Poincare conjecture proven?

[ewmayer]

Originally Posted by akruppa

Due to the digestive tract, should a rabbit not be equivalient to a doughnut (before mashing (the doughnut, not the rabbit))?

Alex

Well, they might come out similarly (except for the little rabbit bones in your poops, if you were careless in preparing your Hasenpfeffer), but they certainly taste quite a bit different going down.

At this point, I defer to the case of Tyson v. Holyfield, a.k.a. the-famous chocolate-bunny-massacre-defense: "I only like to nibble the ears."

I hope that questions your answer...

[bdodson]

Originally Posted by mfgoode

Well thats the incentive- to write an article in a prestigious mag. and see how well it is received by the public. If the response is good then on with the book.
Sylvia Nasar is the author of 'A Beautiful Mind' - the life of the Nobel laureate John Nash, who for most of the time, was a psychizophrenic. I wonder if you have seen the movie as its a very touching story, with a slight departure to the book, though.
I think he is still active today.
It wont be long before she comes out with a book on Grigori Perelman, the Fields medallist.
Mally

A postscript on the Meyer - Mally dispute about credit for posting
the link to the NY'er's malicious gossip regarding Professor
Yau: just finished reading through the 12-page "claims for
defamation" filed against Nasar and her "fact checker" at the
NY'er. Can't say for sure whether we're to expect an apology
and/or retraction from the NewYorker and/or Nasar, but prospects
for a book supposedly on Perelman's acomplishment that spends
a large portion of it's space on establishing Yau as the villain of
the story seems considerably less likely. People from here that
were at the ICM in Spain noted that people reading the electronic
versions of the text might have missed some of the intended flavor
of the article -- the print version includes a full-page cartoon
showing Yau attempting to pull the Fields medal off from around
Perelman's neck. Certainly inconsistent with the Cao-Zhu paper,
which helps to more firmly establish Perelman's work, without
unduly claiming credit. -bd

[mfgoode]

Originally Posted by bdodson

A postscript on the Meyer - Mally dispute about credit for posting

I am not in the least bothered about this priority of the 1st. posting.
What I am depressed about is that I dont qualify for the Fields medal as Im overage!
Mally

[mfgoode]

Originally Posted by ewmayer

On a more humorous note, Comedy Central's The Colbert Report had a funny segment about the Poincare' conjecture and Perelman's declining the Fields Medal last week - here's a copy of the synopsis I sent to a non-mathematical friend about that:

===

Well, here's the gist of it: the Poincare' conjecture is in the area of topology, which deals with the fundamental "shape" of objects in various-dimensional spaces. One of the key tools in topology is the idea that object A is topologically equivalent to object B if A can be deformed (in a mathematically precise sense, but basically without tearing a hole in it) into B (and v.v.). One of the classic analogies used here is that to a topologist a rabbit and a sphere are equivalent because both are objects without holes, unlike, say, a donut.

===

Thats very good Ernst.
Somewhere in the URL on the NYT article, lengthy as it is, there was a fine explanation on the apple and the rubber ring around it. I am not sure whether these two are topologically equivalent or not and I cant put a finger on it from the URL.
AFAIK; it all stems from the Contour integral in a Gaussian plain where the complex values obtained from the Integral have to go around the origin thereby forming a hole around it. The Integral itself is written differently- just the usual S sign but with a small circle at its midst.
I'm referring to the book 'Road to Reality' by Roger Penrose chapter 8 if Im not mistaken. This book has 16 chapters on the basic maths to understand the General and Special theories of Relativity and is a must for anyone wanting to get a gist at least of GEN. REL.
I would appreciate it if you in your inimitable style could explain a bit more on these holes and why different shapes although looking similar are inequivalent topologically. I mean, make it simple for the rest of us.
Thank you,
Mally

[ewmayer]

Originally Posted by bdodson

just finished reading through the 12-page "claims for
defamation" filed against Nasar and her "fact checker" at the
NY'er. Can't say for sure whether we're to expect an apology
and/or retraction from the NewYorker and/or Nasar, but prospects
for a book supposedly on Perelman's acomplishment that spends
a large portion of it's space on establishing Yau as the villain of
the story seems considerably less likely.

Indeed. Here's a Language Log entry on this, which includes a link to the lawyerly letter you mention: from the LL posting:

The article was presented under the heading of The New Yorker: Fact. The authors were Sylvia Nasar and David Gruber, the category was Annals of Mathematics and the title was Manifold Destiny: A legendary problem and the battle over who solved it (New Yorker, 8/28/2006):

But according to a 12-page letter from Todd & Weld LLP, dated 9/18/2006, this gripping morality play, starring the saintly, reclusive genius Grigory Perelman and the pushy, over-the-hill careerist Shing-Tung Yau, was mostly fiction. Or at least, the damning "facts" and "quotes" dealing with Shing-Tung Yau were mostly fabricated, selected from unreliable sources, or presented as uncontested truth despite substantial contrary evidence.

In other words, despite the New Yorker's reputation for diligent fact-checking, it's claimed that this piece of reportage is roughly as accurate as ABC's much-contested mockumentary The Path to 9/11.

[bdodson]

Originally Posted by ewmayer

Indeed. Here's a Language Log entry on this, which includes a link to the lawyerly letter you mention: from the LL posting:

Ah, that was LL's comment. For the record, from the newspaper of record:
http://www.nytimes.com/2006/10/17/sc...7yau.html?8dpc

After further consideration, some of the people quoted in the New Yorker
article seem to be hedging their bets. In Yau's bio, his year at Stony
Brook was my first year of grad school -- we were the only two people
in a course on Algebras, through the zeta function. Can't say that I
recall any conversation. -Bruce

[Kosmaj]

I did some "detective" work using my very poor Chinese but it was enough to confirm that the Xinhua article of June 4 mentioned on LL indeed contains references to 50/25/30% contribution by Hamilton, Perelman, and Chinese guys, and that "30% by Chinese is an important contribution". Obviously, Nasar&Gruber based their story on this article. And one can argue that it's correct because it was the first one published after events on June 3, while the second one on June 9 can be viewed as a kind of retraction/correction of the first one in order to reduce the damage. I don't think the recording of the news conference is crucial because people talk before and after the conference as well. It's also hard to imagine that the journalist came up with 50/25/30% by himself, at least, I think, he would select the numbers to add up to 100%

[bdodson]

Originally Posted by Kosmaj

I did some "detective" work using my very poor
Chinese ... It's also hard to imagine that the journalist came up with
50/25/30% by himself, at least, I think, he would select the numbers to
add up to 100%

Whereas the mathematicians wouldn't have been bothered? The math
faculty at Lehigh received a rather peculiar email from an address at
yahoo with a subject line of "A good article on the Poincare conecture"
and a link to the New Yorker article. The author seems not to have
gotten the memo. Ah, several memos. He also seems not to have noticed
that Cao was one of the recipients. -Bruce

Originally Posted by Qi Qi

One thing is that this article might have downplayed Cao and Zhu's contribution. According to UCLA Prof. Kefeng Liu's interview with a Chinese newspaper recently, there were gaps in Perelman's proof (hence incomplete) and it was Cao and Zhu who filled the gaps and finally completed the proof, kicking the winning goal. The IMU committee on Fields medals did not know if Perelman was right until they read Cao and Zhu's paper. Cao and Zhu did not win the Fields medal because they were over 40.

And Prof. Shing-Tung Yau reiterated that Chinese mathematicians contributed at least 30% when interviewed in China. In his correspondence with Prof. Shouwu Zhang (Columbia), Yau said this should be called Thurston—Yau—Hamilton—Perelman—Cao—Zhu Theorem, where Chinese contributed 50% in number of persons.

Thank you .
Yours,
Qi

[ewmayer]

Originally Posted by Qi Qi, as forwarded by bdodson

Yau said this should be called Thurston—Yau—Hamilton—Perelman—Cao—Zhu Theorem

Oh, good grief! Interesting that Yau's proposed renaming has his name ahead of both Hamilton's and Perelman's, though.

Today's New York Times has a lengthy article on Yau, titled "The Emperor of Mathematics." Some select snippets:

Among those who took up [Hamilton and Thurston's] challenge, at the urging of Dr. Yau, were Huai-Dong Cao of Lehigh University, a former student, and Xi-Ping Zhu of Zhongshan University. Last June, Dr. Yau announced that they had succeeded and that the first complete proof would appear in The Asian Journal of Mathematics, at which he is the chief editor.

In a speech later that month during the string theory conference, Dr. Yau said, “In Perelman’s work, many key ideas of the proofs are sketched or outlined, but complete details of the proofs are often missing,” adding that the Cao-Zhu paper had filled some of these in with new arguments.

This annoyed many mathematicians, who felt that Dr. Yau had slighted Dr. Perelman. Other teams who were finishing their own connect-the-dots proofs said they had found no gaps in Dr. Perelman’s work. “There was no mystery they suddenly resolved,” said John Morgan of Columbia, who was working with Gang Tian of Princeton on a proof.

So it seems it should really be the Poincare'—Thurston—Yau—Hamilton—Perelman—Cao—Zhu—Morgan—Tian Theorem...

[Yau] denied that he had ever said there were gaps in Dr. Perelman’s work. “I said it is not understood by all people,” he said. “That is why it takes three more years.” As a “leading geometer,” Dr. Yau said he had a duty to dig out the truth of the proof.

...or, if Yau himself now denies that were major "holes" in Perelman's contribution, the Poincare'—Thurston—Hamilton—Perelman—Morgan—Tian—Yau—Cao—Zhu Theorem...

In a twist, a flaw has been discovered in the Cao-Zhu paper. One of the arguments that the authors used to fill in Dr. Perelman’s proof is identical to one posted on the Internet in June 2003 by Bruce Kleiner, of Yale, and John Lott, of the University of Michigan, who had been trying to explicate Dr. Perelman’s work.

In an erratum to run in The Asian Journal of Mathematics, Dr. Cao and Dr. Zhu acknowledge the mistake, saying they had forgotten that they studied and incorporated that material into their notes three years ago.

Ah, so it should really be the Poincare'—Thurston—Yau—Hamilton—Perelman—Cao—Zhu—Morgan—Tian—Kleiner—Lott Theorem.

I'm glad that's settled.

[cheesehead]

So we'll have the ABC Conjecture, RST encryption, Mr. MXYZPTLK and now the PTYHPCZMTKL Theorem.

[ewmayer]

Links to other blogs and newspapers where this is being discussed: here, here, here, here, and here.