Chinese Nationalists Steal Credit for Perelman's Proof of Poincare's Conjecture

[DanS]

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.

The referenced article gives a reasonably good explanation.

[DanS]

Originally posted by VetLegion
USA is probably the closest thing the world ever had to true meritocracy

I wonder...

[VetLegion]

Originally posted by DanS


I wonder...

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?

[Kuciwalker]

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.

[DanS]

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?

He was fired? Are you reading between the lines? Or are you creating a scenario?

[VetLegion]

He wasn't re-elected, same thing.

[DanS]

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.

http://www.claymath.org/

To be fair, wouldn't he also have a long list of offers in Europe?

[civman2000]

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.

Don't expect to find anyone who actually truly understands the proof; most mathematicians only have at best a vague idea of how the proof works. I can explain the statement, though.

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).

[VetLegion]

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.

Yeah, I noticed that. I think his ego must be floating high above St. Petersburg right now. There are actually people out there working hard to give him a million dollars, while he is being all "maybe, maybe I allow you to give it to me, maybe not, we shall see" . Hilarious.

To be fair, wouldn't he also have a long list of offers in Europe?

Maybe, I'm not familiar with the academic scene. I know it's very hard in Europe to get a good position, you have to work your way through the ranks and it takes ages. I think US is more open for a star performer, institutions being willing to cut some corners to get him/her

[PuddlewatchHQ]

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.

[Stuie]

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.

Good to see there's one "smart" person who isn't an idiot.

Math
Wine and women

[civman2000]

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.

Topology isn't particularly specialized or fractured from the rest of mathematics. Indeed, all the different areas of mathematics are quite intertwined. The thing is, math is just such a huge field that often no one other than specialists can understand the cutting edge of any one area. Virtually all mathematicians know what the Poincare conjecture says and to some extent why it is important, but unless you're a low-dimensional topologist who knows something about Ricci flow, I imagine you won't get much out of the proof.

[PuddlewatchHQ]

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.

[Urban Ranger]

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.

China has a phenomenal cultural value. The US has very little. If the distance isn't so great many US cities would have flipped.

[DinoDoc]

Civ III heresy!