I'll just google the proof but I know i'll only vaguely understand it if left to my own mathematics education. I was hoping someone here would explain it as I know some of you have had much more study in mathematics.
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Chinese Nationalists Steal Credit for Perelman's Proof of Poincare's Conjecture
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I came upon a barroom full of bad Salon pictures in which men with hats on the backs of their heads were wolfing food from a counter. It was the institution of the "free lunch" I had struck. You paid for a drink and got as much as you wanted to eat. For something less than a rupee a day a man can feed himself sumptuously in San Francisco, even though he be a bankrupt. Remember this if ever you are stranded in these parts. ~ Rudyard Kipling, 1891
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Originally posted by VetLegion
USA is probably the closest thing the world ever had to true meritocracyI came upon a barroom full of bad Salon pictures in which men with hats on the backs of their heads were wolfing food from a counter. It was the institution of the "free lunch" I had struck. You paid for a drink and got as much as you wanted to eat. For something less than a rupee a day a man can feed himself sumptuously in San Francisco, even though he be a bankrupt. Remember this if ever you are stranded in these parts. ~ Rudyard Kipling, 1891
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Originally posted by VetLegion
Well, see Perelman. In Russia they fire him, presumably because he didn't play the institute politics right, and he is now jobless. A genius of his caliber would get a job in US somewhere, no?I came upon a barroom full of bad Salon pictures in which men with hats on the backs of their heads were wolfing food from a counter. It was the institution of the "free lunch" I had struck. You paid for a drink and got as much as you wanted to eat. For something less than a rupee a day a man can feed himself sumptuously in San Francisco, even though he be a bankrupt. Remember this if ever you are stranded in these parts. ~ Rudyard Kipling, 1891
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Hmmm... I didn't catch that nuance. That's really strange. Why would they do that?
I guess that he would have a long list of offers from the US, if he expressed interest. I mean, why not? The Clay Institute is laying the groundwork for him to accept the bulk of their $1 million prize, after all. Commissioning all sorts of papers so that the proof fits its prize criteria. Virtually slobbering over his work.
To be fair, wouldn't he also have a long list of offers in Europe?Last edited by DanS; August 28, 2006, 15:08.I came upon a barroom full of bad Salon pictures in which men with hats on the backs of their heads were wolfing food from a counter. It was the institution of the "free lunch" I had struck. You paid for a drink and got as much as you wanted to eat. For something less than a rupee a day a man can feed himself sumptuously in San Francisco, even though he be a bankrupt. Remember this if ever you are stranded in these parts. ~ Rudyard Kipling, 1891
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Re: I haven't seen the proof and my math training is a distant memory.
Originally posted by PuddlewatchHQ
I'll just google the proof but I know i'll only vaguely understand it if left to my own mathematics education. I was hoping someone here would explain it as I know some of you have had much more study in mathematics.
By useful I just meant is this going to be something to watch for highly interesting applications such as mapping software or navigation systems or some such. The article I read ( maybe from CNN? I can't remember) mentioned the conjecture had to do with determining the shape of an object in a three dimensional space or some such. The article had stated the proof would provide solutions to the possible shape of the universe or some wording to that effect. It was all very vague and of course I don't expect a mainstream media outlet like CNN to publish the whole proof or even the conjecture but I expect them to show at least a few equations to wet one's appetite for further reading in the topic. I was expecting too much or perhaps the science desk wasn't the department that ran the story. And by department I mean the handful of new reporters who get stuck with the science assignments. Minus the very view journalists at mainstream news companies who have science backgrounds or who may be consultants. Or did this story break over the weekend in the US? If it did break on Friday or Saturday then likely the there will be more coverage of it in the mainstream press tonight or well at some point this week.
I haven't seen any word yet from an astrophysicist yet on what this proof might mean for their work. I think that's the part the annoys me the most. I have to confess I am a bit impatient to hear what they have to say.
The Poincare conjecture says that any compact simply connected 3-dimensional manifold is homeomorphic to the 3-sphere. A 3-dimensional manifold is a geometric object that locally looks like 3-dimensional space; a space is simply connected if any loop can be deformed continuously to a point. "Homeomorphic" means, roughly, "the same shape up to bending and stretching". The 2-sphere is what we would ordinarily call the surface of a sphere (which locally looks like a plane); the 3-sphere is similar except it locally looks like 3-space. What Perelman actually proved was Thurston's geometrization conjecture, which says, loosely (I don't know the details of this myself), that every compact 3-manifold can be made to locally look like some "nice", homogeneous geometry. Any such nice geometry that is simply connected must be homeomorphic to a 3-sphere, so Poincare follows.
My knowledge of physics is limited, but I don't see how this could have any direct applications to astrophysics, since I thought that the universe was supposed to be at least 4-dimensional, while the proof is entirely in 3 dimensions (and the Poincare conjecture for 4 dimensions was proved back in the 1980s).
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Originally posted by DanS
The Clay Institute is laying the groundwork for him to accept the bulk of their $1 million prize, after all. Commissioning all sorts of papers so that the proof fits its prize criteria. Virtually slobbering over his work.
To be fair, wouldn't he also have a long list of offers in Europe?
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Thanks for the explanation.
I didn't realize how specialized a field topology is in relation to the rest of mathematics. I guess it's hard to appreciate the nature of the fractured nature of mathematical study from ouside the field.
Well, I was leaving Time out of the model. Perhaps I shouldn't do that. I was thinking of a simple map to represent the universe. I habitually take things to literally.
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Re: Chinese Nationalists Steal Credit for Perelman's Proof of Poincare's Conjecture
Originally posted by DanS
Meanwhile, Hamilton, the American mathematician on whom Perelman's work is based and who will be apportioned a great deal of credit in any event, appears to be above the fray and more interested in wine and women.
Math
Wine and women"Stuie has the right idea" - Japher
"I trust Stuie and all involved." - SlowwHand
"Stuie is right...." - Guynemer
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Re: Thanks for the explanation.
Originally posted by PuddlewatchHQ
I didn't realize how specialized a field topology is in relation to the rest of mathematics. I guess it's hard to appreciate the nature of the fractured nature of mathematical study from ouside the field.
Well, I was leaving Time out of the model. Perhaps I shouldn't do that. I was thinking of a simple map to represent the universe. I habitually take things to literally.
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Right, I didn't mean to imply that level of fracture.
I was expecting a lot more comment from the greater scientific community about how this changes our view of things. Allthough I suppose at this point it would still be speculation.
I don't have the requisite knowledge to discuss this in any technical terms. I'm looking over some online info on basic topology and such. I have a lot of study to do before this would be an interesting course of conversation.
Thanks for the chat and the information. Time to make dinner.Last edited by PuddlewatchHQ; August 28, 2006, 17:33.
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Re: So has anyone here read the proof itself?
Originally posted by PuddlewatchHQ
And I am getting tired of Chinese Americans who identify more strongly with the regime in China then the country in which they have lived the majority of their lives.(\__/) 07/07/1937 - Never forget
(='.'=) "Claims demand evidence; extraordinary claims demand extraordinary evidence." -- Carl Sagan
(")_(") "Starting the fire from within."
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