20031231, 18:03  #1 
Sep 2002
11 Posts 
Poincare conjecture proven?

20031231, 21:30  #2 
Sep 2003
A1D_{16} Posts 
This is not really news.
It's been known for many months now that a proof has been claimed. And it's a very serious proof, it's a Russian guy who pulled an "Andrew Wiles", ie, worked on it in seclusion for many years without publishing anything and finally inventing some new math to come up with a lengthy, complicated proof. He's given seminars and has had a ready answer for any points or issues raised, obviously has thought very deeply about it for a long time. So it will probably be like FLT... there won't be any definite moment in time when people say "aha it's proved". Rather, after enough time without a flaw or counterexample found, acceptance will gradually grow stronger. 
20040517, 14:58  #3 
Dec 2003
Hopefully Near M48
1758_{10} Posts 
http://mathworld.wolfram.com/PoincareConjecture.html
Anyone heard of updates on the verification of this proof? Its been some time since it was first announced. Unfortunately, there are many times when I hear about new developments in math or science in the news, but no followup reports appear for a LONG time, if ever. 
20040517, 15:44  #4  
Banned
"Luigi"
Aug 2002
Team Italia
4,813 Posts 
Quote:
Luigi 

20040907, 07:10  #5 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
A new article on Yahoo News, but the article doesn't seem to have much new in it:
http://story.news.yahoo.com/news?tmp...ience_maths_dc By the way, that article doesn't give the links to Perelman's papers, so I give them here: http://www.arxiv.org/abs/math.DG/0211159 http://www.arxiv.org/abs/math.DG/0303109 Last fiddled with by jinydu on 20040907 at 07:11 
20040907, 07:26  #6  
Banned
"Luigi"
Aug 2002
Team Italia
11315_{8} Posts 
Quote:
Luigi 

20040907, 08:20  #7 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
There has been one more recent paper by Perelman:
http://www.arxiv.org/abs/math.DG/0307245 It was published after the Mathworld article, so there was no link to it from the Mathworld article, which is why it didn't appear in my last post. Actually, Poincare's Conjecture isn't mentioned in the abstracts of any of the 3 papers. Thurston's geometrization conjecture is mentioned once in the abstract of the 1st paper: "We also verify several assertions related to Richard Hamilton's program for the proof of Thurston geometrization conjecture for closed threemanifolds, and give a sketch of an eclectic proof of this conjecture, making use of earlier results on collapsing with local lower curvature bound." [It seems to me he's saying that he's giving just a sketch of a proof, not a fully worked out proof]. The 3rd paper contains the sentence: "Our argument (in conjunction with [P, [some symbol I don't know about] 15]) also gives a direct proof of the so called "elliptization conjecture". However, it appears on the 1st page of the paper, not on the absract. This might be the closest that Perelman gets to explicitly claiming that he has solved the Poincare Conjecture. According to: http://mathworld.wolfram.com/Thursto...onjecture.html "Since the trivial group is in particular a finite group, the elliptization conjecture implies the Poincaré conjecture." Last fiddled with by jinydu on 20040907 at 08:28 
20040907, 12:54  #8 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
11^{2}×79 Posts 
If he doesn't want the $1,000,000, I will take it.

20060815, 19:56  #9  
∂^{2}ω=0
Sep 2002
República de California
2^{2}×3^{2}×17×19 Posts 
And the Winner is...
There's a long article on this in today's New York Times, to the effect that the consensus is that the PC has been proven by Perelman et al. (the wrangling over the "et al" may take some time), and that Perelman himself has apparently vanished off the face of the earth:
http://www.nytimes.com/2006/08/15/science/15math.htm I find the part about the Ricci flow especially interesting, since the mathematics there has deep connections with the maths of general relativity. The resulting problems with singularities remind one of renormalization in quantum mechanics. Fascinating stuff. Article text, in case the above link eventually becomes inactive: Quote:
Last fiddled with by ewmayer on 20060822 at 19:37 

20060815, 19:56  #10  
∂^{2}ω=0
Sep 2002
República de California
2^{2}×3^{2}×17×19 Posts 
(continued from above)
Quote:
Last fiddled with by ewmayer on 20060822 at 19:38 Reason: Reduced text size of quoted material 

20060817, 12:24  #11 
Bronze Medalist
Jan 2004
Mumbai,India
2052_{10} Posts 
Poincare's conjectured proved !
From Slashdot.org 0]Flamerule writes "A New York Times article has finally provided an update on the status of [1]Grigori Perelman's 2003 rough proof of the [2]PoincarÃ© Conjecture. 3 years ago, Perelman published several papers online explaining his idea for proving the conjecture, but after giving lectures at MIT and several other schools ([3]covered on Slashdot) he returned to Russia, where he's remained silent since. Now, mathematicians in the US and elsewhere have finally finished going over his work and have produced several papers, totaling 1000 pages, that give stepbystep, complete proofs of the conjecture. In addition to winning some or all of the $1,000,000 [4]Millennium Prize, Perelman now seems to be the favorite to receive a [5]Fields Medal at the International Mathematics Union meeting next week, but it's not clear that he'll even show up!" Discuss this story at: http://science.slashdot.org/comments.../08/16/0144202 Links: 0. http://slashdot.org/~Flamerule 1. http://www.nytimes.com/2006/08/15/science/15math.html 2. http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture 3. http://science.slashdot.org/article....1337219&tid=14 4. http://en.wikipedia.org/wiki/Clay_Mathematics_Institute 5. http://en.wikipedia.org/wiki/Fields_Medal Mally 
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