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The Poincaré Conjecture has Been Proved

chrisd posted about 12 years ago | from the np-is-the-problem-for-me dept.

Science 307

Martin Dunwoody, a famous mathematician who works in the field of topology has a preprint that provides a proof of the Poincaré conjecture. This was one of the seven Clay Mathematics Institute millenium prize problems (reported on Slashdot here). The solution to each of the problems carries a monetary reward of 1 million dollars. However there are a number of conditions that still need to be met for the prize to be awarded in the case of the Poincaré conjecture.

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This could definitely be (-1, Troll)

Anonymous Coward | about 12 years ago | (#3298318)

A first post for me.

Re:This could definitely be (-1)

YourMissionForToday (556292) | about 12 years ago | (#3298334)

Nope, sorry. Gutless ACs risk no karma, and get no FPs. Try again, this FP belongs to Tasty Beef Jerky, Mayor McPenisman, and all the hardworking trolls and crapflooders who make this site worthwhile.

Dungeon Siege (-1, Troll)

Anonymous Coward | about 12 years ago | (#3298319)

Dungeon Siege is quite possibly one of the best games ever made.

P.S. It is closed source and written by Microsoft.

Hmmm, should I play Dungeon Siege or Tux Racer? I guess I will play Tux Racer since... if its not good enough... hey I can fix it myself, I have the source code.

Re:Dungeon Siege (-1)

Yr0 (224662) | about 12 years ago | (#3298357)

dugnonsiege is shit
buy a gameboy
and then you can install linux on it and have prortable tux racer
even tho thast shit too

Re:Dungeon Siege (-1, Offtopic)

Anonymous Coward | about 12 years ago | (#3298629)

And then there's the bzFlag, which is utter ship, but because Lunix doesn't have any real games, they have to pretend they like bzFlag.

Wierd Problem (3, Interesting)

KagatoLNX (141673) | about 12 years ago | (#3298337)

If you follow the link to the description of the problem, it gets really wierd. Apparently this is one of those problems where you have to prove it for 1=7} but no one ever managed n=3 (which was the original, non-generalized conjecture anyways). Funny that this guy just had to fill in the last blank.

Re:Wierd Problem (1)

squidinkcalligraphy (558677) | about 12 years ago | (#3298351)

seems rather an inelegant way to make a general proof; general proof for n>=5, the seperate proofs for n=1, n=2, n=3 and n=4. Does this new proof just do n=3, or is it a _nice_ general proof?

Re:Wierd Problem (2, Informative)

leviramsey (248057) | about 12 years ago | (#3298398)

seems rather an inelegant way to make a general proof; general proof for n>=5, the seperate proofs for n=1, n=2, n=3 and n=4. Does this new proof just do n=3, or is it a _nice_ general proof?

I see no inelegance to this method. One of the steps in the general proof may only work if n>=5. This does not mean that the general proof is invalid.

Essentially, the same method underlies inductive proof (e.g. a general proof that holds for n>s, and a demonstration that n=s combine to n>=s).

Re:Wierd Problem (3, Funny)

Gary Yngve (416254) | about 12 years ago | (#3298414)

Without reading the preprint, I cannot say (not that I could understand it anyway :) ). But it wouldn't surprise me if the proof was just for 3.

R^3 is kind of a magical place. R^2 might not have enough wiggling room, but R^4 might have too much. There exists a cross product in only R^3.

Re:Wierd Problem (1)

NMSpaz (34277) | about 12 years ago | (#3298483)

Given that one of the links states that all cases other than 3 had already been proven, it's quite likely that the proof indeed for that case. </sarcasm>

Re:Wierd Problem (2, Informative)

avsed (168886) | about 12 years ago | (#3298508)

No, one can have a cross (outer) product in any number of dimensions, just as one can have an inner ("dot") product in any number of dimensions. Tensor calculus is the generalisation of ordinary geometric calculus that describes this.


Re:Wierd Problem (0)

Anonymous Coward | about 12 years ago | (#3298631)

Actually, if you read up on the problem, you'll see that although the proof is for n=3, that actually means he's working in R^4.

Re:Wierd Problem (2, Informative)

splorf (569185) | about 12 years ago | (#3298458)

Here's [wolfram.com] some further info on the Poincare conjecture.

This proof does just d=3 and it's interesting that it's essentially combinatorial. Smale's proof for d>=5 was based on differential topology, a grand and beautiful branch of pure higher math. Freedman's proof for d=4 used Yang-Mills theory developed in particle physics. d=3 looks like essentially a computer scientist's proof.

Disclaimer: I don't understand this stuff in any detail--these remarks are based on looking at the preprint and remembering stuff that I heard in math class long ago. Also, I think I'll wait to hear what the math community says, before believing the problem is really finally solved.

Re:Wierd Problem (1)

richard-parker (260076) | about 12 years ago | (#3298475)

seems rather an inelegant way to make a general proof; general proof for n>=5, the seperate proofs for n=1, n=2, n=3 and n=4. Does this new proof just do n=3, or is it a _nice_ general proof?
M.J.Dunwoody's proof is restricted to the n = 3 case.

now I've seen it all (3, Funny)

squidinkcalligraphy (558677) | about 12 years ago | (#3298339)

The Poincaré Conjecture proved, and microsoft ads on slashdot

What's the problem? (-1, Redundant)

jchawk (127686) | about 12 years ago | (#3298341)

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.

Re:What's the problem? (0)

jojor (545317) | about 12 years ago | (#3298385)

uhm....yeah but who streches rubberbands around donuts?

Re:What's the problem? (0)

Anonymous Coward | about 12 years ago | (#3298547)

>uhm....yeah but who streches rubberbands around donuts?

Man that has to suck, losing karma by getting modded offtopic for telling someone else they're offtopic. Next time instead of trying to scrounge a 'funny' point in something you have no idea about, be a proper karma whore and do a google search. I mean if you're going to make the effort to post why not go the extra distance?

Personally I like to mod people down as overrated when they try to post something funny, although I'm guilty of whoring through humour myself. However if I had it I'd give you that extra point you need just for your anti-american comments, but chances are you'd lose it again next week trying to whore another funny point. Oh well.

Re:What's the problem? (2, Insightful)

psavo (162634) | about 12 years ago | (#3298416)

Interesting stuff.
isn't it 'better' to not think about rubberband at outer surface bat at 'outer rim'. At about below surface of apple/doughnut?
Then one will see that in apple rubberband (even in 3D) is convexish (I mean infinitely thin rubberband), but in doughnut, there is no way to see some part of rubberband unless it's quantized.
Same applies fo 'standard' universe and with one which has a 'pen'-hole which goes straight through rubberband (some odds for that..).

Re:What's the problem? (5, Informative)

Anonymous Coward | about 12 years ago | (#3298440)

You show great skill at cut & pasting from http://www.claymath.org/prizeproblems/poincare.htm [claymath.org] : )

Just kidding. Go ahead, enjoy the cut & paste karma.

busted (0)

Anonymous Coward | about 12 years ago | (#3298446)

good catch, i don't mind when people do that, but they should give props to the reference material and not just post it as their own.

Re:What's the problem? (2)

Gary Yngve (416254) | about 12 years ago | (#3298441)

Here's an algebraic topology version of the problem:

Given a simply connected tetrahedral mesh, show that the mesh can be collapsed by topologically invariant operations to a single tetrahedron.

Re:What's the problem? (3, Informative)

metlin (258108) | about 12 years ago | (#3298455)

Which is exactly what they've done in the paper. They've depicted on how the mesh could possibly collapse.

They have depicted an 8-gon curve which satisfies the intersection properties, extrapolate using a 2 vertex model and use that to show the possible collapse. They've not depicted the collapse per-se in action tho. :-(

The problem is... (0)

Anonymous Coward | about 12 years ago | (#3298525)

They're offering $1m for Clay mation. Hell I can wad up a ball of playdoh in my basement and get prettier pictures.

It just goes to show if it isn't one thing, its another. If it isn't a ball of clay, its, its...

Oh, Clay Mathematics. That's different.

Never mind.

Linux reviewed (-1, Troll)

Anonymous Coward | about 12 years ago | (#3298348)

At last an objective reviewer has compared Linux to some of the more professional operating systems out there. Read Truth Media's article here [somethingawful.com].

luser (-1, Flamebait)

autopr0n (534291) | about 12 years ago | (#3298366)

Hah, sa's 'professional' trolls. And they didn't even bother to get their own domain. You're an idiot.

I have the way out! (-1, Troll)

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Re:I have the way out! (-1)

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Well.. (0, Troll)

autopr0n (534291) | about 12 years ago | (#3298358)

Thanks for explaning what it is... or at least what it applies to/why it's important.

Re:Well.. (0)

Anonymous Coward | about 12 years ago | (#3298408)

Yeah, fucking hell. I read that Mathworld stuff three times and I'm still barely any the wiser.

Anyone want to take a shot at explaining this without using "homeomorphic" and "simply-connected."

Re:Well.. (1)

nucal (561664) | about 12 years ago | (#3298507)

All right, I'll bite - and please correct me if I'm wrong. Basically I think that the gist of the Poincaré's Conjecture is that in a given dimension all surfaces of a certain class are equivalent. In other words, you could (virtually) remold a solid cube into a solid sphere - but if you have a cube with a hole running through it, you can't remold the cube into a solid sphere without closing the hole, but you could remold it into a donut. So my simple-minded way of looking at this is that all non-holed objects are equivalent, all one-holed objects are equivalent, all two holed objects are equivalent, etc., and represent distinct classes of objects.

How'd I do math-jocks?

Re:Well.. (2, Informative)

danielrose (460523) | about 12 years ago | (#3298511)

I don't get it, what is so difficult? Here is one more time for you slow guys:

The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical, n = 3 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 n >= 7 by Smale in 1961. Smale subsequently extended his proof to include n >= 5.

Now what part doesn't make sense? *efg*

Mmmmm... Math... (0)

Anonymous Coward | about 12 years ago | (#3298545)


Re:Well.. (0)

Anonymous Coward | about 12 years ago | (#3298601)

Because not everyone is busy running porn sites like you. There are others here who'd contribute a lot more constructively to society, like doing maths & physics, and leading a life that's intellectually satisfying.

(disgruntled nerd)

Re:Well.. (0)

Anonymous Coward | about 12 years ago | (#3298661)

For the record, from appearances, he doesn't run a pr0n site for a living. Plus, it's free-as-in-free-beer pr0n (+1 nerd), and he's looking at women, which means he's either male, horny, and without outlet for sexual tension (in varying degrees, +1 to +5 nerd), or a horny bi/lesbian fem-nerd (+500 nerd, in the hope one will sleep with me in return for my free nerd-points).

teacup == donut (1, Funny)

Anonymous Coward | about 12 years ago | (#3298359)

so we finally have mathematical proof that a teacup is a donut for every teacup in the known (Euclidean) universe

Re:teacup == donut (2, Funny)

Quirk (36086) | about 12 years ago | (#3298402)

Charles Dodgson, somewhere thru the looking glass, is at tea with the Mad Hatter discussing this very matter.


Re:teacup == donut (2)

JabberWokky (19442) | about 12 years ago | (#3298645)

No, we're doing soirees and diagramming whether or not the bat can be black at dawn.

The JabberWokky (yes, I know. It's intentional to create a unique string.)

Re:teacup == donut (1)

Jouster (144775) | about 12 years ago | (#3298675)

Actually, a teacup does not equal (!=, or <> for you freaky folks) a donut. Properly wrapped, a "rubber band" could become smaller and smaller while maintaining definition, since the bottom of the teacup is a definite surface. Now, were said rubber band wrapped around the rim, you'd be correct.

What does this amount to? Look at the difference between a donut and the "donut holes" sold by some bakeries. A donut is a surface with a hole in the center; a donut hole is a hole with a surface in the center. From this, is becomes clear that ANYTHING can be said to be encased within a larger "hole".

Feel free to do your own extrapolation from there--personally, I stop just short of a unified field theory before logic stemming from that conjecture breaks down.


Proof (0, Troll)

droyad (412569) | about 12 years ago | (#3298361)

Anything can be proved with enough flawed mathematics. Think how many times things have been proven, only to be found flawed later on? That is the foundation of the scientific method.

Re:Proof (1)

phooka.de (302970) | about 12 years ago | (#3298413)

Anything can be proved with enough flawed mathematics. Think how many times things have been proven, only to be found flawed later on? That is the foundation of the scientific method.

Nope, this is where you're wrong. Math is different from any other science when in comes to "proving" things.Compared to a mathematical proof, any other scentific "proof" is just a currently accepted working theory.

That's the strangth and beauty of mathematics: once it's proven, we know that it's true until the end of days, not even God could change it if he exists. not even if the laws of physuics suddenly changed and altered all we know about the universe would our mathematical proof become untrue.

Compared to mathematics, even physics is - as a science - not much more proovable than sociology.

Re:Proof (0)

Anonymous Coward | about 12 years ago | (#3298419)

Of course it depends what axioms you take to be true to start with.

Re:Proof (1)

phooka.de (302970) | about 12 years ago | (#3298423)

For which reason all mathematic proofs should start with something like "given that the following assumptions are true" or "based on the following axioms...".

I guess calling it a mathematical proof includes this, though.

Re:Proof (4, Insightful)

bentini (161979) | about 12 years ago | (#3298451)

Wow. I wish I could highlight a section of your post to point out as being wrong as you did the the grandparent. Unforutnately, I can't. You're wrong all throughout.

First, how do you show something is proven? Well, you give a proof. How do I know the proof is correct? I work through all the steps... But what if I mess up and sneeze and my thinking gets confused and I accept something that isn't true? It could happen. Well, I'll just push it through a formal logic computer program that checks it.
But what if the computer has a glitch and a 0 or a 1 gets accepted. Or worse, I made the error while programming the formal logic system. Or more subtly, the compiler or hardware.

Basically, it's like this, proofs are as much a social event as a mathematical cedrtainty. Proofs are presented, and believed, and then refuted. Mathematical proof is a social process carried on by mathamaticians, and you can't forget that. I'm sure that I've proved things incorrectly before, and believed them. Just because nobody's found an error in a published and accepted proof doesn't mean one doesn't exist. If you think that humans can do ANYTHING with probability 1, you're sorely mistaken and are seeing the world in too convenient terms.

Sorry to burst your bubble, but there's a lot of thinking in this. Peer review does not imply flawlessness.

Re:Proof (2)

mizhi (186984) | about 12 years ago | (#3298469)

Isn't this just Godel's theorem? That in any axiomatic schema, there will be certain propositions that can not be proven within it.

Nope (2, Insightful)

dark-nl (568618) | about 12 years ago | (#3298572)

This is very different. Bentini's theorem is simply "Mathematicians can be wrong" :-)

I agree with that one. Some proofs are large and complicated, and they might have bugs in them that haven't been noticed yet. I even think it's possible that human minds have bugs which makes them incapable of noticing certain kinds of errors.

More straightforwardly, some proofs have computer-generated parts and their verification is computer-assisted (the four-colour problem, IIRC), and we all know that computer programs have bugs :-)

Blind faith in Mathematics (2, Insightful)

ynotds (318243) | about 12 years ago | (#3298521)

I write this as a reformed Mathematician of sorts, which is analogous to being a reformed smoker ... the expectations that half an education in Math gives as to the existence of right and wrong answers sure looks ugly once you can escape its grip.

And faith in Mathematical proof is counterproductive at a level beyond that ... it hides the beautiful truth that Math is something that can be joyously explored in its multitudinous riches without any need for the reality checking of the (would be) sciences.

Personally I have come to see both Math and Science (or more strictly the scientific method) as but potent toolsets, and to confine my own quest for more profound truths [amazon.com] to those "interdisciplinary" comparisons that have been called anything from "complex systems" to "general evolution".

This step is a bit like the step from geometry to topology which has clearly escaped the wit of the moderator who took offense at a not quite successful attempt to make something funny out of teacups and donuts.

Um... (2)

rakslice (90330) | about 12 years ago | (#3298591)

Are the expectations you speak of about mathematical truth? Or about truth in general? If you have expectations about truths about the properties of the universe, I don't see what that has to do with math; perhaps these expectations are less the result of an education in mathematics, and more the result of half an education in mathematics...

Re:Proof (1)

cheezehead (167366) | about 12 years ago | (#3298467)

Anything can be proved with enough flawed mathematics.

No, it's the other way around. Kurt Gödel proved that there will always be mathematical truths that cannot be proven with a mathematical system, no matter how the mathematical theorems and rules are extended. This caused quite a shock in the mathematical circles early last century. It took Douglas Hofstadter (See: Gödel, Escher, Bach : An Eternal Golden Braid, ISBN 0465026567) an entire book to explain this. No way I could explain it here, even if I could remember :-).

Re:Proof (1)

ariels (6608) | about 12 years ago | (#3298536)

Of course this is untrue. Using flawed Mathematics, one can do anything. Specifically, Gödel showed that a first-order logic axiomatization of any "sufficiently complex" system (arithmetic is more than complex enough) is either inconsistent or incomplete. What you describe is incompleteness. But of course any system which can prove P and also ~P (i.e. is inconsistent) can prove anything (and its negation); you don't need Gödel for that!

As I always say, "if 2+2=5, then the Poincar Conjecture is true".

Troll, or uninformed post? [*free clue enclosed*] (2)

rakslice (90330) | about 12 years ago | (#3298543)

Don't confuse mathematics with science. The scientific method likes induction from a limited set of cases. Mathematical methods of proof won't touch that kind of reasoning with an 10-foot pole.

"Anything can be proved with enough flawed mathematics." How does one prove something with flawed mathematics? Certainly, one can attempt to prove something with flawed mathematics, but if the mathematics are flawed, what does it prove?

"Think how many times things have been proven, only to be found flawed later on?" Okay. Zero. See above.

now sing along! (-1)

YourMissionForToday (556292) | about 12 years ago | (#3298386)

Wiener song

I know a wiener man

he owns a wiener stand

he sells most everything from hot dogs to clams (boom boom boom)

and in my later life

i'll be his wiener wife

hot dog i love that wiener man

GPL'ed (-1, Troll)

Anonymous Coward | about 12 years ago | (#3298400)

Has it been GPL'ed? And I can type that in well under 20 seconds.

Let's wait on calling it "proved" (2, Informative)

Anonymous Coward | about 12 years ago | (#3298403)

Nothing is proven until it is peer reviewed and published in a prestigious journal, and then it must to be out there for some time before it is truly accepted. Also, there may be a mistake that throws the proof off for a few years [pbs.org].


Anonymous Coward | about 12 years ago | (#3298410)

My eyes are bleeding from clicking on that link! Is the PBS webmaster blind?

Re:GOOD LORD! (-1)

October_30th (531777) | about 12 years ago | (#3298425)

What do you mean? It's clear and sharp black text on a green background.

Maybe your eyes are bleeding from reading stuff on X11 with its crappy fonts. Try switching to something like WinXP (and ClearType if you've got an LCD screen) and your eyes will thank you.

Re:GOOD LORD! (0, Offtopic)

DGolden (17848) | about 12 years ago | (#3298612)

Or just Xft on X. No need to subject yourself to the nightmare of running a Mickeyshaft "O"S

33. (-1)

GafTheHorseInTears (565684) | about 12 years ago | (#3298426)

In the whole psychology of the "Gospels" the concepts of guilt and punishment are lacking, and so is that of reward. "Sin," which means anything that puts a distance between God and man, is abolished--this is precisely the "glad tidings." Eternal bliss is not merely promised, nor is it bound up with conditions: it is conceived as the only reality--what remains consists merely of signs useful in speaking of it.

The results of such a point of view project themselves into a new way of life, the special evangelical way of life. It is not a "belief" that marks off the Christian; he is distinguished by a different mode of action; he acts differently. He offers no resistance, either by word or in his heart, to those who stand against him. He draws no distinction between strangers and countrymen, Jews and Gentiles ("neighbour," of course, means fellow-believer, Jew). He is angry with no one, and he despises no one. He neither appeals to the courts of justice nor heeds their mandates ("Swear not at all") . He never under any circumstances divorces his wife, even when he has proofs of her infidelity.--And under all of this is one principle; all of it arises from one instinct.--

The life of the Saviour was simply a carrying out of this way of life--and so was his death. . . He no longer needed any formula or ritual in his relations with God--not even prayer. He had rejected the whole of the Jewish doctrine of repentance and atonement; he knew that it was only by a way of life that one could feel one's self "divine," "blessed," "evangelical," a "child of God."Not by "repentance,"not by "prayer and forgiveness" is the way to God: only the Gospel way leads to God--it is itself "God!"--What the Gospels abolished was the Judaism in the concepts of "sin," "forgiveness of sin," "faith," "salvation through faith"--the wholeecclesiastical dogma of the Jews was denied by the "glad tidings."

The deep instinct which prompts the Christian how to live so that he will feel that he is "in heaven" and is "immortal," despite many reasons for feeling that he isnot "in heaven": this is the only psychological reality in "salvation."--A new way of life, not a new faith.

In related news.... 4 = 5 (1, Funny)

dimator (71399) | about 12 years ago | (#3298429)

Here's the proof:

assume a, b, c such that: a + b = c

then 5a + 5b = 5c
and 4c = 4a + 4b

adding the two: 5a + 5b + 4c = 4a + 4b + 5c

shifting some terms around: 5a + 5b - 5c = 4a + 4b - 4c

simplifying: 5 (a + b - c) = 4 (a + b - c)

dividing by the common factor (a + b - c): 5 = 4


Re:In related news.... 4 = 5 (1)

phooka.de (302970) | about 12 years ago | (#3298435)

Always nice to see how division by zero can be masked ;-)

Re:In related news.... 4 = 5 (1)

Xerithane (13482) | about 12 years ago | (#3298474)

The horrible thing about this, I saw that proof and looked at it. The first thought that popped into my head was, "No.. that can only be true if it's an illegal divison by zero and then it would crash."

Life as a programmer is fun, especially when your mind fails to seperate out normal things that don't crash. Like paper for instance.

Re:In related news.... 4 = 5 (0)

Anonymous Coward | about 12 years ago | (#3298452)

Except a+b-c = 0. Therefore you are dividing by zero, yielding infinity.

Infinity * 4 = Infinity * 5

is by definition

Infinity = Infinity

Your proof is flawed QED.

Re:In related news.... 4 = 5 (2, Insightful)

frinsore (153020) | about 12 years ago | (#3298566)

Actually dividing by zero doesn't give you infinity, it yeilds an undefined. If 4 / 0 was infinity then 0 * infinity would be 4, which it's not.

Also Infinity doesn't always equal Infinity. There are many different types of infinity that may or may not equal. Consider all the counting numbers, thats an Infinity. Now consider all the real numbers, that's a different Infinity. The second Infinity is greater then the first (counting numbers are a subset of all real numbers), hence Infinity doesn't equal Infinity

Re:In related news.... 4 = 5 (0)

Anonymous Coward | about 12 years ago | (#3298593)

Actually 4/0 is infinity, but 0*infinity is undefined, because it could be 4, or it could be 5, or it could be a lot of things.

Re:In related news.... 4 = 5 (0)

Anonymous Coward | about 12 years ago | (#3298654)

x/0 is undefined!!!! for all x real

Re:In related news.... 4 = 5 (1, Redundant)

nucal (561664) | about 12 years ago | (#3298453)

If a + b = c

then (a + b - c) = 0

so 5*0 = 4*0

someone had to do it ....

Re:In related news.... 4 = 5 (1)

Mindfool (570751) | about 12 years ago | (#3298460)

The problem with this proof is that, since a+b=c, a+b-c must be 0 (zero), and you can't divide by zero.

Re:In related news.... 4 = 5 (2, Funny)

Rhinobird (151521) | about 12 years ago | (#3298500)

oh sure you can, but then winston churchill becomes a carrot...and other such nonsense.

YAY! (-1, Troll)

Fuck You Faggot (560952) | about 12 years ago | (#3298430)

For all the math Fagots out there. Why don't u fucks get laid instead of proving shit.

Re:YAY!-- (-1, Offtopic)

Anonymous Coward | about 12 years ago | (#3298476)

Hey! Why "instead"? I've proven that I can laid, experimentaly!

Re:YAY! (-1, Offtopic)

Anonymous Coward | about 12 years ago | (#3298505)

If you fuck "fagots", what does that make you?

I gave up being a math major (0)

Anonymous Coward | about 12 years ago | (#3298436)

because mathematicians really love to use arcane terminology when half the time they could use plain English. Seeing 10 terms in 2 sentences of the Poincare Conjecture description just reminds me why I now only read mathematics books when I want, even if in this case most of the terms are necessary.

Re:I gave up being a math major (0)

Anonymous Coward | about 12 years ago | (#3298516)

because mathematicians really love to use arcane terminology when half the time they could use plain English. Seeing 10 terms in 2 sentences of the Poincare Conjecture description...

yes, it was bullshit.

but then again, most professional cliques do this.

but then again, most professional cliques are bullshit as well.

"Been PROVEN" not "Been PROVED" (-1, Offtopic)

Anonymous Coward | about 12 years ago | (#3298471)


The homosexual spelling correction conspiracy. (0)

Anonymous Coward | about 12 years ago | (#3298630)

You would ask: "What is the connection between spelling correction and faggotry ?"
The explanation is rather simple.

Fag is always is desperate need of a buttsex partner. However, approaching and normal heterosexual might make them give them their teeth or genitals back in a bag. So they were is desparate need for secret sign to recognize each other.
It the year 1869 at the WFC (word fag congress) the solution was found: pedantic spelling correction.
And it was a good one. Just correcting little spelling mistakes of other people seems a little pedantic but not homosexual. Non-fags wouldn't suspect anything. And it's a 100% sure way to recognize each other.

Q: I'm a normal heterosexual and just corrected a little spelling mistake of someone else. Is this dangerous ?
A: Yes. All faggots think now you are one of their kind and will molest you. Nothing can save you now. This all-too-gentle knock on your door isn't your girlfriend. You are beyond all hope.

Old news... (1, Troll)

Junior J. Junior III (192702) | about 12 years ago | (#3298487)

I already read about this, like, three zillion years from now. Can't you find anything to report about that HASN'T already happened?

Re:Old news... (2, Insightful)

Beautyon (214567) | about 12 years ago | (#3298618)

Can't you find anything to report about that HASN'T already happened?

How can ANY editor report something that HASN'T YET HAPPENED??

Vindication (1, Troll)

PhysicsGenius (565228) | about 12 years ago | (#3298509)

I've been saying for years that our combinatorial place value system of numbers locks people into a limited mindset of numerical thinking. So I feel vindicated by the fact that this guy solved the Poincare Conjecture using Roman numerals. They are better all round and easily manipulable.

proof has been announced (5, Insightful)

call -151 (230520) | about 12 years ago | (#3298528)

Normally it take a while for a proof to be verified- a better title would be `A Proof has been announced for the Poincare Conjecture.' The Poincare conjecture has attracted a great deal of attention and lots of remarkable, deep work, but it has also had its fair share of proofs which fell apart under serious scrutiny. Most notably, Colin Rourke and a co-author I can't remember had claimed a proof of the Poincare conjecture in 1987 which took something like a year-plus before the mistakes were found, and took a great deal of energy by a number of mathematicians to find the errors.

That being said, Martin Dunwoody is a remarkable researcher and this work relies on important, ground-breaking work of Abby Thompson and Hyam Rubenstein, and this preprint sounds very promising!

Statement of conjecture on wolfram incorrect? (5, Informative)

Anonymous Coward | about 12 years ago | (#3298579)

Surely it should read:

The conjecture that every *compact* simply connected 3-manifold is homeomorphic to the 3-sphere,

Normal euclidean space R^3 is simply connected,
and definitely NOT homeomorphic to to the
3-sphere !!

(That they are not homeomorphic can be proved by
comparing their homotopy or homology groups).


Re:Statement of conjecture on wolfram incorrect? (2)

p3d0 (42270) | about 12 years ago | (#3298692)

Mods, I think the parent may be a gem lost in the abyss of anonymity. Do what you think is right.

books on this stuff (2)

danny (2658) | about 12 years ago | (#3298589)

Maybe it's time for me to make a fourth attempt at reading Harper and Greenberg's Algebraic Topology: A First Course. I think I got three quarters of the way through last time...

Can anyone recommend any other books on algebraic topology?


Re:books on this stuff (0)

Anonymous Coward | about 12 years ago | (#3298627)

Try M.A.Armstrong's Basic Topology published by Springer-Verlag New York Inc., ISBN 0387908390.

It's a fairly solid book on the subject. I haven't seen Harper and Greenberg though so I can't say how it compares.

Re:books on this stuff (1)

Pepeee (233622) | about 12 years ago | (#3298665)

Look for W. Massey's books: "Algebraic Topology, A First Course" and "Singular Homology Theory" in Springer's Graduate Texts in Mathematics. That's where I learned all my Algebraic Topology.

Re:books on this stuff (1)

jasoegaard (103287) | about 12 years ago | (#3298667)

Bredon's "Topology and Gemetry" is a modern classic.

The old one was Spanier's "Algebraic Topology".
(which is also quite nice).

Re:books on this stuff (1)

Pepeee (233622) | about 12 years ago | (#3298674)

How can you call Spanier nice?? I don't know of anybody who's been able to read more than two pages! It's dense and very confusing in its "great generality"! Completely unreadable!

English please! (2, Interesting)

prestwich (123353) | about 12 years ago | (#3298603)

Can someone explain what the hell this problem is about in English please? (Preferably avoiding the word manifold).
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