Poincaré Conjecture May Be Solved
CmdrTaco posted more than 11 years ago
299Flamerule writes "The New York Times is now reporting that Dr. Grigori (Grisha) Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, appears to have solved the famous Poincaré Conjecture, one of the Clay Institute's milliondollar Millennium Prize problems. I first noticed a short blurb about this at the MathWorld homepage last week, but Google searches have revealed almost nothing but the date and times of some of his lectures this month, including a packed session at MIT (photos), in which he reportedly presented material that proves the Conjecture. More specifically, the relevant material comes from a paper ("The entropy formula for the Ricci flow and its geometric applications") from last November, and a followup that was just released last month."
Congratulations on your FP! For FURTHER Torlling (1, Troll)
Anonymous Coward  more than 11 years ago  (#5735276)
http://www.jesusgeeks.net [jesusgeeks.net]
http://www.christdot.org [christdot.org]
for your torll tuesday needs!
Re:Congratulations on your FP! For FURTHER Torllin (1, Offtopic)
Anonymous Coward  more than 11 years ago  (#5735537)
Much thanks!
hb/n
If this is not the first post... (1, Troll)
Anonymous Coward  more than 11 years ago  (#5735277)
As always, links to pictures will be posted.
Re:If this is not the first post... (1, Offtopic)
Eric Ass Raymond (662593)  more than 11 years ago  (#5735328)
See you in the news, then.
Y'know (2, Insightful)
DarenN (411219)  more than 11 years ago  (#5735280)
Re:Y'know (2, Insightful)
kvn299 (472563)  more than 11 years ago  (#5735297)
Re:Y'know (1)
Kosi (589267)  more than 11 years ago  (#5735393)
Re:Y'know (2, Informative)
robslimo (587196)  more than 11 years ago  (#5735479)
So here is the Google/NYT partner link [nytimes.com]
Re:Y'know (1)
Kosi (589267)  more than 11 years ago  (#5735574)
But, why in the world keep people posting this reg. req'd. links if there is a way without registration?
Re:Y'know (1)
DetrimentalFiend (233753)  more than 11 years ago  (#5735456)
Re:Y'know (1, Flamebait)
Anonymous Coward  more than 11 years ago  (#5735325)
Re:Y'know (4, Funny)
LordYUK (552359)  more than 11 years ago  (#5735362)
You're new here, arent you?
Goddamn Frogs (1, Troll)
Anonymous Coward  more than 11 years ago  (#5735281)
Cool. (3, Funny)
Anonymous Coward  more than 11 years ago  (#5735286)
Re:Cool. (2, Funny)
cannonfodda (557893)  more than 11 years ago  (#5735483)
What about the Dunwoody paper? (5, Interesting)
Glyndwr (217857)  more than 11 years ago  (#5735296)
The link to mathworld.wolfram.com [wolfram.com] from the post says:
So, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?
Re:What about the Dunwoody paper? (4, Informative)
Darnit (75420)  more than 11 years ago  (#5735356)
It seems as if he missed a step and couldn't figure it out.
Re:What about the Dunwoody paper? (1)
ideonode (163753)  more than 11 years ago  (#5735366)
Here's his (potential) proof. [soton.ac.uk]
Re:What about the Dunwoody paper? (5, Informative)
rasafras (637995)  more than 11 years ago  (#5735371)
From the site:
It is unclear as of this writing if Dunwoody's proof will last even a fraction of that duration.
In fact, it appears that the purported proof has already been found lacking, judging by the facts that (1) the abstract begins, "We give a prospective [italics added] proof of the Poincaré Conjecture" and (2) the revised April 11 version of the preprint contains a small but significant change in title from "A Proof of the Poincaré Conjecture" to "A Proof of the Poincaré Conjecture?" In particular, a critical step in the paper appears to remain unproven, and Dunwoody himself does not see how to fill in the missing proof.
Re:What about the Dunwoody paper? (5, Informative)
King Babar (19862)  more than 11 years ago  (#5735386)
A gap or three in the proof were found within days, and a mathematician friend of mine reported that it didn't look like solutions to these problems were immediately forthcoming.
The excitement about this paper comes from the fact that the guy who did the work has come up with impressive results in the past, builds on important and cutting edge work, and seems to have a really thorough command of the potential difficulties. (In other words, when he is asked questions about the tricky points, he immediately responds with what look like strong and wellthoughtout answers.) For that matter, his work claims to prove a more general conjecture of which Poincare is a special case, and so this work could have more general significance to many other problems, even if there turns out to be a glitch or two in this iteration of the proof.
It's a very hard problem, and this answer could be wrong, too. But there's a big difference between tossing a paper up on a preprint server and giving a lecture at MIT where nobody can (yet) touch you. :)
Re:What about the Dunwoody paper? (5, Funny)
Eccles (932)  more than 11 years ago  (#5735462)
The part of the proof where it says "then a miracle occurs..." is being questioned by numerous mathematicians.
Re:What about the Dunwoody paper? (1)
GeckoX (259575)  more than 11 years ago  (#5735523)
3) ?
4) Profit!
Re:What about the Dunwoody paper? (2, Funny)
Glyndwr (217857)  more than 11 years ago  (#5735546)
I prefer to think of it as
public static void main (String[] args) {
doStuff();
}
Re:What about the Dunwoody paper? (1)
stanmann (602645)  more than 11 years ago  (#5735585)
And the answer is... (0)
Anonymous Coward  more than 11 years ago  (#5735313)
Re:And the answer is... (1, Funny)
Cached Hit (651577)  more than 11 years ago  (#5735324)
Re:And the answer is... (1)
pVoid (607584)  more than 11 years ago  (#5735635)
"It was in fact a trick question. Coventry City have never won the FA Cup."
Donuts, apples, I'm hungry (2, Funny)
stanmann (602645)  more than 11 years ago  (#5735315)
Re:Donuts, apples, I'm hungry (1)
ePhil_One (634771)  more than 11 years ago  (#5735426)
(And there is no truth to the rumor that the Macintosh Firewire icon is secretly a Flux Capacitor icon)
Re:Donuts, apples, I'm hungry (0)
Anonymous Coward  more than 11 years ago  (#5735433)
Ya'know, animals are 3 dimensional objects with holes. In fact, animals too are toriods of a sort...the body surrounds one elongated hole...the digestive tract. To further enlighten your perspective and for your viewing enjoyment observe yet another fine example of a toroid here:
http://goatse.cx/
Re:Donuts, apples, I'm hungry (1)
stanmann (602645)  more than 11 years ago  (#5735448)
Of course, it was the Orings that caused the first shuttle disaster.
Re:Donuts, apples, I'm hungry (0)
Anonymous Coward  more than 11 years ago  (#5735454)
Only a specific subset of 3dimensional objects have holes or cavities that are facinating.
Re:Donuts, apples, I'm hungry (4, Funny)
override11 (516715)  more than 11 years ago  (#5735555)
Women, right???
Re:Donuts, apples, I'm hungry (1)
stanmann (602645)  more than 11 years ago  (#5735691)
What the heck is this? (0, Redundant)
CmdrWass (570427)  more than 11 years ago  (#5735319)
Re:What the heck is this? (1)
Junks Jerzey (54586)  more than 11 years ago  (#5735344)
You don't need to ask Slashdot. Google is your friend.
Explanation (5, Informative)
MaestroSartori (146297)  more than 11 years ago  (#5735331)
Now, can someone tell me what practical applications there might be of this? Or is it strictly an abstract concept?
Re:Explanation (4, Funny)
jkramar (583118)  more than 11 years ago  (#5735370)
Has Fermat's Last Theorem actually been used in practical applications? I don't think so...
Re:Explanation (5, Insightful)
Vann_v2 (213760)  more than 11 years ago  (#5735455)
sigh (5, Insightful)
danro (544913)  more than 11 years ago  (#5735482)
Has Fermat's Last Theorem actually been used in practical applications? I don't think so...
If everyone thought like you we'd still be living in caves.
Just because practical applications aren't totally obvious for a layman (or even a matematician) doesn't mean this will never be of practical use.
Even if no practical applications are ever found, this proof (if it survives peer review) may well pave the way for something else that is immensly useful.
There's just no way to tell right now.
Re:Explanation (0)
Anonymous Coward  more than 11 years ago  (#5735512)
Wiles' proof of FLT also proved (IIRC) the TaniyamaShimura (sp?) conjecture, on which a large chunk of modern mathematics is based.
Troglodyte...
Re:Explanation (0)
K. (10774)  more than 11 years ago  (#5735379)
Re:Explanation (1)
n3k5 (606163)  more than 11 years ago  (#5735421)
Re:Explanation (4, Funny)
CommieLib (468883)  more than 11 years ago  (#5735529)
Re:Explanation (5, Funny)
jalet (36114)  more than 11 years ago  (#5735553)
> applications there might be of this?
An application would be to make better doughnuts, I suppose.
Re:Explanation (1)
chchuck (9622)  more than 11 years ago  (#5735587)
I mean, seriously, when someone grabs an oblong pigskin full of compressed air, runs with it down a field with some guys trying to help and other guys trying to stop him, and does it better than anybody else, does that have any practical application? Yes it does! Entertainment, advertising, etc etc.
Re:Explanation (1)
LMCBoy (185365)  more than 11 years ago  (#5735624)
M's Dad: "Oh, son. The answer to that question has no practical applications. Ask me about the commodities market instead."
It's not too late, Maestro!
Google Partner Link (3, Informative)
Anonymous Coward  more than 11 years ago  (#5735334)
Re:Google Partner Link (0, Offtopic)
Kosi (589267)  more than 11 years ago  (#5735473)
Re:Google Partner Link (1)
Bendy Chief (633679)  more than 11 years ago  (#5735489)
Replace the "www" in the NYT URL with "archive"
Jebus, editors, is it really that hard?
Re:Google Partner Link (1)
Bendy Chief (633679)  more than 11 years ago  (#5735528)
Oh no.. (0)
Anonymous Coward  more than 11 years ago  (#5735335)
I try, God knows I try, but after about thirty seconds' worth of attempting to read the explanations ("homeomorphic", "closed manifolds", "simply connected") something in my brain goes "Pfffft" and I have to give up.
In short, these articles make me feel very, very stupid. Is it just me?
Explanation (2, Informative)
Andy Tanenbaum (655028)  more than 11 years ago  (#5735337)
I solved this first!! (0, Funny)
LordYUK (552359)  more than 11 years ago  (#5735340)
Re:I solved this first!! (1)
GeckoX (259575)  more than 11 years ago  (#5735504)
Law & Order (1, Offtopic)
Anonymous Coward  more than 11 years ago  (#5735345)
What's that conjecture again? (4, Informative)
n3k5 (606163)  more than 11 years ago  (#5735349)
Re:What's that conjecture again? (1, Funny)
simong_oz (321118)  more than 11 years ago  (#5735416)
Well why didn't you just say so in the first place. It's so simple when you put it in plain english
[/sarcasm]
Re:What's that conjecture again? (1)
n3k5 (606163)  more than 11 years ago  (#5735459)
On the other hand, 'simply connected' is both shorter and more precise, but most people don't know what it means. However, you can look up very fine definitions at Mathworld [wolfram.com] or the Wikipedia [wikipedia.org] .
Re:What's that conjecture again? (1)
The Only Druid (587299)  more than 11 years ago  (#5735466)
There is a certain minimum amount of familiarity with the relevant field that is demanded when discussing certain concepts.
Re:What's that conjecture again? (1, Flamebait)
Anonymous Coward  more than 11 years ago  (#5735588)
Re:What's that conjecture again? (5, Informative)
Alsee (515537)  more than 11 years ago  (#5735615)
[/sarcasm]
Ok, try this:
We long ago proved that an ordinary sphere is the only shape in 3 dimentions with no holes in it.
Note that the "shape" is "made of clay". You are allowed to stretch it, squish it, and bend it all you want. You aren't allowed to cut it or put a hole in it. And you can't "meld" parts togther.
A coffee cup is the same "shape" as a donut because you can smoothly "flow" the cup part into the handle and you get a donut.
What they just proved is that a 4dimentional sphere is the only shape with no holes in it.
So what? Well if you have some wierd complex 4 dimentional "thing" and you know it doesn't have any holes in it then you now know it has to be equal to a sphere. It SEEMS obvious, but it was still important to prove. It is important for many other proofs.
Better?

A solution was repoted one year ago... (0, Redundant)
little1973 (467075)  more than 11 years ago  (#5735352)
Competition? (0, Redundant)
frostman (302143)  more than 11 years ago  (#5735358)
IANAMathematician, but according to the summary of the Conjecture on the Wolfram site:
So it sounds to me like either Dunwoody gets it in 2004, or Perelman in 2005, or neither if the papers don't "survive academic scrutiny."
Nope. (3, Interesting)
mekkab (133181)  more than 11 years ago  (#5735413)
Here's to Perelman.
regardless, as the article suggests, even if it doesn't solve the poincare conjecture, the work will hopefully remove anaomalies in Ricci flows. Which is exciting if you are a mathematician and not very interesting at all if you are at a coctail party (unless you are three sheets to the wind, and then the mathematicians around you can talk about the topographic properties of those sheets...)
perhaps a lesson in logic (1)
jonnyfivealive (611482)  more than 11 years ago  (#5735538)
or perhaps i misuderstood your post, whichever
What is it ? (2, Informative)
Anonymous Coward  more than 11 years ago  (#5735360)
Easy, i shall explain
The conjecture that every simply connected closed 3manifold is homeomorphic to the 3sphere. This conjecture was first proposed in 1904 by H. Poincaré (Poincaré 1953, pp. 486 and 498), and subsequently generalized to the conjecture that every compact nmanifold is homotopyequivalent to the nsphere iff it is homeomorphic to the nsphere. The generalized statement reduces to the original conjecture for n = 3.
The Poincaré conjecture has proved a thorny problem ever since it was first proposed, and its study has led not only to many false proofs, but also to a deepening in the understanding of the topology of manifolds (Milnor). One of the first incorrect proofs was due to Poincaré himself (1953, p. 370), stated four years prior to formulation of his conjecture, and to which Poincaré subsequently found a counterexample. In 1934, Whitehead (1962, pp. 2150) proposed another theorem which proved to be incorrect, then discovered a counterexample (the Whitehead link) to his own theorem.
The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical, n = 3 (the original conjecture) remains open, n = 4 was proved by Freedman (1982) (for which he was awarded the 1986 Fields medal), n = 5 by Zeeman (1961), n = 6 by Stallings (1962), and by Smale in 1961. Smale subsequently extended his proof to include
you see ?, its all quite clear if you think about it
Re:What is it ? (Translation to make it easier) (5, Informative)
MarvinMouse (323641)  more than 11 years ago  (#5735525)
basically all the poincare conjecture says is that if you have a 3 dimensional figure which is closed (therefore, it it bounded (doesn't go off to infinity in either direction), and doesn't have any "holes" in it (like a donut)) then you can take every point and map it to a point in an equivalent sphere without losing continuity (therefore, everypoint will have the same "neighbourhood" of points as it had in the initial shape.)
ie. You can map a cube into a sphere, or a dodecahedron, or a weird globlike thing that doesn't fold back on itself, or a whole piece of paper (without holes), or a pencil, or a lot of different figures.
As well, this conjecture also handles figures with holes in them (like donuts), and maps them all to simpler figures.
It's a very simple concept, but has been incredibly hard to prove, and what makes this conjecture even more frustrating is the fact that 1 and 2dimensional forms of this conjecture were incredibly easy to prove, as well as 4 and up have been solved, and were reasonably easy as well. Yet for some reason the 3 dimensional version does not lend itself easily to a simple proof.
Everyone generally believes this is true, but no one has been able to prove or disprove it.
If proven, this is an important aspect of topology, because then we can map all ndimensional figures to a simpler form (like a sphere) and know that the continuity and general structure of the figure will remain the same.
Yeah you and me! (0, Offtopic)
Anonymous Coward  more than 11 years ago  (#5735372)
to have you all jumping, shouting saying it.
Let's just say that it's a measure of disorder,
in a system that is closed, like with a border.
It's sorta, like a, well a measurement of randomness,
proposed in 1850 by a German, but wait I digress.
"What the fuck is entropy?", I here the people still exclaiming,
it seems I gotta start the explaining.
You ever drop an egg and on the floor you see it break?
You go and get a mop so you can clean up your mistake.
But did you ever stop to ponder why we know it's true,
if you drop a broken egg you will not get an egg that's new.
That's entropy or ENTRO to the P to the Y,
the reason why the sun will one day all burn out and die.
Order from disorder is a scientific rarity,
allow me to explain it with a little bit more clarity.
Did I say rarity? I meant impossibility,
at least in a closed system there will always be more entropy.
That's entropy and I hope that you're all down with it,
if you are here's your membership.
Re:Yeah you and me! (1)
ActiveSX (301342)  more than 11 years ago  (#5735524)
Missed a bit... (0)
Anonymous Coward  more than 11 years ago  (#5735570)
'cause disorder as a definition doesn't cover heat.
So my first definition I would now like to withdraw,
and offer one that fits thermodynamics second law.
First we need to understand that entropy is energy,
energy that can't be used to state it more specifically.
In a closed system entropy always goes up,
that's the second law, now you know what's up.
You can't win, you can't break even, you can't leave the game,
'cause entropy will take it all 'though it seems a shame.
The second law, as we now know, is quite clear to state,
that entropy must increase and not dissipate.
Creationists always try to use the second law,
to disprove evolution, but their theory has a flaw.
The second law is quite precise about where it applies,
only in a closed system must the entropy count rise.
The earth's not a closed system' it's powered by the sun,
so fuck the damn creationists, Doomsday get my gun!
That, in a nutshell, is what entropy's about,
you're now down with a discount.
From here [mchawking.com]
Not debunked but perforated ;) (0)
Anonymous Coward  more than 11 years ago  (#5735373)
Seems likely. Googling reveals:
http://mathworld.wolfram.com/news/2002
Quick! (0)
Joey7F (307495)  more than 11 years ago  (#5735383)
Joey
I'm pretty sure this is a dupe (1)
stratjakt (596332)  more than 11 years ago  (#5735387)
Re:I'm pretty sure this is a dupe (1)
MarvinMouse (323641)  more than 11 years ago  (#5735453)
Re:I'm pretty sure this is a dupe (1, Funny)
Anonymous Coward  more than 11 years ago  (#5735497)
My teacher asks me "Whats the difference between the Reimann hypothesis and the poincare conjecture?"
And I go "That's what I say, whats the fucking difference?"
Now THATS Patience... (4, Interesting)
drgroove (631550)  more than 11 years ago  (#5735388)
"However, according to the rules of the Clay Institute, the paper must survive two years of academic scrutiny before the prize can be collected."
So, all told, Perelman is going to wait a total of 10 years from the time he started to work on the solution to the Conjecture, to the time where the scientific community lets him know if his answer is correct. Wow.
Sequel (2, Funny)
telstar (236404)  more than 11 years ago  (#5735392)
Re:Sequel (1)
adamofgreyskull (640712)  more than 11 years ago  (#5735595)
Poincare Conjecture Solved Ages Ago (5, Funny)
The Real Minister (666077)  more than 11 years ago  (#5735394)
Now I Understand... (5, Funny)
masq (316580)  more than 11 years ago  (#5735403)
Re: Now I Understand... (1)
acehole (174372)  more than 11 years ago  (#5735496)
Re: Now I Understand... (2, Funny)
rayauch (454705)  more than 11 years ago  (#5735630)
Re:Now I Understand... (1)
Mr. Bad Example (31092)  more than 11 years ago  (#5735613)
("Christina had that notsofresh feeling..." Oh, come on. Like I'm the only one who thought that.)
Perl? (5, Funny)
comet_11 (611321)  more than 11 years ago  (#5735661)
A packed session at MIT indeed... (1, Interesting)
Anonymous Coward  more than 11 years ago  (#5735404)
squarepoint (1, Funny)
eurostar (608330)  more than 11 years ago  (#5735431)
are you some sort of unamerican antipatriot ?
better change his name to "squarepoint" before this site gets banned...
Re:squarepoint (0)
Anonymous Coward  more than 11 years ago  (#5735552)
Maybe you could start by telling us an example of an American mathematician. And no, immigrants and nonUS pepople do not count in this question.
Re:squarepoint (1)
CausticWindow (632215)  more than 11 years ago  (#5735658)
Well, this guy, George Bush jr., have come up with a whole new branch of logic. It's called "If you're not with us, you're against us".
It replaces the far more common concept of modus ponens with something like this:
If a then b; lies, bloody lies; therefore b;What's next? (0)
Anonymous Coward  more than 11 years ago  (#5735443)
Re:What's next? (0)
Anonymous Coward  more than 11 years ago  (#5735517)
Mathworld!? (0)
Anonymous Coward  more than 11 years ago  (#5735492)
Re:Mathworld!? (0)
Anonymous Coward  more than 11 years ago  (#5735599)
That makes.... (1, Flamebait)
Anonymous Coward  more than 11 years ago  (#5735533)
To a Russian.
Wait for it wait for it.... (4, Insightful)
I Want GNU! (556631)  more than 11 years ago  (#5735542)
Those pics remind me of... (0, Offtopic)
brendotroy (251962)  more than 11 years ago  (#5735548)
"The faculty have answered (a longsincedead guy), and answered with vigor"
Typo... (2, Funny)
mrtroy (640746)  more than 11 years ago  (#5735560)
It is not "mathematician"
Please make the appropriate corrections.
Proof of Poincare conjecture.... (2, Funny)
Dthoma (593797)  more than 11 years ago  (#5735563)
(This of course assumes that 3manifolds are malleable.)
WTF!!??? (1, Offtopic)
Anonymous Coward  more than 11 years ago  (#5735580)
this can't be (2, Funny)
paiute (550198)  more than 11 years ago  (#5735626)
1. When Wolfram and Hart were all killed by the Beast, Wolfram was in the house.
2. Wolfram is human and isn't as smart as the papers say.
3. He stepped up to MCHawking and is now hanging from a tree with a sign pinned to him that reads: WHACK EMCEE.