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Has The Poincare Conjecture Been Solved?

simoniker posted more than 10 years ago | from the let's-conject-together dept.

292

Zack Coburn writes "An article in the Boston Globe alludes to the Poincare Conjecture being solved, possibly. For those who are unfamiliar with the conjecture, the article gives a brief description: "To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe." Apparently Grigory Perelman may have proved it, which would mean a $1 million award from the Clay Mathematics Institute." We've previously discussed other possible Poincare proofs.

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292 comments

GNAA: Happy Nig Year (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850543)

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Re:GNAA: Happy Nig Year (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850834)

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Happy new year from GNAA (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850544)

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# Important Smurfs: Please try to keep posts on Smurfette.
# Try to spooge on other people's comments instead of starting new threads (of semen.)
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Problems regarding accounts or comment posting should be sent to Hitler [tiscali.dk]

# Important Smurfs: Please try to keep posts on Smurfette.
# Try to spooge on other people's comments instead of starting new threads (of semen.)
# Read George Bush's subliminablble messages before posting your own to avoid simply duplicating what has already been said. (Like George W and his Dad)
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Problems regarding accounts or comment posting should be sent to Hitler [tiscali.dk]

# Important Smurfs: Please try to keep posts on Smurfette.
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Problems regarding accounts or comment posting should be sent to Hitler [tiscali.dk]

frist nye postz (-1, Troll)

lamery (598414) | more than 10 years ago | (#7850547)

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Similar article (-1)

Anonymous Coward | more than 10 years ago | (#7850553)

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In 2002, I researched the COSMIC background (-1, Troll)

Amsterdam Vallon (639622) | more than 10 years ago | (#7850555)

(First off, remember that us MATHEMATICANS DO IT SMOOTHLY AND CONTINUOUSLY.) Hehehe, wow, too many New Year's drinks. Anyway, on to the story.

Last year I assisted with some research involving Poincare along with four other professors. We studied weak wide-angle temperature correlations in the cosmic MICROWAVE background.

There exists a simple geometric model of a NON-INFINITE and NON-NEGATIVE curved space, which we call the POINCARE space.

This may sound foreign to you, and I'd probably be worried if it didn't, but this POINCARE space can account for these observations with no fine-tuning.

From our "Nature" (425 2003 593) article: "If confirmed, the model will answer the ancient question of whether space is finite or infinite, while retaining the standard Friedmann-Lemaitre foundation for local physics."

So, yes, Poincare is VERY important, and this postulate as well as the query as to whether it's been appropriately solved has a HUGE impact on all kinds of other research (math, physics, computer science, etc.) such as this very research that I participated in.

Re:In 2002, I researched the COSMIC background (-1, Redundant)

RealProgrammer (723725) | more than 10 years ago | (#7850612)

Mod parent up.

Re:In 2002, I researched the COSMIC background (0)

Anonymous Coward | more than 10 years ago | (#7850654)

Mod parent up.

WTF? Parent was total bullshit.

Re:In 2002, I researched the COSMIC background (0)

Anonymous Coward | more than 10 years ago | (#7850665)

Proof? Or are you just trolling?

Re:In 2002, I researched the COSMIC background (1)

Smitedogg (527493) | more than 10 years ago | (#7850693)

There is no Slaughter college, and he is a known troll. dogg

Re:In 2002, I researched the COSMIC background (0)

Anonymous Coward | more than 10 years ago | (#7850705)

What about actually disproving what he says instead of making cheapshots at his college and suposed troll status?

Re:In 2002, I researched the COSMIC background (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850765)

Karma whores must be killed in front of their loved ones, then raped, bukkake'd on, and then shit on. Karma whores are the lowest forms of "life" on the planet. A. Vallon is a prime example of pure human shit. And the piece of shit faggot even is a slashdot subscriber. WHAT A FAGGOT! This turd even PAYS cmdrsuckoff to TROLL! What kind of WORTHLESS FAGGOT pays a shit website to do this?

Re:In 2002, I researched the COSMIC background (3, Informative)

Smitedogg (527493) | more than 10 years ago | (#7850813)

Last year I assisted with some research involving Poincare along with four other professors. We studied weak wide-angle temperature correlations in the cosmic MICROWAVE background.

There exists a simple geometric model of a NON-INFINITE and NON-NEGATIVE curved space, which we call the POINCARE space.

First, he states that he is either Jean-Pierre Luminet, Alain Riazuelo, Jeffery Weeks, Jean-Philippe Uzan, or Roland Lehoucq, none of whom are Computer Science professors as his sig claims him to be. Second, none of these gentlemen teach at 'slaughter college', which once again does not exist.

Finally, that particular study was interesting, but solving Poincare's theory wouldn't affect it at all. He wrongly used Poincare's significance. The Planck surveryor data should determine Omega0 to within 1%, and from that it will be simple to conclude (as the fine men who studied this did) that if Omega0 is less than 1.01, Poincare's dodecahedron makes a bad model of the universe, and if it's greater then it's a good model. This is not dependant on proving Poincare's theorum.

dogg

I'd believe you... (0)

Anonymous Coward | more than 10 years ago | (#7850616)

...if your past posts weren't virtually all trolls.

Re:I'd believe you... (0)

Anonymous Coward | more than 10 years ago | (#7850656)

aren't most of AC's posts trolls?

So why should I believe you?

Re:I'd believe you... (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850812)

SUCK MY COCK VALLON, OR WHICHEVER FAGGOT KARMAWHORE FRIEND OF HIS POSTED THIS PRIME EXAMPLE OF PURE FAGGOTRY. HEY FUCKER, YOU GOT A LOT OF BOYCUM DRIPPING FROM YOUR MOUTH. BETTER WASH THAT OFF BEFORE DADDY COMES HOME AND SHOVES HIS BIG COCK DOWN YOUR LOSER THROAT! *_g_o_a_t_s_e_x_*_g_o_a_t_s_e_x_*_g_o_a_t_s_e_x_*_
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s___|_________/_/______\__/\___/____|__________|s_ _
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Important Stuff: Please try to keep posts on topic. Try to reply to other people's comments instead of starting new threads. Read other people's messages before posting your own to avoid simply duplicating what has already been said. Use a clear subject that describes what your message is about. Offtopic, Inflammatory, Inappropriate, Illegal, or Offensive comments might be moderated. (You can read everything, even moderated posts, by adjusting your threshold on the User Preferences Page) If you want replies to your comments sent to you, consider logging in or creating an account.

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Important Stuff: Please try to keep posts on topic. Try to reply to other people's comments instead of starting new threads. Read other people's messages before posting your own to avoid simply duplicating what has already been said. Use a clear subject that describes what your message is about. Offtopic, Inflammatory, Inappropriate, Illegal, or Offensive comments might be moderated. (You can read everything, even moderated posts, by adjusting your threshold on the User Preferences Page) If you want replies to your comments sent to you, consider logging in or creating an account.

Re:In 2002, I researched the COSMIC background (5, Funny)

kurosawdust (654754) | more than 10 years ago | (#7850661)

(First off, remember that us MATHEMATICANS DO IT SMOOTHLY AND CONTINUOUSLY.)

Yes but Godel showed that you never do it completely.

Re:In 2002, I researched the COSMIC background (1)

TexVex (669445) | more than 10 years ago | (#7850700)

See my sig...

Re: In 2002, I researched the COSMIC background (4, Funny)

Black Parrot (19622) | more than 10 years ago | (#7850674)


> In 2002, I researched the COSMIC background

Yeah, lots of people do that in college... Usually with the help of LSD and stuff.

PARENT IS TROLL, CHECK HISTORY, MOD DOWN (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850687)

like the fucking loser faggot he is

PARENT IS TROLL MOD DOWN (0)

Anonymous Coward | more than 10 years ago | (#7850768)

ac is a loser faggot. check his other posts

Re:PARENT IS TROLL MOD DOWN (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850808)

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g_______________________________________________g_ _
o_/_____\_____________\____________/____\_______o_ _
a|_______|_____________\__________|______|______a_ _
t|_______`._____________|_________|_______:_____t_ _
s`________|_____________|________\|_______|_____s_ _
e_\_______|_/_______/__\\\___--___\\_______:____e_ _
x__\______\/____--~~__________~--__|_\_____|____x_ _
*___\______\_-~____________________~-_\____|____*_ _
g____\______\_________.--------.______\|___|____g_ _
o______\_____\______//_________(_(__>__\___|____o_ _
a_______\___.__C____)_________(_(____>__|__/____a_ _
t_______/\_|___C_____)/______\_(_____>__|_/_____t_ _
s______/_/\|___C_____)_______|__(___>___/__\____s_ _
e_____|___(____C_____)\______/__//__/_/_____\___e_ _
x_____|____\__|_____\\_________//_(__/_______|__x_ _
*____|_\____\____)___`----___--'_____________|__*_ _
g____|__\______________\_______/____________/_|_g_ _
o___|______________/____|_____|__\____________|_o_ _
a___|_____________|____/_______\__\___________|_a_ _
t___|__________/_/____|_________|__\___________|t_ _
s___|_________/_/______\__/\___/____|__________|s_ _
e__|_________/_/________|____|_______|_________|e_ _
x__|__________|_________|____|_______|_________|x_ _
*_g_o_a_t_s_e_x_*_g_o_a_t_s_e_x_*_g_o_a_t_s_e_x_*_


Important Stuff: Please try to keep posts on topic. Try to reply to other people's comments instead of starting new threads. Read other people's messages before posting your own to avoid simply duplicating what has already been said. Use a clear subject that describes what your message is about. Offtopic, Inflammatory, Inappropriate, Illegal, or Offensive comments might be moderated. (You can read everything, even moderated posts, by adjusting your threshold on the User Preferences Page) If you want replies to your comments sent to you, consider logging in or creating an account.

Important Stuff: Please try to keep posts on topic. Try to reply to other people's comments instead of starting new threads. Read other people's messages before posting your own to avoid simply duplicating what has already been said. Use a clear subject that describes what your message is about. Offtopic, Inflammatory, Inappropriate, Illegal, or Offensive comments might be moderated. (You can read everything, even moderated posts, by adjusting your threshold on the User Preferences Page) If you want replies to your comments sent to you, consider logging in or creating an account.

Important Stuff: Please try to keep posts on topic. Try to reply to other people's comments instead of starting new threads. Read other people's messages before posting your own to avoid simply duplicating what has already been said. Use a clear subject that describes what your message is about. Offtopic, Inflammatory, Inappropriate, Illegal, or Offensive comments might be moderated. (You can read everything, even moderated posts, by adjusting your threshold on the User Preferences Page) If you want replies to your comments sent to you, consider logging in or creating an account.

MOD DOWN (0)

Anonymous Coward | more than 10 years ago | (#7850689)

Known troll. If you look at his posting history, he posts total BS to every thread he can get his unwashed claws on.

Re:MOD DOWN (0)

Anonymous Coward | more than 10 years ago | (#7850719)

Can you prove that this is total BS, or are you just a jerk that just goes aruond getting people modded down?

Re:MOD DOWN (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850748)

Is that you, Vallon? RKZ perhaps? Regardless, you are a pathetic cocksucker. I hope you witness your mother getting raped then killed, then raped again.

Re:In 2002, I researched the COSMIC background (0)

Anonymous Coward | more than 10 years ago | (#7850698)

What is this +5 Informative shiat? You mods are tools.

Poster also claims to be consultant for the Israeli Ministry of Commerce [slashdot.org] , a National Weather Service researcher [slashdot.org] , and other assorted hooey.

Re:In 2002, I researched the COSMIC background (3, Funny)

Guppy06 (410832) | more than 10 years ago | (#7850702)

"(First off, remember that us MATHEMATICANS DO IT SMOOTHLY AND CONTINUOUSLY.)"

They also DO IT with GRATUITOUS USE of CAPITAL LETTERS! Lay off the shift key!

Man, who let Shatner have the keyboard?

-1 Troll (1)

dafoomie (521507) | more than 10 years ago | (#7850735)

Mod parent down. He's claimed to be all sorts of things and is just a pain in the ass. He's not even funny. Jesus man, at least be a funny troll. Or good. You're neither.

Re:-1 Troll (0)

Anonymous Coward | more than 10 years ago | (#7850760)

I tried. It was moded back up before the page refresh completed. Read his history, if he is all that he claims, he is a unique person.

Re:-1 Troll (-1, Offtopic)

Anonymous Coward | more than 10 years ago | (#7850786)

Actually I think he's actually a very good troll. He even researched to find a real "Nature" article to refer to. That takes dedication.

Re:In 2002, I researched the COSMIC background (1)

slubberdegullion (544119) | more than 10 years ago | (#7850742)

Maybe before condemning him as a "troll," you losers should actually look into what he's talking about.

"Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background" did appear in Nature, as a quick search will show.

Re:In 2002, I researched the COSMIC background (1)

Darby (84953) | more than 10 years ago | (#7850846)

Maybe before condemning him as a "troll," you losers should actually look into what he's talking about.

A quick perusal of his homepage was illuminating.

Oh well, wife's ready. Off to the party.

Re:In 2002, I researched the COSMIC background (1)

benna (614220) | more than 10 years ago | (#7850769)

The "Nature" article he refers to can be found here [arxiv.org] however im not sure I believe he is who he says he is because this article has no mention of Poincare space. Not to mention the history of this poster as a troll.

Re:In 2002, I researched the COSMIC background (1)

harlows_monkeys (106428) | more than 10 years ago | (#7850836)

[...]this article has no mention of Poincare space

Uhm, it's mentioned 20 times, including a mention right in the abstract. Download the TeX source and look at lines 76, 144, 147, 158, 164, 175, 176, 180, 197, 215, 223, 226, 340, 342, 345, 386, 390, 399, 400, and 405.

Re:In 2002, I researched the COSMIC background (1)

RealProgrammer (723725) | more than 10 years ago | (#7850837)

The "Nature" article he refers to can be found here however im not sure I believe he is who he says he is because this article has no mention of Poincare space. Not to mention the history of this poster as a troll.

Here we present a simple geometrical model of a finite, positively curved space - the Poincare dodecahedral space - which accounts for WMAP's observations with no fine-tuning required. Circle searching (Cornish, Spergel and Starkman, 1998) may confirm the model's topological predictions, while upcoming Planck Surveyor data may confirm its predicted density of 0 1.013 > 1. If confirmed, the model will answer the ancient question of whether space is finite or infinite, while retaining the standard Friedmann-Lematre foundation for local physics.

Uh, are you sure it's not relevant? Seems fairly on target to me. But then, I'm not a Real Mathematician.

Always be prepared to learn from any source, from the silliest, drunken troll to the most sober robed judge.

Re:In 2002, I researched the COSMIC background (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850787)

I HOPE SOME AIDS-RIDDEN CRACK ADDICT STABS YOU IN THE THROAT WITH A SHARD OF BROKEN GLASS. YOU DESERVE NO LESS YOU GODDAMNIT FUCKING KARMAWHORE! WHORING FOR KARMA IS WORSE THAT PEDOPHILIA AND NECROPHILIA COMBINED!

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Re:In 2002, I researched the COSMIC background (0)

Anonymous Coward | more than 10 years ago | (#7850844)

Lol, you know the trolls are frustrated when they resort to this kind of stuff to get their point across.

Pretty pathetic but amusing

A line-by-line proof... (4, Informative)

James A. C. Joyce (733782) | more than 10 years ago | (#7850839)

...of why this guy is a troll and all who modded him up must be smoking the $2 crack.
"(First off, remember that us MATHEMATICANS DO IT SMOOTHLY AND CONTINUOUSLY.) Hehehe, wow, too many New Year's drinks. Anyway, on to the story."

OK, a fairly unfunny introduction. Fair enough.

"Last year I assisted with some research involving Poincare along with four other professors."

There's no evidence of this; we don't even know who this person is. There's very little research done merely 'involving' Poincare, and this claim is just so nonspecific it could mean anything. 'Poincare' could mean anything of his, not necessarily his infamous Conjecture.

"We studied weak wide-angle temperature correlations in the cosmic MICROWAVE background."

This has nothing to do with the Poincare Conjecture at all. Nor mathematics in general. This makes little sense, and is totally offtopic.

"There exists a simple geometric model of a NON-INFINITE and NON-NEGATIVE curved space, which we call the POINCARE space."

This is the only ontopic sentence here, and it's just been copy-and-pasted from the article and capitalised strangely.

"This may sound foreign to you, and I'd probably be worried if it didn't, but this POINCARE space can account for these observations with no fine-tuning."

The reason it sounds foreign is because it makes no sense. "I'd probably be worried if you didn't" is just message padding, and the final clause of the sentence refers to 'observations' which no one, not even the poster himself, mentioned. "no fine-tuning" is just more message padding.

"From our "Nature" (425 2003 593) article: "If confirmed, the model will answer the ancient question of whether space is finite or infinite, while retaining the standard Friedmann-Lemaitre foundation for local physics.""

I can't find any such quote on Google. The "425 2003 593" is simply a US court case reference number. Friedmann-Lemaitre is just two random names stuck together. "foundation for local physics" means nothing.

"So, yes, Poincare is VERY important"

Sweeping into the conclusion in response to a nonexistent question ("Is Poincare important?")

"and this postulate"

Why does he refer to it as a postulate and not 'Conjecture' all of a sudden?

"as well as the query as to whether it's been appropriately solved has a HUGE impact on all kinds of other research (math, physics, computer science, etc.) such as this very research that I participated in."

This very research which you just made up out of thin air, yes. And while Poincare's Conjecture is quite important in number theory, topology and consequently numerical cryptography, it has little relevance to physics or other sciences. He's just listed these to sound credible.

And there you have it. One of the most effective trolls today, and you all fell for it. *Sigh.*

SFC (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850557)

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Re:SFC (0)

Anonymous Coward | more than 10 years ago | (#7850589)

can members of the simonigger fan club still be modded -1 by timothy and michael?

huh? (-1, Offtopic)

Anonymous Coward | more than 10 years ago | (#7850571)

Could I have a different story? One that I even remotely relate to?

Re:huh? (0)

Anonymous Coward | more than 10 years ago | (#7850701)

Could I have a different story? One that I even remotely relate to?

OK. New headline:

Has The Pope's Conjecture Been Solved?

An article in the Boston Globe alludes to the Pope's Conjecture being solved, possibly. For those who are unfamiliar with the conjecture, the article gives a brief description: "God exists. He is the answer to everything. To solve it, we have to burn every scientist and return to the good old ways of gathering the truth. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.

Apparently Bernardo Gui may have proved it, which would mean a $1 million award from the Rome Theological Institute. In other news, Bernardo Gui applied for a patent describing a method of oxidizing witches by attaching them to heaps of burning cellulose.

I proved it (2, Funny)

Anonymous Coward | more than 10 years ago | (#7850576)

But I've been too busy trying to get first post to tell someone. I wonder how many other huge discoveries are stopped by the same problem. It's a good thing Einstein didn't have Slashdot.

Has the Poincare Conjecture Been Solved? (5, Informative)

James A. C. Joyce (733782) | more than 10 years ago | (#7850579)

No.

(It even says in the freaking article stub that the proof is merely alluded to, for crying out loud.)

ATTN - JOYCE (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850615)

THIS IS RKZ SPEAKING, I HAVE JOINED THE GAY NIGGERS.

I got a better job and dont have time for properly trolling. But the #GNAA a great organization, irc://irc.foxlink.net/#gnaa

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OMG, RKZ! THEY HIJAX0RED J00R ACCOUNTZOR! (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850638)

"No wonder they say dirty things to you when you walk past. You're asking for it. If you get raped you deserve it."
She'd break down immediately into sobbing hysteria.

I, for one, (3, Funny)

bersl2 (689221) | more than 10 years ago | (#7850584)

welcome our new topological overlord.

will gnu millennium end corepirate nazi execrable? (-1, Troll)

Anonymous Coward | more than 10 years ago | (#7850588)

we won't be needing nearly as much phonIE ?pr? ?firm? 'security' as we're being subjected to now, upon completion of the disempowerment of the greed/fear/ego based corepirate nazis, aka unprecedented evile.

as for seeking their acceptance/approval? that must be something robbIE made up to appear to be more of a corepirate nazi sucksass than was previously thought.

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mynuts won, expatriated?

Due to excessive bad posting from this IP or Subnet, comment posting has temporarily (forever, when we can purchase some ept) been disabled. If it's you, consider this a chance to sit in the timeout corner. If it's someone else, this is a chance to hunt them down like with father william's phonIE bouNTy huNTer scams. If you think this is unfair, we don't care, as we're now way into the gnu dating 'business'. maybe, while your posting 'privleges' have been suspended, you'd like to check out our stable of won-eyed girls, like the won in the jump-you ads?

Re:will gnu millennium end corepirate nazi execrab (0)

Anonymous Coward | more than 10 years ago | (#7850663)

Happy new year, and to robbIE too, while you're at it.

Awesome! (0)

Aphex Junkie (633436) | more than 10 years ago | (#7850592)

Hooray for Russians :)
But in all seriousness, if he really solved it, then this could mean all kinds of "kewl" stuff will be coming out of the field of topology...

I thought... (2, Interesting)

ameoba (173803) | more than 10 years ago | (#7850600)

I remember seeing a (webcasted) talk given by the Clay Institute about their $1M math prizes, in particular, the one about P=NP. In it, the speaker said that "if P=NP is proven, then all the others are going to fall in short time, making that solution worth $8M" (or $1M * the number of problems).

I was really hoping that that kind of money would get the P=NP results first...

Re:I thought... (2, Funny)

jrockway (229604) | more than 10 years ago | (#7850734)

Well, it's a hard problem. If it was an easy problem, then it would have been solved.

You might say that it's an NP hard problem. Hahah. *crickets* Oh well.

Description of the new shape (5, Funny)

SeanTobin (138474) | more than 10 years ago | (#7850602)

Let me guess.. he says that the new topological object is universe-shaped?

Fuck! (1, Funny)

Anonymous Coward | more than 10 years ago | (#7850603)

I was planning on proving it for my Phd Thesis...
Now, what am I supposed to talk about ? :/

mirror (1, Troll)

Anonymous Coward | more than 10 years ago | (#7850604)

in case of slashdotting...

BERKELEY, Calif. -- A reclusive Russian mathematician appears to have answered a question that has stumped mathematicians for more than a century.

After a decade of isolation in St. Petersburg, over the last year Grigory Perelman posted a few papers to an online archive. Although he has no known plans to publish them, his work has sent shock waves through what is usually a quiet field.

At two conferences held during the last two weeks in California, a range of specialists scrutinized Perelman's work, trying to grasp all the details and look for potential flaws.

If Perelman really has proved the so-called Poincare Conjecture, as many believe he has, he will become known as one of the great mathematicians of the 21st century and will be first in line for a $1 million prize offered by the Clay Mathematics Institute in Cambridge.

Colleagues say Perelman, who did not attend the California conferences and did not respond to a request for comment, couldn't care less about the money, and doesn't want the attention. Known for his single-minded devotion to research, he seldom appears in public; he answers e-mails from mathematicians, but no one else.

"What mathematicians enjoy is the chase of really difficult problems," said Hyam Rubinstein, a mathematician who came from Australia to attend meetings at the Mathematical Sciences Research Institute in Berkeley and the American Institute of Mathematics in Palo Alto, Calif., hoping to better understand Perelman's solution. "This problem is like the Mount Everest of math conjectures, so everyone wants to be the first to climb it."

The Poincare Conjecture, named after the Frenchman who proposed it in 1904, is the question that essentially founded the field of topology, the "rubber-sheet geometry" that looks at the properties of surfaces that don't change no matter how much you stretch or bend them.

To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.

Dozens of the best mathematicians of the last century tried with all kinds of approaches to solve the conjecture. Some thought they had it for months, even years, but counter-examples and flaws just kept springing up. Simply-stated but elusive to prove -- like Fermat's Last Theorem -- this conjecture has spurred the development of whole branches of mathematics.

A decade ago, after some work in the United States that colleagues described as "brilliant," Perelman gave up a promising career to work in seclusion in St. Petersburg. Although he appears occasionally, most recently for lectures at the Massachusetts Institute of Technology and several other US schools last spring, he keeps a very low profile.

Even in mathematical circles, surprisingly little is known about him, and those who know him often don't want to speak publicly about his work.

At any rate, he seems to have used his time alone wisely. While working out the Poincare Conjecture, Perelman also seems to have established a much stronger result, one that could change many branches of mathematics. Called the "Geometrization Conjecture," it is a far-reaching claim that joins topology and geometry, by stating that all space-like structures can be divided into parts, each of which can be described by one of three kinds of simple geometric models. Like a similar result for surfaces proved a century ago, this would have profound consequences in almost all areas of mathematics.

As the foundation for his proof, Perelman used a method called Ricci flow, invented in the mid-1980s by Columbia University mathematician Richard Hamilton, which breaks a surface into parts and smooths these parts out, making them easier to understand and classify.

Although some mathematicians find it disturbing that Poincare's simple question could have such a complicated answer, Hamilton is not worried. After so many failed proofs, he said, "no one expected it to be easy."

Hamilton calls Perelman's work original and powerful -- and is now running a seminar at Columbia devoted to checking Perelman's proof in all its detail.

If the proof is vetted, the Clay Mathematics Institute may face a difficult choice. Its rules state that any solution must be published two years before being considered for the $1 million prize. Perelman's work remains unpublished and he appears indifferent to the money. Hamilton, on the other hand, did the foundational work on which the proof is based -- but that was over a decade ago. And, as with any major finding, many people have contributed in some degree.

Huge financial prizes raise the stakes for assigning credit for major proofs like this one. For the time being, however, researchers are sharing their approaches with a sense of openness. And the mood is one of cautious optimism that Perelman's approach, even if flawed, will eventually be the one that works.

It takes years for a solution to make the leap from being just another claim to actually being considered "true." Perelman's work will be digested by a wide range of mathematicians in the next few years, said University of California at Davis mathematician Joel Hass. Steps that Perelman pushed through by brute force will be replaced with simpler methods, and his work will be integrated into other fields, Hass said.

And while the equivalent of the Poincare conjecture has already been proven for dimensions four and up, no one yet has any idea how to classify all the spaces that appear in higher dimensions. This state of ignorance is what prods mathematicians to keep working.

"It's interesting how a really good felching can sometimes be much better than a really good man-on-man blowjob," Rubinstein said with a grin.

Christina Ricci Flow (0, Offtopic)

Anonymous Coward | more than 10 years ago | (#7850621)

Perelman used a method called Ricci flow

Now, I'm as much a fan of Christina Ricci as the next guy, but knowing about her flow is beyond the limits of what I'd like to know about her. I do wonder, however, how that guy from "Beauty and the Beast" is involved.

TROLL (1, Informative)

Anonymous Coward | more than 10 years ago | (#7850660)

"It's interesting how a really good felching can sometimes be much better than a really good man-on-man blowjob," Rubinstein said with a grin

Last line, devious bugger ;)

What is PoinCare? (0)

Anonymous Coward | more than 10 years ago | (#7850605)

Come join "PoinCare", the medical plan for nerds!

Formerly known as "Poindexter Medicare", this might be the plan for you!

Have you have carpal tunnel from too much keyboard use since age 3?

Do you have teeth braces so you can't say "Linux" without it coming out all slushy?

Are you glasses now 3 inches thick from squinting at screens?

Worried that you still can't "respond" in a male fashion when 7 of 9 appears on the screen?

PoinCare might be the cure to these and many more problems that afflict the geek community!

Oh man! (0)

Anonymous Coward | more than 10 years ago | (#7850611)

I wish they'd help me fold my one dimensional shape!

duh (0)

tiredwired (525324) | more than 10 years ago | (#7850620)

um, so you can't create a hole just by bending stuff. I have been going about hole creating all the wrong way. How will I plant this tree?

Finite Universe (2, Interesting)

Anonymous Coward | more than 10 years ago | (#7850624)

Imagine a square sheet of rubber (so we can stretch, bend as we like). It has a finite area, and four edges. We choose one edge and glue it to its opposite edge. Now if you start from one point and draw a line in the right direction, you'll get back to where you started. Otherwise you'll just spiral around until you hit an edge.

Now we take the two circular edges and we glue them together, giving a donut (a torus). Now if you go in [what you see as] a straight line in any direction, you'll never reach an edge. The surface of the donut doesn't have any sides in the way the original sheet of rubber did, but it still covers a finite area.

N.b. The problem with this example is that it's difficult to think of just the surface of the donut, without imagining it being 'in' some larger space such as the 3D world.

Now if you want a headache, try to imagine doing this starting not with a square, but rather a cube, and joining opposing faces together. The first pair is easy - you get a sort of square donut shape. The second pair gives you a donut with an inner donut removed - something like the inner tube in a tyre.

The third one is the real bugger - you have to imagine joining the inner surface of the tube to the outer one, without going through the tube. I've seen a video [uiuc.edu] that included a representation of what a similar manouvre (sp?) would look like in the 3D world that the cube started in, and I still can't fully get my head around it.

No matter what direction you moved in this weird twisted-cube-thingy, you'd never see an edge. It would give you the same effect as if there were an infinite array of cubes , with the exact same thing happening in each one. When you reach the edge of one cube, you ust move into the next one ... which is identical to the last one.

This article says that the Universe is doing the same sort of thing, only starting with a dodecahedron instead of a cube (i.e. 6 pairs of faces instead of 3). Don't seriously try to picture this, or your head'll explode ...


-----
What Happened to the Censorware Project? [sethf.com]
Censorship: The Battle Begins At Home [kuro5hin.org]

Using the troll database? (0)

Anonymous Coward | more than 10 years ago | (#7850666)

Seen this exact post before.

PARENT IS LYING (0)

Anonymous Coward | more than 10 years ago | (#7850673)

How is this a troll? And what does an AC have to gain anyway?

Re:Using the troll database? (1, Funny)

Tablizer (95088) | more than 10 years ago | (#7850792)

Seen this exact post before.

Holy groundhog, Batman! Slashdot posts are stuck in an infinite hyper-toroid loop!

Re:Finite Universe (0)

Anonymous Coward | more than 10 years ago | (#7850682)

ahem.......

a donut has a hole you dork!!!!

Re:Finite Universe (1)

David Price (1200) | more than 10 years ago | (#7850703)

It helps, for the 3-D version, to visualize a square sheet of rubber with some thickness, rather than a cube. My visualizing intuition didn't want to swallow the idea of a rubber cube that was stretchy enough so that one face could be pulled around to touch the other.

Re:Finite Universe (4, Informative)

Bombcar (16057) | more than 10 years ago | (#7850716)

I've seen a video [uiuc.edu]

Just a little note for moderators: If you see something like that, it means the post was cut 'n' pasted from another slashdot post!

Here! [slashdot.org]

With italics and everything, including the link!

Google!

Re:Finite Universe (1)

Tablizer (95088) | more than 10 years ago | (#7850829)

Don't seriously try to picture this, or your head'll explode ...

If you think Mars probes are hard to guide, wait until we have Universe probes. 5D trig has gotta be hard to grope.......I mean grasp. -- Calif. Govnr.

Sphere? (1)

Saint Stephen (19450) | more than 10 years ago | (#7850629)

Surely they mean obloid? An egg doesn't have holes. Can anybody provide a better description?

Re:Sphere? (1)

superwiz (655733) | more than 10 years ago | (#7850724)

Egg is toplologically equivalent to a sphere. Roughly speaking, shapes are toplologically equivalent (i.e. homeomorphic) if you can get one from the other by stretching, shrinking or bending without creating any new holes and without forcing any points that previously didn't touch to touch.

Re:Sphere? (2, Interesting)

Saint Stephen (19450) | more than 10 years ago | (#7850755)

Oh, I knew that. I got a BS in math, but I never took any topology classes. I know a bit informally though, via my bro. in law who got a masters.

Even though they're topologically equivalent, I would have expected them to call the "obloids" or "closed simply connected two dimensional surfaces", instead of spheres. In linear algebra or measure theory its usually called a "ball".

Re:Sphere? (1)

superwiz (655733) | more than 10 years ago | (#7850820)

Well, actually B^n is an n-dimensional ball. It is the whole ball -- including the points inside of it. S^(n-1) is an n-dimensional sphere. Meaning just the countour -- the outside. S circle is usually denoted as S^1. Btw, B^n is sometimes written as D^n (d stands for disk). The n-1 instead of n is there because S^(n-1) is locally diffeomorphic to R^(n-1). That is a circle locally looks just like a line and a sphere locally looks just like a plane.

Is Collatz Next? (1)

kantai (719870) | more than 10 years ago | (#7850634)

ah, yes, the red-headed stepchild of the conjecture family - Collatz!

People have been going at Collatz Conjecture For Years, and maybe this recluse is giving that a swing next time.

For Information regarding Collatz Conjecture seek The Collatz Conjecture [216.239.39.104]

This Proof Isn't New (4, Informative)

muon1183 (587316) | more than 10 years ago | (#7850635)

This proof has been out for about 9 months, and so far has stood up to intense scrutiny. Perelman is considered one of the top mathematicians in his field, and other mathematicians believe his proof is likely correct, although it is still being scrutinized. I recently attended a lecture by Richard Hamilton, who has been leading a team going through the proof, and he showed the method used and which sections of the proof had already been verified. It appears that the Poincare Conjecture finally has been solved.

If you are interested in the method of proof, Perelman used the Ricci Flow, blow-up arguments, and surgery to prove the Thurston Geometrization conjecture (a theorem far more powerful than the Poincare Conjecture alone).

Re:This Proof Isn't New (1)

Tablizer (95088) | more than 10 years ago | (#7850802)

I am not an expert in mathematical proofs, but I wonder why computers can't be used to varify (or help verify) the logic of given proofs?

Re:This Proof Isn't New (0)

Anonymous Coward | more than 10 years ago | (#7850814)

I wonder why computers can't be used to varify (or help verify) the logic of given proofs?

They don't seem to work on spelling verification, so why should we trust them on math? :-)

Re:This Proof Isn't New (3, Funny)

InternalWave (546747) | more than 10 years ago | (#7850806)

What's really important is that this proof was put out by a reclusive Russian mathematician. That pretty much clinches it.

I'm confused... (3, Insightful)

Magic5Ball (188725) | more than 10 years ago | (#7850637)

"To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes ... And while the equivalent of the Poincare conjecture has already been proven for dimensions four and up..."

Being a non-math person, it seems to me if it has been solved for two dimensions (has it?) and four and up, wouldn't three dimensions just be a special case of the many (four and up) dimensions proof? Or is there something special about that proof that limits it to four and up? Or perhaps something in a form like the two dimension proof?

Perhaps my simple understanding of proofs in euclidian geometry doesn't scale up like this :-)

Re:I'm confused... (1)

Deraj DeZine (726641) | more than 10 years ago | (#7850718)

Maybe they didn't think of that? Most mathematicians are rathe eccentric...

Re:I'm confused... (5, Insightful)

sam_nead (607057) | more than 10 years ago | (#7850762)

Indeed, the Poincare Conjecture (that every n-manifold with the homotopy groups of an n-sphere is homeomorphic to an n-sphere) has been solved in dimensions n = 1, 2, 4, 5, 6, ... The only missing case is n = 3, which is the case originally conjectured (well, really "asked about") by Poincare.

The cases n = 1, 2 are not so hard and may be explained to undergraduates. n = 5 and above are not easy but not impossible to explain, either -- Smale got a Fields medal for his work in this area. It can now be covered in a single graduate level mathematics course. The idea (if I remember correctly) basically boils down to "in high enough dimensions, there is enough elbow room". To give a better analogy, generically straight lines in two dimensions meet but in three dimensions they do not. (And to really say what is going on "Two-dimensional surfaces generically do not meet each other if embedded in a five-dimensional space")

The case n = 4 was handled by Michael Freedman using very subtle techniques (at least to me!) but again relying on "having enough space to move around in".

I don't understand the n = 3 case at all, really -- no one has given a simple "These techniques should work because x, y, znd z" sort of explaination, yet. The closest they come is to mutter uncomprehensible things about the heat equation... Suffice to say -- in dimension three there is not enough room to move around in. So it is not a complete surprise that the proof for n = 3 is rather different from higher n.

Re:I'm confused... (1)

superwiz (655733) | more than 10 years ago | (#7850770)

Well... no, it doesn't work that way. Just because something works in higher dimensions, doesn't mean it works in lower. Here's the simplest example I can think of. If you "live" in 2 dimensions, and you see a squared in from of you, you can "walk around" it. If, on the other hand, you live in 1 dimension (a line) and you see a line segment in front of you, you can't "walk around" it. This is not really related to the Pointcare. It's just an example of how properties of space don't neccesserily get prerved as you move up or down dimesnions.

Pure science is pure science... (1)

criordan (733016) | more than 10 years ago | (#7850655)

Pure science is pure science. All great discoveries that have ever existed have been because of small, previously unrelated pure mathematical works (or other pure true sciences), which when done on their own seem to have no superficial meaning to someone such as an engineer or common layman, but pure mathematics is akin to pieces of a grand puzzle. Each piece is intrinsically linked to the whole picture. Looking at each piece will not reveal the puzzle, although solving each piece on its own will. This proof need not prove anything to an engineer, a computer scientist, a ballerina, or the mailman, but to a mathematician and others who understand its significance (among others) this proof advances the pure science of mathematics...and by that the world will eventually be forever changed.

I've found a remarkable proof of this fact... (0, Redundant)

Anonymous Coward | more than 10 years ago | (#7850672)

...but there is not enough space in this Slashdot comment to write it.

Reeeeee- (1)

OtakuHawk (682073) | more than 10 years ago | (#7850685)

POST!

Followup (0, Troll)

Anonymous Coward | more than 10 years ago | (#7850691)

There is more coverage at the Smegma Research Institute [smegma.ca] 's information page

Random thought... (4, Interesting)

HaloZero (610207) | more than 10 years ago | (#7850692)

  • There is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.


How do you know that the shape of the universe does not include holes?

My fucking hero. (1)

conner_bw (120497) | more than 10 years ago | (#7850695)

Colleagues say Perelman, who did not attend the California conferences and did not respond to a request for comment, couldn't care less about the money, and doesn't want the attention. Known for his single-minded devotion to research, he seldom appears in public; he answers e-mails from mathematicians, but no one else.

My fucking hero. Thank you Russia for consistently producing maniacs like this man.

Re:My fucking hero. (0)

Anonymous Coward | more than 10 years ago | (#7850810)

Really. Somebody should go to Russia and rough him up. Why can't he just drink beer and watch football like everybody else?

Who Cares! or An Exciting Time To Be Alive (1, Insightful)

thelizman (304517) | more than 10 years ago | (#7850706)

For those of you wondering "who cares" or "what's the point", well there really is none. Poincare's conjecture has no immediate practical application, or even in the near future. However, proving Poincare's conjecture is a shot in the arm for Special Relativity, which is still a "theory" (much like I have a theory that slashdot exists).

This is an exciting time to be alive. The Riemann hypothesis has been proven [slashdot.org] .The 16th Hilbert problem has been solved [slashdot.org] (by a student no less - proof that important discoveries in science are still an individual sport). After thousands of years, Archimedes Loculus has been solved [slashdot.org] . While these are airy egg-head endeavours, so was once the notion of Diracs Quantum Electrodynamics. Today, the antimatter particles predicted by QED are used to image and diagnose diseases of the brain (Positron Emission Tomography), produce light (Light Emitting Diodes), and they make transistors and diodes work. Having a mathematical proof for Poincare's conjecture could lead to new ways of structuring matters behaviors, including time-dependant transformations. For instance, shorter crumple zones which absorb more energy in automotive collisions.

Re:Who Cares! or An Exciting Time To Be Alive (0)

Anonymous Coward | more than 10 years ago | (#7850773)

I SALUTE YOU SUR!

Re:Who Cares! or An Exciting Time To Be Alive (1)

rupe (118491) | more than 10 years ago | (#7850795)

Dont substitute enthusiasm for ignorance.

Proof Smoof (3, Informative)

Anonymous Coward | more than 10 years ago | (#7850737)

Here is an article from the current issue of Discover magazine on the state of the Poincare proof, and mathematical proofs in general. Sorry not a full text. Go to your library.

http://www.discover.com/issues/jan-04/features/m at hematics/

Re:Proof Smoof (1, Interesting)

Anonymous Coward | more than 10 years ago | (#7850750)

linkified [discover.com]

Just a thought... (1, Insightful)

RedHat_Linux_Man (692702) | more than 10 years ago | (#7850743)

But our universe is not 3-dimensional... it is 4-dimensional(so far as we know):
Physical dimensions 1.length, 2.width, 3.height
AND 4.time
So it would seem to me that Poincare would describe only the physical aspects of our universe, but not the universe as a whole.
One other thing, we don't know for sure that there is only one way to bend 3 dimensional space into a shape with no holes', the dimension number/num. shapes could be related to a different pattern, such as the fibbonachi sequence (0,1,1,2,3,5,8...)

I am only a high school math student, so if there are any other mathemeticians out there that can disprove any of my 'conjectures', please post.

Usefulness? (1)

Dan East (318230) | more than 10 years ago | (#7850774)

In what way would this proof be applied outside the realm of the mathematica and theory?

Grand Unified Theory? Time Travel? Big Crunch?

Dan East

Website getting slow...Article text: (1, Redundant)

sparklingfruit (736978) | more than 10 years ago | (#7850798)

Century-old math problem may have been solved
By Jascha Hoffman, Globe Correspondent, 12/30/2003

BERKELEY, Calif. -- A reclusive Russian mathematician appears to have answered a question that has stumped mathematicians for more than a century.

After a decade of isolation in St. Petersburg, over the last year Grigory Perelman posted a few papers to an online archive. Although he has no known plans to publish them, his work has sent shock waves through what is usually a quiet field.

At two conferences held during the last two weeks in California, a range of specialists scrutinized Perelman's work, trying to grasp all the details and look for potential flaws.

If Perelman really has proved the so-called Poincare Conjecture, as many believe he has, he will become known as one of the great mathematicians of the 21st century and will be first in line for a $1 million prize offered by the Clay Mathematics Institute in Cambridge.

Colleagues say Perelman, who did not attend the California conferences and did not respond to a request for comment, couldn't care less about the money, and doesn't want the attention. Known for his single-minded devotion to research, he seldom appears in public; he answers e-mails from mathematicians, but no one else.

"What mathematicians enjoy is the chase of really difficult problems," said Hyam Rubinstein, a mathematician who came from Australia to attend meetings at the Mathematical Sciences Research Institute in Berkeley and the American Institute of Mathematics in Palo Alto, Calif., hoping to better understand Perelman's solution. "This problem is like the Mount Everest of math conjectures, so everyone wants to be the first to climb it."

The Poincare Conjecture, named after the Frenchman who proposed it in 1904, is the question that essentially founded the field of topology, the "rubber-sheet geometry" that looks at the properties of surfaces that don't change no matter how much you stretch or bend them.

To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.

Dozens of the best mathematicians of the last century tried with all kinds of approaches to solve the conjecture. Some thought they had it for months, even years, but counter-examples and flaws just kept springing up. Simply-stated but elusive to prove -- like Fermat's Last Theorem -- this conjecture has spurred the development of whole branches of mathematics.

A decade ago, after some work in the United States that colleagues described as "brilliant," Perelman gave up a promising career to work in seclusion in St. Petersburg. Although he appears occasionally, most recently for lectures at the Massachusetts Institute of Technology and several other US schools last spring, he keeps a very low profile.

Even in mathematical circles, surprisingly little is known about him, and those who know him often don't want to speak publicly about his work.

At any rate, he seems to have used his time alone wisely. While working out the Poincare Conjecture, Perelman also seems to have established a much stronger result, one that could change many branches of mathematics. Called the "Geometrization Conjecture," it is a far-reaching claim that joins topology and geometry, by stating that all space-like structures can be divided into parts, each of which can be described by one of three kinds of simple geometric models. Like a similar result for surfaces proved a century ago, this would have profound consequences in almost all areas of mathematics.

As the foundation for his proof, Perelman used a method called Ricci flow, invented in the mid-1980s by Columbia University mathematician Richard Hamilton, which breaks a surface into parts and smooths these parts out, making them easier to understand and classify.

Although some mathematicians find it disturbing that Poincare's simple question could have such a complicated answer, Hamilton is not worried. After so many failed proofs, he said, "no one expected it to be easy."

Hamilton calls Perelman's work original and powerful -- and is now running a seminar at Columbia devoted to checking Perelman's proof in all its detail.

If the proof is vetted, the Clay Mathematics Institute may face a difficult choice. Its rules state that any solution must be published two years before being considered for the $1 million prize. Perelman's work remains unpublished and he appears indifferent to the money. Hamilton, on the other hand, did the foundational work on which the proof is based -- but that was over a decade ago. And, as with any major finding, many people have contributed in some degree.

Huge financial prizes raise the stakes for assigning credit for major proofs like this one. For the time being, however, researchers are sharing their approaches with a sense of openness. And the mood is one of cautious optimism that Perelman's approach, even if flawed, will eventually be the one that works.

It takes years for a solution to make the leap from being just another claim to actually being considered "true." Perelman's work will be digested by a wide range of mathematicians in the next few years, said University of California at Davis mathematician Joel Hass. Steps that Perelman pushed through by brute force will be replaced with simpler methods, and his work will be integrated into other fields, Hass said.

And while the equivalent of the Poincare conjecture has already been proven for dimensions four and up, no one yet has any idea how to classify all the spaces that appear in higher dimensions. This state of ignorance is what prods mathematicians to keep working.

"It's interesting how a really good problem can sometimes be much better than a really good answer," Rubinstein said with a grin.

Not the time... (3, Funny)

Gyorg_Lavode (520114) | more than 10 years ago | (#7850803)

I'm so drunk I can't s up strait and we're asking if some mathematical conjecture has been proved? Is this really the right storey for New Years Eve? Lets go with stories about things that are bright and shiny.

where are the documents? (1)

stock (129999) | more than 10 years ago | (#7850826)

So where are the documents/papers by Dr. Perelman describing his proof of the Poincare Conjecture? Or are they on purpose not being put available for the grand public?

Robert

MARK OWEN HATES OPEN SOURCE (0)

Anonymous Coward | more than 10 years ago | (#7850841)

MARK OWEN, AOSM - Anti-Open Source Movement.

[22:33] @Mark: Time to build in a new mode to CR - I'm sorry but this person doesn't want to be /whois'd
[22:33] @masked: doesn't he know -y does the trick?
[22:33] @masked: idiot

irc.webchat.org /whois mark /whois scottk /whois kc
they have a mode +y that lets them know when someone does a /whois on them.

HI!
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