Has The Poincare Conjecture Been Solved?

Zack Coburn writes "An article in the Boston Globe alludes to the Poincare Conjecture being solved, possibly. For those who are unfamiliar with the conjecture, the article gives a brief description: "To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe." Apparently Grigory Perelman may have proved it, which would mean a $1 million award from the Clay Mathematics Institute." We've previously discussed other possible Poincare proofs.

Comments

Has the Poincare Conjecture Been Solved?

[James A. C. Joyce]

No.

(It even says in the freaking article stub that the proof is merely alluded to, for crying out loud.)

This Proof Isn't New

[muon1183]

This proof has been out for about 9 months, and so far has stood up to intense scrutiny. Perelman is considered one of the top mathematicians in his field, and other mathematicians believe his proof is likely correct, although it is still being scrutinized. I recently attended a lecture by Richard Hamilton, who has been leading a team going through the proof, and he showed the method used and which sections of the proof had already been verified. It appears that the Poincare Conjecture finally has been solved.

If you are interested in the method of proof, Perelman used the Ricci Flow, blow-up arguments, and surgery to prove the Thurston Geometrization conjecture (a theorem far more powerful than the Poincare Conjecture alone).

Re:Finite Universe

[Bombcar]

I've seen a video [uiuc.edu]

Just a little note for moderators: If you see something like that, it means the post was cut 'n' pasted from another slashdot post!

Here!

With italics and everything, including the link!

Google!

A line-by-line proof...

[James A. C. Joyce]

...of why this guy is a troll and all who modded him up must be smoking the $2 crack.

"(First off, remember that us MATHEMATICANS DO IT SMOOTHLY AND CONTINUOUSLY.) Hehehe, wow, too many New Year's drinks. Anyway, on to the story."

OK, a fairly unfunny introduction. Fair enough.

"Last year I assisted with some research involving Poincare along with four other professors."

There's no evidence of this; we don't even know who this person is. There's very little research done merely 'involving' Poincare, and this claim is just so nonspecific it could mean anything. 'Poincare' could mean anything of his, not necessarily his infamous Conjecture.

"We studied weak wide-angle temperature correlations in the cosmic MICROWAVE background."

This has nothing to do with the Poincare Conjecture at all. Nor mathematics in general. This makes little sense, and is totally offtopic.

"There exists a simple geometric model of a NON-INFINITE and NON-NEGATIVE curved space, which we call the POINCARE space."

This is the only ontopic sentence here, and it's just been copy-and-pasted from the article and capitalised strangely.

"This may sound foreign to you, and I'd probably be worried if it didn't, but this POINCARE space can account for these observations with no fine-tuning."

The reason it sounds foreign is because it makes no sense. "I'd probably be worried if you didn't" is just message padding, and the final clause of the sentence refers to 'observations' which no one, not even the poster himself, mentioned. "no fine-tuning" is just more message padding.

"From our "Nature" (425 2003 593) article: "If confirmed, the model will answer the ancient question of whether space is finite or infinite, while retaining the standard Friedmann-Lemaitre foundation for local physics.""

I can't find any such quote on Google. The "425 2003 593" is simply a US court case reference number. Friedmann-Lemaitre is just two random names stuck together. "foundation for local physics" means nothing.

"So, yes, Poincare is VERY important"

Sweeping into the conclusion in response to a nonexistent question ("Is Poincare important?")

"and this postulate"

Why does he refer to it as a postulate and not 'Conjecture' all of a sudden?

"as well as the query as to whether it's been appropriately solved has a HUGE impact on all kinds of other research (math, physics, computer science, etc.) such as this very research that I participated in."

This very research which you just made up out of thin air, yes. And while Poincare's Conjecture is quite important in number theory, topology and consequently numerical cryptography, it has little relevance to physics or other sciences. He's just listed these to sound credible.

And there you have it. One of the most effective trolls today, and you all fell for it. *Sigh.*

Re:Who Cares! or An Exciting Time To Be Alive

[noonien_soong]

You seem to be misinformed. The Riemann hypothesis has not been proven. If it had, we would have heard about it; it is one of the current holy grails of mathematics. The 16th Hilbert problem has not been solved. The student in question only claimed to have solved part of it, and she was dead wrong. Positrons have nothing to do with LEDS, transistors, or diodes, and QED was not relevant to the invention of any of them. "structuring matters behaviors, including time-dependEnt transformations"---what does that even mean? Nothing. You made it up. Having a proof of Poincare's conjecture has absolutely nothing to do with crumple zones, or any engineering problem, for that matter.

I agree that it's an exciting time to be alive, but if you are as ignorant about science as your post would suggest, you would do well to confine your comments to generalities and stop spreading misinformation.