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Millennium Prize Awarded For Perelman's Poincaré Proof

Posted by timothy on from the now-prove-perelman-exists dept.

epee1221 writes "The Clay Mathematics Institute has announced its acceptance of Dr. Grigori Perelman's proof of the Poincaré conjecture and awarded the first Millennium Prize. Poincaré questioned whether there exists a method for determining whether a three-dimensional manifold is a spherical: is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point? The Poincaré conjecture is that there is no such 3-manifold, i.e. any boundless 3-manifold in which the condition holds is homeomorphic to the 3-sphere. A sketch of the proof using language intended for the lay reader is available at Wikipedia."

8 of 117 comments (clear)

  1. Re:what about... by MR.Mic · · Score: 4, Informative

    You can easily determine the cubic volume of a spherical cavity by using the formula: V = 4/3 PI R^3.

    However, in the case of your image, the volume would probably be better matched by a cylindrical volume: V = PI R^2 H

    On second thought, a one-sheet hyperboloid would probably be the best match.

  2. Some background by ThoughtMonster · · Score: 5, Informative

    For those just in, here's an article covering Perelman and his theorem.

    This wikipedia entry covers some controversies following the article.

  3. Great news by Frans+Faase · · Score: 5, Informative

    I am very happy that they have awarded the price only to him, although he did meet the requirement that the proof should be published in a peer-reviewed journal. I am very happy that they did not included those two Chinese guys who did write down the proof (about 260 pages) and claimed that they had proven the conjecture. Perelman was very upset by this especially that other mathematics did not raise their voice. I hope that Perelman will accept the price. He said (some years ago) that he would only decide when the offer was made, if he would except the price or not.

  4. So will he accept? by Puff_Of_Hot_Air · · Score: 5, Informative

    Perelman has famously turned down the fields medal and shunned the world since the whole Yau political saga. Will he take this prize? I hope that he will. I think that the whole Yau trying to take the credit for the proof issue, sullied the entire world for Perelman. Perhaps now that the honour is being fairly directed at him in response to his work, Perelman will be able to re-enter society and enjoy some of the fruits of his labour.

    1. Re:So will he accept? by Obyron · · Score: 5, Interesting

      I can't take credit for finding this. Another Slashdotter was kind enough to link it the last time Perelman came up, but I found this to be very enlightening and illustrative of Perelman's personality as well as the whole Yau controversy. It's an article from the New Yorker co-written by Sylvia Nasar, who wrote the biography of John Nash, A Beautiful Mind. It contains what was at the time the only interview with Grigori Perelman, but I'm not sure if that's still true.

      Annals of Mathematic: Manifold Destiny

      --
      --Obyron
    2. Re:So will he accept? by Vellmont · · Score: 4, Insightful


      Has anyone had a hard answer as to why he turned down the prizes and medals?

      What his friends have said is he believes actually proving it is reward enough. It's like being the first person to land on the moon, and someone gives you a "you landed on the moon" prize.

      Still, a million dollars is something that can give you a lot of freedom. Turning it down is something that he might regret later.

      --
      AccountKiller
    3. Re:So will he accept? by Puff_Of_Hot_Air · · Score: 5, Insightful

      Perelman is not a normal guy (obvious I realize, but hear me out). People like to subscribe 'normal' motives for behaviour they see as abnormal. I think this is why the idea that the fields medal was rejected as 'beneath' him was put forward. Arrogance is simple to understand. But what did Perelman actually say? "[the prize] was completely irrelevant for me. Everybody understood that if the proof is correct then no other recognition is needed". What Perelman was looking for was recognition for solving the problem. This was more important than the fields medal! What he got instead, was Yau and his cohorts claiming to have "really solved it." In Perelman's mind, political play such as this has no place in mathematics! Worse, his peers were not standing up to a) condemn this behaviour, and b) defend his paper. I think an important missing piece was that Perelman had not been officially recognized as having solved the Poincare conjecture. Now that this had been rectified, perhaps the world will be in enough order for him to rejoin it.

  5. Re:English Please by pomakis · · Score: 4, Informative

    I think the question is easier to understand if you knock everything down a dimension, because then it can actually be visualized. Take the surface of any three-dimensional object that doesn't contain any holes (e.g., a cup, but NOT a coffee mug with a handle). Can the surface be stretched/distorted to be shaped into a sphere? The answer is fairly obviously yes. But is this also true for four-dimensional objects? Stop trying to visualize it; you can't. You have to rely on the math instead. But that, I believe, is the question.