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Poincaré Conjecture May Be Solved

Flamerule writes "The New York Times is now reporting that Dr. Grigori (Grisha) Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, appears to have solved the famous Poincaré Conjecture, one of the Clay Institute's million-dollar Millennium Prize problems. I first noticed a short blurb about this at the MathWorld homepage last week, but Google searches have revealed almost nothing but the date and times of some of his lectures this month, including a packed session at MIT (photos), in which he reportedly presented material that proves the Conjecture. More specifically, the relevant material comes from a paper ("The entropy formula for the Ricci flow and its geometric applications") from last November, and a follow-up that was just released last month."

26 of 284 comments (clear)

  1. Cool. by Anonymous Coward · · Score: 3, Funny

    Only two years more of eating noodles before he's rich!

    1. Re:Cool. by cannonfodda · · Score: 2, Funny

      Nah ! That's two academic years! That translates to 200,001,22123.828299121 years for the rest of us.

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      Hmmmmmm
  2. Donuts, apples, I'm hungry by stanmann · · Score: 2, Funny

    The subject of 3 dimensional objects with holes is quite fascinating... wouldn't it be awesome if it was discovered that toroids are actually some extradimensional manifestation... Or even that Toroids have special properties allowing FTL travel...

    --
    Food not Bombs is a nice platitude but it breaks down when you notice that the Bombees are usually well fed
    1. Re:Donuts, apples, I'm hungry by override11 · · Score: 4, Funny

      Only a specific subset of 3-dimensional objects have holes or cavities that are facinating

      Women, right???

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      No I didnt spell check this post...
  3. Re:And the answer is... by Cached+Hit · · Score: 1, Funny

    i thought it was 42

    --
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  4. I solved this first!! by LordYUK · · Score: 0, Funny

    The Solution: Yes, I do have Grey Poupon.

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  5. Re:Y'know by LordYUK · · Score: 4, Funny

    "...in the hope that someone explains it in a manner I can understand"

    You're new here, arent you?

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    This is my sig. Its pathetic.
  6. Re:Explanation by jkramar · · Score: 4, Funny

    Silly people... this is TOPOLOGY! It's not meant for people to USE it! It's just for mathematicians to RUMINATE UPON!

    Has Fermat's Last Theorem actually been used in practical applications? I don't think so...

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    true && more || less
  7. Sequel by telstar · · Score: 2, Funny

    Complex mathematics? Looks like its time for Matt Damon and Pretty-Boy Affleck to write Good Will Hunting II.

  8. Poincare Conjecture Solved Ages Ago by The+Real+Minister · · Score: 5, Funny
  9. Now I Understand... by masq · · Score: 5, Funny
    ... why we love talking about Linux so much - It's so damn USER-FRIENDLY compared to other geek pursuits!
    We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1) Ricci flow, considered on the space of riemannian metrics modulo diffeomorphism and scaling, has no nontrivial periodic orbits (that is, other than fixed points); (2) In a region, where singularity is forming in finite time, the injectivity radius is controlled by the curvature; (3) Ricci flow can not quickly turn an almost euclidean region into a very curved one, no matter what happens far away. We also verify several assertions related to Richard Hamilton's program for the proof of Thurston geometrization conjecture for closed three-manifolds, and give a sketch of an eclectic proof of this conjecture, making use of earlier results on collapsing with local lower curvature bound.
    1. Re: Now I Understand... by ray-auch · · Score: 2, Funny

      I guess it depends on whether or not the popup is simply connected, and, if so, if it is homoemorphic to the 3-sphere (this may depend on whether or not it is open or closed but I'm not sure on that bit).

  10. Re:What's that conjecture again? by simong_oz · · Score: 1, Funny

    Loosely speaking, this means that every 3-dimensional object that has a set of sphere-like properties can be stretched or squeezed until it is a 3-sphere without breaking it. Note that a 3-sphere consists of all those points in 4-dimensional space R4 that have a distance of 1 from the origin.

    Well why didn't you just say so in the first place. It's so simple when you put it in plain english ...
    [/sarcasm]

    --
    "Because it's there." - George Mallory, when asked why he wanted to climb Mt Everest, March 18, 1923 (New York Times)
  11. squarepoint by eurostar · · Score: 1, Funny

    an article about a FRENCH mathematician ?
    are you some sort of unamerican antipatriot ?
    better change his name to "squarepoint" before this site gets banned...

  12. Re:What about the Dunwoody paper? by Eccles · · Score: 5, Funny

    So, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?

    The part of the proof where it says "then a miracle occurs..." is being questioned by numerous mathematicians.

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    Ooh, a sarcasm detector. Oh, that's a real useful invention.
  13. Re:I'm pretty sure this is a dupe by Anonymous Coward · · Score: 1, Funny

    Well, to paraphrase a Dice Clay joke...

    My teacher asks me "Whats the difference between the Reimann hypothesis and the poincare conjecture?"

    And I go "That's what I say, whats the fucking difference?"

  14. Re:Explanation by CommieLib · · Score: 4, Funny

    Mmmmm...hypothetical donut...

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  15. Re:What about the Dunwoody paper? by Glyndwr · · Score: 2, Funny

    I prefer to think of it as

    public static void main (String[] args) {
    doStuff();
    }

    --
    You win again, gravity!
  16. Re:Explanation by jalet · · Score: 5, Funny

    > Now, can someone tell me what practical
    > applications there might be of this?

    An application would be to make better doughnuts, I suppose.

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  17. Typo... by mrtroy · · Score: 2, Funny

    It appears most people are spelling incorrectly! Including the sites included in the post!

    It is not "mathematician" ..... its "mathemagician"

    Please make the appropriate corrections. :)

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    [I can picture a world without war, without hate. I can picture us attacking that world, because they'd never expect it]
  18. Proof of Poincare conjecture.... by Dthoma · · Score: 2, Funny

    Me. Hammer. Pliers. Every available 3-manifold. Can I have my $1 million please?

    (This of course assumes that 3-manifolds are malleable.)

    --

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  19. this can't be by paiute · · Score: 2, Funny

    I thought that this Wolfram guy was the smartest man in the universe and had all the answers. Now some brie-muncher comes along and proves something in math that Wolfram couldn't? This can only be due to one of three reasons:

    1. When Wolfram and Hart were all killed by the Beast, Wolfram was in the house.
    2. Wolfram is human and isn't as smart as the papers say.
    3. He stepped up to MCHawking and is now hanging from a tree with a sign pinned to him that reads: WHACK EMCEE.

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  20. Perl? by comet_11 · · Score: 5, Funny

    I swear that looks like perl.

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  21. Re:sigh by jensend · · Score: 2, Funny

    Remember the mathematicians' toast, though: "Here's to pure mathematics! May it never be of any use to anybody!" I think it's attributed to GH Hardy.

  22. Re:Explanation by Enonu · · Score: 3, Funny

    How can you break the rubber band in order to get the doughnut to go to a point without breaking the doughnut too?

  23. Re:Explanation by gughunter · · Score: 2, Funny

    If this proof is correct, it will forever change the way we do texture-mapping on 4-dimensional graphics cards.