number of ideas and constructions used in his proof. Unfortunately, upon closer inspection a serious error was discovered: it seemed to lead to the breakdown of this original proof. Wiles and Taylor then spent about a year trying to revive the proof. In September 1994, they were able to resurrect the proof with some different, discarded techniques that Wiles had used in his earlier attempts."

[Blue_Ridge_Mtn_Geek]

Sorry, I'm wrong about the Fermat Theorem being one of the Millenium Seven - - - it was solved in 1994, before Clay Institute even announced the "Millenium Problems". I need to get some sleep! Good morning.

[Blue_Ridge_Mtn_Geek]

Sorry, one more reference I can't resist sharing, then to bed:

http://math.stanford.edu/~lekheng/flt/
Bluff your way in Fermat's Last Theorem

[ThePythonicCow]

When our ears "pop", the air flow is threw the Eustachian tube, between the middle ear and the back of the throat. Nothing flows past the ear drum. When your sinuses are clear, the Eustachian tubes let the air flow more freely.

[ThePythonicCow]

*threw*through*

[syriacus]

The Poincare conjecture states (roughly) that 3-dimensional balls are, give or take some stretching, the only 3-dimensional object that has no holes.

Maybe that is why 3-dimensional balls are so stable and have the greatest volume.

No weak spots. No leaky spots.

[USCG SimTech]

But is matter truly everything?

Matter is the eventual resultant after results of another forward initiative by Infinite Mind in an effort to become greater than It's own Infinite status...by becoming also finite, in unlimited ways, degrees, over eternity (creating time) then that Self occupying those structures in Witness.

There eat that for breakfast

[saganite]

Matter is the eventual resultant after results of another forward initiative by Infinite Mind in an effort to become greater than It's own Infinite status...by becoming also finite, in unlimited ways, degrees, over eternity (creating time) then that Self occupying those structures in Witness.

There eat that for breakfast


I think that's what the 60's drug culture was all about. In fact, I think they often "ate that for breakfast".

[dalight]

I still count 5. As the nose actually still has two that form a connected passage back through the mouth.

[camle]

"To a topologist, a rabbit is the same as a sphere. Neither has a hole."

wonder how a rabbit eats, etc. if it ain't got no hole?

[cricket]

EVERYTHING matters...

. . .if you think about it. . .

[cricket]

There seems to be no concern espressed here; so am assuming 'someone' knows where Perelman is and that there is no reason for alarm at the 'lack of sightings' or the fact he does not respond to his e-mail. . .

. . .and for sure, the man knows his mushrooms. .

[sportutegrl]

I'd be interested to know if this proof has any practical implications or uses.

You remind me of those kids in class who were always asking, "Is this gonna be on the test?", just when the prof was getting to an interesting math concept.

[sportutegrl]

So we are donuts. JFK was right.