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Poincaré Conjecture May Be Solved

CmdrTaco posted about 11 years ago

Science 299

Flamerule 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 million-dollar 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 follow-up that was just released last month."

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299 comments

Congratulations on your FP! For FURTHER Torlling (-1, Troll)

Anonymous Coward | about 11 years ago | (#5735276)

consider visiting:
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 | about 11 years ago | (#5735537)

Hi! I was wondering: I'm looking for some panties for my new girl. You know the ones, the have Jeeeebus' image on the front and they say "What would Jeeeebus do?" Any information on where I can find these would help a lot!

Much thanks!
-hb/n

If this is not the first post... (-1, Troll)

Anonymous Coward | about 11 years ago | (#5735277)

I will strap PVC pipes to my chest and go through an El-Al terminal at LAX.

As always, links to pictures will be posted.

Y'know (2, Insightful)

DarenN (411219) | about 11 years ago | (#5735280)

for the first time in ages, I'm looking forward to the discussion on this, in the hope that someone explains it in a manner I can understand

:)

Re:Y'know (2, Insightful)

kvn299 (472563) | about 11 years ago | (#5735297)

I actually thought the article did a great job at explaining the problem. Did you read it?

Re:Y'know (1)

Kosi (589267) | about 11 years ago | (#5735393)

Maybe you are registered, I'm not. So no way for me to read the story unless people gather their wits and mirror such articles before posting about!

Re:Y'know (2, Informative)

robslimo (587196) | about 11 years ago | (#5735479)

Yah. Looks like NYT got wise to us. Replacing 'www' with 'archive' no longer works. Just redirects to the main page.

So here is the Google/NYT partner link [nytimes.com]

Re:Y'know (1)

Kosi (589267) | about 11 years ago | (#5735574)

Thanks for the link, found it some way down already.

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) | about 11 years ago | (#5735456)

I read the article, but I'm still having some trouble understanding it. I'm guessing that it's something that I'll need higher level math to understand better (I'm only in Highschool calculus). But, is there a chance that anyone has a link to a good resource for explaining it to someone like me? It would be much appreciated. Thanks.

Re:Y'know (-1, Flamebait)

Anonymous Coward | about 11 years ago | (#5735325)

I AM ANAL MASTER

Re:Y'know (4, Funny)

LordYUK (552359) | about 11 years ago | (#5735362)

"...in the hope that someone explains it in a manner I can understand"

You're new here, arent you?

Goddamn Frogs (-1, Troll)

Anonymous Coward | about 11 years ago | (#5735281)

and their fucking accent marks.

Cool. (3, Funny)

Anonymous Coward | about 11 years ago | (#5735286)

Only two years more of eating noodles before he's rich!

What about the Dunwoody paper? (5, Interesting)

Glyndwr (217857) | about 11 years ago | (#5735296)

The link to mathworld.wolfram.com [wolfram.com] from the post says:

In April 2002, M. J. Dunwoody produced a five-page paper that purports to prove the conjecture. 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, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?

Re:What about the Dunwoody paper? (5, Informative)

rasafras (637995) | about 11 years ago | (#5735371)

It doesn't appear that the paper will survive the two years... [wolfram.com]

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) | about 11 years ago | (#5735386)

So, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?

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 well-thought-out 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) | about 11 years ago | (#5735462)

So, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?

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) | about 11 years ago | (#5735523)

You mean the infamous step 3 do you not: ...
3) ?
4) Profit!

Re:What about the Dunwoody paper? (2, Funny)

Glyndwr (217857) | about 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) | about 11 years ago | (#5735585)

Well, just because he has to wait for the prize, doesn't mean that the proof cannot be reasonably evaluated today... to acertain that the paper provides a valid proof... two years is rather a long time since most broken proofs, like Dunwoody or the various Fermat failures start to show holes in hours or days... and within a week or so the "holes" found, tend to be things that can be fixed or resolved...

And the answer is... (0)

Anonymous Coward | about 11 years ago | (#5735313)

Trick question: Green!

Re:And the answer is... (1)

pVoid (607584) | about 11 years ago | (#5735635)

Obligatory Monty Python reference:

"It was in fact a trick question. Coventry City have never won the FA Cup."

Donuts, apples, I'm hungry (2, Funny)

stanmann (602645) | about 11 years ago | (#5735315)

The subject of 3 dimensional objects with holes is quite fascinating... wouldn't it be awesome if it was discovered that toroids are actually some extradimensional manifestation... Or even that Toroids have special properties allowing FTL travel...

Re:Donuts, apples, I'm hungry (1)

ePhil_One (634771) | about 11 years ago | (#5735426)

Silly person, everyone knows its the Flux capacitor that allows FTL travel...

(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 | about 11 years ago | (#5735433)

The subject of 3 dimensional objects with holes is quite fascinating...

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) | about 11 years ago | (#5735448)

That wasn't a flying saucer, it was a flying donut.

Of course, it was the O-rings that caused the first shuttle disaster.

Re:Donuts, apples, I'm hungry (0)

Anonymous Coward | about 11 years ago | (#5735454)

No,

Only a specific subset of 3-dimensional objects have holes or cavities that are facinating.

Re:Donuts, apples, I'm hungry (4, Funny)

override11 (516715) | about 11 years ago | (#5735555)

Only a specific subset of 3-dimensional objects have holes or cavities that are facinating

Women, right???

Explanation (5, Informative)

MaestroSartori (146297) | about 11 years ago | (#5735331)

Shamelessly stolen from here [claymath.org] :

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.


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) | about 11 years ago | (#5735370)

Silly people... this is TOPOLOGY! It's not meant for people to USE it! It's just for mathematicians to RUMINATE UPON!

Has Fermat's Last Theorem actually been used in practical applications? I don't think so...

Re:Explanation (5, Insightful)

Vann_v2 (213760) | about 11 years ago | (#5735455)

That's not really fair. There is a lot of mathematics that is useful, especially to scientists, but something like Fermat is just one of those mathematical problems which are interesting because 1) they look very simple, but 2) turn out to be maddeningly difficult to prove. To say Fermat, which is basically a mathematical problem akin to getting Linux running on your toaster, is indicative of the field of mathematics is unfair.

sigh (5, Insightful)

danro (544913) | about 11 years ago | (#5735482)

Silly people... this is TOPOLOGY! It's not meant for people to USE it! It's just for mathematicians to RUMINATE UPON!
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 | about 11 years ago | (#5735512)

Do a goddamn google search.

Wiles' proof of FLT also proved (IIRC) the Taniyama-Shimura (sp?) conjecture, on which a large chunk of modern mathematics is based.

Troglodyte...

Re:Explanation (1)

n3k5 (606163) | about 11 years ago | (#5735421)

Now, can someone tell me what practical applications there might be of this? Or is it strictly an abstract concept?
The conjecture itself is something fairly abstract, but it's widely considered the most important unsolved problem in topology and has so far induced a long list of false claims and proofs, some of which have led to a better understanding of low-dimensional topology. Solving the problem would further increase knowledge about topology and many fields of research in mathematics, geometry, physics etc. would benefit from that.

Re:Explanation (5, Funny)

jalet (36114) | about 11 years ago | (#5735553)

> Now, can someone tell me what practical
> applications there might be of this?

An application would be to make better doughnuts, I suppose.

Re:Explanation (1)

ch-chuck (9622) | about 11 years ago | (#5735587)

The practical application is to bring fame, fortune, prizes, publishing royalties and paid speaking engagements in the math world to whoever solves it.

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) | about 11 years ago | (#5735624)

MaestroSartori (age 8): "Daddy, why is the sky blue?"

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 | about 11 years ago | (#5735334)

For the lazy/paranoid [nytimes.com] .

Re:Google Partner Link (0, Offtopic)

Kosi (589267) | about 11 years ago | (#5735473)

If there is a way to read this NY Times stuff without reg., why do people keep posting this annoying "reg. req'd." links?

Re:Google Partner Link (1)

Bendy Chief (633679) | about 11 years ago | (#5735489)

There's an even easier way than using Google:

Replace the "www" in the NYT URL with "archive"
Jebus, editors, is it really that hard?

Oh no.. (0)

Anonymous Coward | about 11 years ago | (#5735335)

I hate stories like this on /. - they bring back memories of highschool maths classes.
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) | about 11 years ago | (#5735337)

For those who do not know about the Poincare Conjecture, copied from http://www.claymath.org/Millennium_Prize_Problems/ Poincare_Conjecture/ If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

Law & Order (-1, Offtopic)

Anonymous Coward | about 11 years ago | (#5735345)

Bah...First they say he solved it, then they put him away for murder...

What's that conjecture again? (4, Informative)

n3k5 (606163) | about 11 years ago | (#5735349)

for the first time in ages, I'm looking forward to the discussion on this, in the hope that someone explains it in a manner I can understand
The explanation in the article [nytimes.com] is not too bad; the Wikipedia [wikipedia.org] contains a better explanation [wikipedia.org] :
[The Poincaré] conjecture is that every simply connected compact 3-manifold without boundary is homeomorphic to a 3-sphere.


Loosely speaking, this means that every 3-dimensional object that has a set of sphere-like properties can be stretched or squeezed until it is a 3-sphere without breaking it. Note that a 3-sphere consists of all those points in 4-dimensional space R4 that have a distance of 1 from the origin.

Re:What's that conjecture again? (1, Funny)

simong_oz (321118) | about 11 years ago | (#5735416)

Loosely speaking, this means that every 3-dimensional object that has a set of sphere-like properties can be stretched or squeezed until it is a 3-sphere without breaking it. Note that a 3-sphere consists of all those points in 4-dimensional space R4 that have a distance of 1 from the origin.

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) | about 11 years ago | (#5735459)

It's so simple when you put it in plain english ...
The 'plain English' version, despite being much longer, is not a perfect translation. It mentions 'a set of sphere-like properties', without defining which properties are included in that set.

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) | about 11 years ago | (#5735466)

I have to tell you, if that definition isn't clear to you, then there's no point in explaining the concept to you.

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 | about 11 years ago | (#5735588)

No, the explanation can be made simpler and easier to understand, you're just unwilling to. This kind of arrogance in academia isn't surprising.

Re:What's that conjecture again? (5, Informative)

Alsee (515537) | about 11 years ago | (#5735615)

It's so simple when you put it in plain english ...
[/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 4-dimentional 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?

-

Competition? (0, Redundant)

frostman (302143) | about 11 years ago | (#5735358)

IANAMathematician, but according to the summary of the Conjecture on the Wolfram site:

"In April 2002, M. J. Dunwoody produced a five-page paper that purports to prove the conjecture. 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 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) | about 11 years ago | (#5735413)

Darnit's post [slashdot.org] has it that dunwoody has holes.

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) | about 11 years ago | (#5735538)

the parent to your post gave all three possible options, including the one you bring up. he simply stated the dates that they would get it if they did. then, he said there is the possiblity that neither will. that looks like all the options to me.

or perhaps i misuderstood your post, whichever

What is it ? (2, Informative)

Anonymous Coward | about 11 years ago | (#5735360)


Easy, i shall explain

The conjecture that every simply connected closed 3-manifold is homeomorphic to the 3-sphere. 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 n-manifold is homotopy-equivalent to the n-sphere iff it is homeomorphic to the n-sphere. 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. 21-50) 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) | about 11 years ago | (#5735525)

translation to make it easier.

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 2-dimensional 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 n-dimensional 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 | about 11 years ago | (#5735372)

Entropy, how can I explain it? I'll take it frame by frame it,
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 E-N-T-R-O 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.

Missed a bit... (0)

Anonymous Coward | about 11 years ago | (#5735570)

Defining entropy as disorder's not complete,
'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 | about 11 years ago | (#5735373)


So, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?

Seems likely. Googling reveals:
http://mathworld.wolfram.com/news/2002-0 4-18_poinc are/

I'm pretty sure this is a dupe (1)

stratjakt (596332) | about 11 years ago | (#5735387)

I distinctly remember not understanding what the fuck I was reading about the first time it was posted.

Re:I'm pretty sure this is a dupe (1)

MarvinMouse (323641) | about 11 years ago | (#5735453)

You are thinking of the Riemann hypothesis. This one is the Poincare conjecture. They are completely different aspects of they Clay Mathematics Institute "competition".

Re:I'm pretty sure this is a dupe (1, Funny)

Anonymous Coward | about 11 years ago | (#5735497)

Well, to paraphrase a Dice Clay joke...

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) | about 11 years ago | (#5735388)

"Though his early work has earned him a reputation as a brilliant mathematician, Dr. Perelman spent the last eight years sequestered in Russia, not publishing."

"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) | about 11 years ago | (#5735392)

Complex mathematics? Looks like its time for Matt Damon and Pretty-Boy Affleck to write Good Will Hunting II.

Re:Sequel (1)

adamofgreyskull (640712) | about 11 years ago | (#5735595)

"Good Will Hunting II: Hunting Season" Was being filmed at the same time as Jay & Silent Bob were trying to get the movie about the comic-book characters that were based on them stopped so that "ball-lickers" on the "internet" would stop besmirching their good names.
...

Now I Understand... (5, Funny)

masq (316580) | about 11 years ago | (#5735403)

... why we love talking about Linux so much - It's so damn USER-FRIENDLY compared to other geek pursuits!
We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1) Ricci flow, considered on the space of riemannian metrics modulo diffeomorphism and scaling, has no nontrivial periodic orbits (that is, other than fixed points); (2) In a region, where singularity is forming in finite time, the injectivity radius is controlled by the curvature; (3) Ricci flow can not quickly turn an almost euclidean region into a very curved one, no matter what happens far away. We also verify several assertions related to Richard Hamilton's program for the proof of Thurston geometrization conjecture for closed three-manifolds, and give a sketch of an eclectic proof of this conjecture, making use of earlier results on collapsing with local lower curvature bound.

Re: Now I Understand... (1)

acehole (174372) | about 11 years ago | (#5735496)

Would you prefer the pop-up book version?

Re: Now I Understand... (2, Funny)

ray-auch (454705) | about 11 years ago | (#5735630)

I guess it depends on whether or not the popup is simply connected, and, if so, if it is homoemorphic to the 3-sphere (this may depend on whether or not it is open or closed but I'm not sure on that bit).

Re:Now I Understand... (1)

Mr. Bad Example (31092) | about 11 years ago | (#5735613)

I don't know...going into mathematics might almost be worth it to be able to say "Ricci flow" with a straight face.

("Christina had that not-so-fresh feeling..." Oh, come on. Like I'm the only one who thought that.)

A packed session at MIT indeed... (1, Interesting)

Anonymous Coward | about 11 years ago | (#5735404)

Y'know - if there's ampty seats, then it can't really be described as packed. I remember the day when people sat on the floor in the aisles to receive words of mathematical wisdom from Dmitri [bath.ac.uk] [www.bath.ac.uk].

squarepoint (1, Funny)

eurostar (608330) | about 11 years ago | (#5735431)

an article about a FRENCH mathematician ?
are you some sort of unamerican antipatriot ?
better change his name to "squarepoint" before this site gets banned...

Re:squarepoint (0)

Anonymous Coward | about 11 years ago | (#5735552)

> an article about a FRENCH mathematician ?

Maybe you could start by telling us an example of an American mathematician. And no, immigrants and non-US pepople do not count in this question.

Re:squarepoint (1)

CausticWindow (632215) | about 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 | about 11 years ago | (#5735443)

Now that Poincaré's Conjecture has been solved, let's get going on Portnoy's Complaint.

Re:What's next? (0)

Anonymous Coward | about 11 years ago | (#5735517)

Portnoy's Complaint n. [after Alexander Portnoy (1933- )] A disorder in which strongly-felt ethical and altruistic impulses are perpetually warring with extreme sexual longings, often of a perverse nature. Spielvogel says: 'Acts of exhibitionism, voyeurism, fetishism, auto-eroticism and oral coitus are plentiful; as a consequence of the patient's "morality," however, neither fantasy nor act issues in genuine sexual gratification, but rather in overriding feelings of shame and the dread of retribution, particularly in the form of castration.' (Spielvogel, O. "The Puzzled Penis," Internationale Zeitschrift für Psychoanalyse, Vol. XXIV, p. 909.) It is believed by Spielvogel that many of the symptoms can be traced to the bonds obtaining in the mother-child relationship.

Mathworld!? (0)

Anonymous Coward | about 11 years ago | (#5735492)

Nerd Alert!

Re:Mathworld!? (0)

Anonymous Coward | about 11 years ago | (#5735599)

Calling All Nerds!

That makes.... (-1, Flamebait)

Anonymous Coward | about 11 years ago | (#5735533)

...one more French defeated.
To a Russian.

Wait for it wait for it.... (4, Insightful)

I Want GNU! (556631) | about 11 years ago | (#5735542)

Mathematical rigor demands we see the proof first. One decade ago Wiles thought he solved Fermat's Last Theorem but a mistake was found and worked again for several months before ultimately solving it. Faulty proofs are made all the time. Until it undergoes peer review I will be very skeptical.

Those pics remind me of... (0, Offtopic)

brendotroy (251962) | about 11 years ago | (#5735548)

Good Will Hunting...

"The faculty have answered (a long-since-dead guy), and answered with vigor"

Typo... (2, Funny)

mrtroy (640746) | about 11 years ago | (#5735560)

It appears most people are spelling incorrectly! Including the sites included in the post!

It is not "mathematician" ..... its "mathemagician"

Please make the appropriate corrections. :)

Proof of Poincare conjecture.... (2, Funny)

Dthoma (593797) | about 11 years ago | (#5735563)

Me. Hammer. Pliers. Every available 3-manifold. Can I have my $1 million please?

(This of course assumes that 3-manifolds are malleable.)

WTF!!??? (-1, Offtopic)

Anonymous Coward | about 11 years ago | (#5735580)

What the fuck is a Micro$soft Visual Studio.net advertisement doing on SLASHDOT!!!??? I click to see the Poincare Conjecture article and that gawd aweful eyesore pops up on my Macintosh screen. How dare you! Are you guys that hard up for cash that you'd take money from the BORG?

this can't be (2, Funny)

paiute (550198) | about 11 years ago | (#5735626)

I thought that this Wolfram guy was the smartest man in the universe and had all the answers. Now some brie-muncher comes along and proves something in math that Wolfram couldn't? This can only be due to one of three reasons:

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.

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