Latest on Poincare

A new 473-page paper by Gang Tian and my colleague John Morgan that gives a complete proof of the Poincare conjecture based upon the argument outlined by Grigori Perelman (which carries out the program of my other Columbia colleague Richard Hamilton) is now available as a preprint on the arXiv entitled Ricci Flow and the Poincare Conjecture. This paper is in the process of being refereed and should ultimately appear as a book in the monograph series that the Clay Math Institute publishes with the AMS.

Morgan and Tian just provide a proof of Poincare, not the full geometrization conjecture. Other sources for worked out details of Perelman’s argument are the notes by Kleiner and Lott, and the recent paper by Cao-Zhu that appeared in the Asian Journal of Mathematics. Cao-Zhu provide fewer details than Morgan-Tian, but do give a proof of geometrization. Until very recently the Cao-Zhu paper was only available in the paper version of the journal, for sale by International Press for $69.00. Yesterday the journal put the full paper on-line, and it’s available here.

Latest rumor I hear is that the Fields Medal committee has definitely chosen Perelman as a Fields medalist, with the appearance of these detailed proofs using his arguments clinching the deal. However it remains unclear whether he’ll show up in Madrid, or even actually accept the honor being offered him.

Update: There’s an article about this in this week’s Nature.

Update: The September issue of the Notices of the AMS has an excellent article by Allyn Jackson about this. Next week’s Science Times is supposed to have an article by Dennis Overbye.

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106 Responses to Latest on Poincare

  1. James says:

    Dear Tg and Whu: Your views about the mainstream media’s treatment of China may well be accurate, but either way, I do not see any reason to believe that this article was “anti-China”, or that the authors acted on some presumed motivation to malign the country.

    The article was about Perelman, and it can hardly be regarded as a selective choice of examples to pick the major controversy surrounding his results as an illustration of the causes of his disillusionment with the Mathematics community. Should the article instead have focused on some other minor dispute? Or not have been written?

    I believe that if we regard nationalism and parochialism as undesirable traits, we should try to be the first to criticize our own countries and compatriots, rather than feeling personally responsible for defending them. As a foreigner myself, I know it can be difficult to resist the temptation to identify with my own nationality, but it is important to try, otherwise ugly scenes ensue – as anyone witnessing an international sports event can surely attest.

  2. Student says:

    Excuse me, but when did the New Yorker become a major math journal?

    I would think that people who frequent here would be more interested in what the relevant mathematicians have to say than what reporters said. It apparently is still too early for the experts to have a consensus on how much each involved party has contributed, therefore what the New Yorker article said is really irrelevant — let’s wait until Clay writes the check (even that could still be premature).

    Perelman put it excellently: “If the proof is correct, then no other recognitions are necessary.” Of coruse, he got the “everyone knows” part wrong …


  3. Walt says:

    Student: And how is this expert consensus going to be communicated to the hoi polloi? In the Notices? Through word of mouth?

  4. Pingback: Ars Mathematica » Blog Archive » More Manifold Destiny

  5. Ken Dev says:

    I spent more than an hour in a bookshop today reading Sylvia Nassar’s story on Perelman in the New Yorker. It was sad to read that he has decided to leave mathematics, a tragedy. Hope he changes his mind. Well, I know at least two people who refused the Nobel Prize [Literature and Peace]. What was disturbing about Nassar’s article is the intrigue, backstabbing etc. by a Field Medalist, a famous Chinese mathematician against his own student, also a Chinese, who is now a Professor of Maths at Harvard. To the Professor’s credit, he refuses to protest his teacher’s behavior– he says it is the Chinese tradition.

    I used to teach a very simple first year undergraduate course on visual topology, years ago, in a British University. Never did I think that a topic on topology will be such a sensational story 20 years later. Later on in my life, I switched to biology after arriving at MIT as a Visiting Scientist. We were all captivated by Watson’s “Double Helix.” In particular, it was absorbing to read how top scientists can be ordinary human beings with all their faults etc. Nassar’s story reminded me of those events. Who knows, maybe, Ms. Nassar will write a book that will be made into film like, “A Beautiful Mind,” on John Nash’s life? What is needed is a very simplified description of how Poincare’s Conjecture was solved by Perleman. All the articles that have appeared so far, including several in the NYT, do not quite get it. I hope someone succeeds in doing that. It deserves to be told, now that it took hundred years to solve it!

  6. woit says:

    I’m shutting down comments here. It’s wasting too much time deleting the endless Tian vs. Yau nonsense that some people are trying to spam this blog with.

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