Poincare' Conjecture

tullio
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Topic 191333

According to the Italian newspaper 'La Repubblica" (www.repubblica.it) which cites the June issue of the Asian Journal of Mathematics, the Poincare' Conjecture on the topological properties of the n-sphere has been proven by two Chinese mathematicians, Zhu Ziping and Cao Huaidong, Such a result is worth a million dollar prize by the Clay Institute, the newspaper reports, since it is one of the seven Millenium problems (not to be confused with the Hilbert list of problems, which dates 1900). The Conjecture was put forward by Jules Henri Poincare' in 1904. So it seems that topology has some practical utility...
Tullio

kinhull
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Poincare' Conjecture

Quote:
According to the Italian newspaper 'La Repubblica" (www.repubblica.it) which cites the June issue of the Asian Journal of Mathematics, the Poincare' Conjecture on the topological properties of the n-sphere has been proven by two Chinese mathematicians, Zhu Ziping and Cao Huaidong, Such a result is worth a million dollar prize by the Clay Institute, the newspaper reports, since it is one of the seven Millenium problems (not to be confused with the Hilbert list of problems, which dates 1900). The Conjecture was put forward by Jules Henri Poincare' in 1904. So it seems that topology has some practical utility...
Tullio

Here's some sort of explanatory link (not that I understood a word of it!!!):

The Poincaré conjecture

Clay Mathematics Institute

  • If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.
Odysseus
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Here’s another summary,

Here’s another summary, including a substantial list of references:

Eric W. Weisstein. "Poincaré Conjecture." From MathWorld--A Wolfram Web Resource.

tullio
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There is a readable article

There is a readable article on the online NYTimes 14 August edition (registration required). It looks like the conjecture proof first advanced by the Russian mathematician G.Perelman shall be discussed this week in an International Mathematical Union conference held in Madrid.
Tullio

Bird-Dog
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Story in The Times (uk) today

Story in The Times (uk) today that Perelman has solved it and is not interested in material things so is unlikely to claim the prize or any awards that go with it.

edit spelling

debugas
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did i understand right that

Message 36606 in response to message 36605

did i understand right that Perelman has proved a more general theorem than Zhu Ziping and Cao Huaidong did ? Or do i miss something here?

tullio
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RE: did i understand right

Message 36607 in response to message 36606

Quote:
did i understand right that Perelman has proved a more general theorem than Zhu Ziping and Cao Huaidong did ? Or do i miss something here?


Frankly, I cannot answer this question. The article in the La Repubblica paper did not even mention Perelman's name, while the New York Times article is centered about Perelman and makes only a passing reference to the two Chinese scientists.
Maybe a professional mathematician could answer this, I am only a physicist. Cheers.
Tullio

tullio
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RE: RE: did i understand

Message 36608 in response to message 36607

Quote:
Quote:
did i understand right that Perelman has proved a more general theorem than Zhu Ziping and Cao Huaidong did ? Or do i miss something here?

Frankly, I cannot answer this question. The article in the La Repubblica paper did not even mention Perelman's name, while the New York Times article is centered about Perelman and makes only a passing reference to the two Chinese scientists.
Maybe a professional mathematician could answer this, I am only a physicist. Cheers.
Tullio


According to a New Scientist article, Perelman is going to refuse to accept the Fields Medal, the mathematicians' Nobel, which should be presented to him by the King of Spain on August 22. In doing this he would follow the steps of Alexander Grothendieck, who refused it for political reasons, but later accapted it. Nobody knows where Perelman is now.

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