Chinese Mathematicians Prove Poincare Conjecture

Joe Lau writes to mention a story running on the Xinhua News Agency site, reporting a proof for the Poincare Conjecture in an upcoming edition of the Asian Journal of Mathematics. From the article: "A Columbia professor Richard Hamilton and a Russian mathematician Grigori Perelman have laid foundation on the latest endeavors made by the two Chinese. Prof. Hamilton completed the majority of the program and the geometrization conjecture. Yang, member of the Chinese Academy of Sciences, said in an interview with Xinhua, 'All the American, Russian and Chinese mathematicians have made indispensable contribution to the complete proof.'"

Comments

It's all a conjecture

[The Bungi]

I looked at TFA, and I was kind of lost after reading this:

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, where a three-sphere is simply a generalization of the usual sphere to one dimension higher.

Homeomorphic. Thank god, they dumb it down a bit later:

More colloquially, the conjecture says that the three-sphere is the only type of bounded three-dimensional space possible that contains no holes. This conjecture was first proposed in 1904 by H. Poincaré Eric Weisstein's World of Biography (Poincaré 1953, pp. 486 and 498), and subsequently generalized to the conjecture that every compact n-manifold is homotopy-equivalent to the n-sphere if it is homeomorphic to the n-sphere. The generalized statement reduces to the original conjecture for n==3.

More colloquially, it's homotopy-equivalent to the n-sphere! Of course!

Slow news day?

Re:It's all a conjecture

[Umbral Blot]

You might think that this is useless to you. However simply memorize those quotes and you can be prepared for any situation. Boss unexpectedly wants a status report? Sure boss, currently my I'm developong a compact n-manifold that is homotopy-equivalent to the n-sphere if it is homeomorphic to the n-sphere. We'll be done in a couple of weeks. Wife bothering you to take out the trash? Sure honey right after I demonstrate that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, where a three-sphere is simply a generalization of the usual sphere to one dimension higher. Never be at a loss for words again!

Re:It's all a conjecture

[S3D]

echnically, it's more like proving P != NP, since that's the current accepted belief. Proving P=NP would be huge - this would give polynomial time algorithms for Travelling Salesman Problem, Boolean Satisiability Problem, and a slew of others (that all reduce to each other in polynomial time).

Proving P=NP would cause doors to the Cthulhu dimention opened, as was shown by Charlse Stross in The Atrocity Archives

Chinese == Good at Math

[hyeh]

Wow, Chinese people solved a math problem?

This is news?

(j/k... I am Chinese).

Re:Chinese == Good at Math

[dartarrow]

NO the news is that the lest of the wold undestan wen thee Chinese peopre EXPRAIN the sorusion to the plobrem.

*ducks*

Re:Ok, in plain english

[binarybum]

I think it basically has something to do with:

    If poincare conjecture = proved , my homepage switches to harsh new look. QED.

Re:This is...

[nacturation]

One down, seven more to go!

Given that there are seven questions total, maybe you know the mystery surrounding the elusive eighth question: "What is seven minus one?"

Re:Ok, in plain english

[mozu]

Seems like whats been proven is that a doughnut != sphere.

Re:Ok, in plain english

[david.given]

In topology spheres are identical to cubes and pyramids.

A topologist is someone who doesn't know whether to dip their doughnut into their coffee mug, or vice versa...

Re:This is...

[mlow82]

There are actually 8 problems now. I added the Twin Prime Conjecture via one mighty edit to the Wikipedia article!

Just kidding, of course. ;)

Re:Dear God

[grolschie]

Does He read /. ?

What does it all mean?

[distantbody]

What are the useful applications of this? Can I get a quantum computer next week!?

Re:What does it all mean?

[Anonymous Coward]

Hell, no. You'll get your quantum computer last week.

Here is a conjecture

[2Bits]

I assert that there is a torrent of the proof somewhere on the net. Now can someone prove that, please?

Joe Public goes

[advocate_one]

"isn't that like the Da Vinci Code???"

I think it makes a good thriller title... "The Poincare Conjecture"

Re:This is...

[ozbird]

Given that there are seven questions total, maybe you know the mystery surrounding the elusive eighth question: "What is seven minus one?"

Forty-two?

Re: They are the kind of people ...

[140Mandak262Jamuna]

... who would pour their coffee into their doughnuts and dunk their cups in the soggy mess and look surprised. They are topologists. They cant tell a cup from a doughnut. When they need a ball in a hurry they will break off the handle of their coffee cup and try to bounce it on the court. These topologists are the most confused/confusing mathematicians around. ;-) They could make their math easier for us lesser mortals to understand. But they would rather knot.

Re:Dear God

[Anonymous Coward]

How can you complain? The plans have been available in the local planning office for the last nine months.

Re:A translation...

[Anonymous Coward]

It proves that topologically there is no difference between you yesterday, and you now with your head up your ass.

Re:A translation...

[OldManAndTheC]

You lost me after 'First,'

Re:A translation...

[Anonymous Coward]

This is going to be huge in the glassblowing world ...