# The Poincaré Conjecture has Been Proved

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

307Martin 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.

## This could definitely be (-1, Troll)

## Anonymous Coward | more than 12 years ago | (#3298318)

## Re:This could definitely be (-1)

## YourMissionForToday (556292) | more than 12 years ago | (#3298334)

## Dungeon Siege (-1, Troll)

## Anonymous Coward | more than 12 years ago | (#3298319)

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) | more than 12 years ago | (#3298357)

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 | more than 12 years ago | (#3298629)

## Wierd Problem (3, Interesting)

## KagatoLNX (141673) | more than 12 years ago | (#3298337)

## Re:Wierd Problem (1)

## squidinkcalligraphy (558677) | more than 12 years ago | (#3298351)

## Re:Wierd Problem (2, Informative)

## leviramsey (248057) | more than 12 years ago | (#3298398)

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) | more than 12 years ago | (#3298414)

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) | more than 12 years ago | (#3298483)

quitelikely that the proof indeed for that case. </sarcasm>## Re:Wierd Problem (2, Informative)

## avsed (168886) | more than 12 years ago | (#3298508)

Dan

## Re:Wierd Problem (0)

## Anonymous Coward | more than 12 years ago | (#3298631)

## Re:Wierd Problem (2, Informative)

## splorf (569185) | more than 12 years ago | (#3298458)

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) | more than 12 years ago | (#3298475)

n= 3 case.## For 1=7 (2)

## XNormal (8617) | more than 12 years ago | (#3298457)

## Re:For 1=7 (0)

## Frank.B.Parker (520642) | more than 12 years ago | (#3298479)

n >= 7, and the HTML just ate the >.## Re:For 1=7 (1)

## DNAGuy (131264) | more than 12 years ago | (#3298646)

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

## squidinkcalligraphy (558677) | more than 12 years ago | (#3298339)

## Re:now I've seen it all (-1)

## Yr0 (224662) | more than 12 years ago | (#3298379)

they've stooped to an alltime low advertizing fucking Katz now.

look, heres a link to his fucken book [amazon.com]

dont buy this book.

its written by katz

## Re:now I've seen it all (-1)

## Yr0 (224662) | more than 12 years ago | (#3298397)

FUCK you katz NO ONE want to buy your FUCKEN BOOOK[slashdot.org]## What's the problem? (-1, Redundant)

## jchawk (127686) | more than 12 years ago | (#3298341)

## Re:What's the problem? (0)

## jojor (545317) | more than 12 years ago | (#3298385)

## Re:What's the problem? (0)

## Anonymous Coward | more than 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) | more than 12 years ago | (#3298416)

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 | more than 12 years ago | (#3298440)

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

## busted (0)

## Anonymous Coward | more than 12 years ago | (#3298446)

## Re:What's the problem? (2)

## Gary Yngve (416254) | more than 12 years ago | (#3298441)

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) | more than 12 years ago | (#3298455)

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 | more than 12 years ago | (#3298525)

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 | more than 12 years ago | (#3298348)

## luser (-1, Flamebait)

## autopr0n (534291) | more than 12 years ago | (#3298366)

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

## Anonymous Coward | more than 12 years ago | (#3298352)

HOWTO : The way out

Version 1.1.2

Fed up of cryptic commands such as

ls

dd

gcc

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Blind from the brain damaged fonts?

Well don't worry, I have the way out of these crappy operating systems,

just follow these commands.

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or

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8. If you really want the command line, install DOS, the original and

best!

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

## Yr0 (224662) | more than 12 years ago | (#3298432)

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## Well.. (0, Troll)

## autopr0n (534291) | more than 12 years ago | (#3298358)

## Re:Well.. (0)

## Anonymous Coward | more than 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) | more than 12 years ago | (#3298507)

solidsphere 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) | more than 12 years ago | (#3298511)

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 | more than 12 years ago | (#3298545)

## Re:Well.. (0)

## Anonymous Coward | more than 12 years ago | (#3298601)

:-/

(disgruntled nerd)

## Re:Well.. (0)

## Anonymous Coward | more than 12 years ago | (#3298661)

## teacup == donut (1, Funny)

## Anonymous Coward | more than 12 years ago | (#3298359)

## Re:teacup == donut (2, Funny)

## Quirk (36086) | more than 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) | more than 12 years ago | (#3298645)

--

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

## Re:teacup == donut (1)

## Jouster (144775) | more than 12 years ago | (#3298675)

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.

Jouster

## Proof (0, Troll)

## droyad (412569) | more than 12 years ago | (#3298361)

## Re:Proof (1)

## Quirk (36086) | more than 12 years ago | (#3298382)

Popper fan I presume.

:)## Re:Proof (1)

## phooka.de (302970) | more than 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

knowthat 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 | more than 12 years ago | (#3298419)

## Re:Proof (1)

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

"given that the following assumptions are true"or"based on the following axioms...".I guess calling it a

mathematicalproof includes this, though.## Re:Proof (4, Insightful)

## bentini (161979) | more than 12 years ago | (#3298451)

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) | more than 12 years ago | (#3298469)

## Nope (2, Insightful)

## dark-nl (568618) | more than 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) | more than 12 years ago | (#3298521)

And faith in Mathematical proof is counterproductive at a level beyond that

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) | more than 12 years ago | (#3298591)

halfan education in mathematics...## Re:Proof (1)

## cheezehead (167366) | more than 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

truthsthat 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) | more than 12 years ago | (#3298536)

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) | more than 12 years ago | (#3298543)

"Anything can be proved with enough flawed mathematics." How does one prove something with flawed mathematics? Certainly, one can

attemptto 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.

## Interesting... (0)

## Thaidog (235587) | more than 12 years ago | (#3298374)

## Re:Interesting... (1)

## Krapangor (533950) | more than 12 years ago | (#3298622)

## now sing along! (-1)

## YourMissionForToday (556292) | more than 12 years ago | (#3298386)

Wiener songI 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 | more than 12 years ago | (#3298400)

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

## Anonymous Coward | more than 12 years ago | (#3298403)

## GOOD LORD! (0)

## Anonymous Coward | more than 12 years ago | (#3298410)

## Re:GOOD LORD! (-1)

## October_30th (531777) | more than 12 years ago | (#3298425)

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) | more than 12 years ago | (#3298612)

## 33. (-1)

## GafTheHorseInTears (565684) | more than 12 years ago | (#3298426)

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) | more than 12 years ago | (#3298429)

assume a, b, c such that:

a + b = cthen

5a + 5b = 5cand

4c = 4a + 4badding the two:

5a + 5b + 4c = 4a + 4b + 5cshifting some terms around:

5a + 5b - 5c = 4a + 4b - 4csimplifying:

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) | more than 12 years ago | (#3298435)

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

## Xerithane (13482) | more than 12 years ago | (#3298474)

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

## blah blah blah im so smart and funny oh yes (-1)

## Yr0 (224662) | more than 12 years ago | (#3298448)

DICKwad

suxor

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

## Anonymous Coward | more than 12 years ago | (#3298452)

Infinity * 4 = Infinity * 5

is by definition

Infinity = Infinity

Your proof is flawed QED.

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

## frinsore (153020) | more than 12 years ago | (#3298566)

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 | more than 12 years ago | (#3298593)

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

## Anonymous Coward | more than 12 years ago | (#3298654)

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

## nucal (561664) | more than 12 years ago | (#3298453)

a + b = cthen

(a + b - c) = 0so

5*0 = 4*0someone had to do it ....

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

## nucal (561664) | more than 12 years ago | (#3298456)

someone had to do it ....make that everyone had to do it

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

## Mindfool (570751) | more than 12 years ago | (#3298460)

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

## Rhinobird (151521) | more than 12 years ago | (#3298500)

## YAY! (-1, Troll)

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

## Re:YAY! (-1)

## October_30th (531777) | more than 12 years ago | (#3298461)

And it's faggot, not fagot.

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

## Anonymous Coward | more than 12 years ago | (#3298476)

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

## Anonymous Coward | more than 12 years ago | (#3298505)

## Pah, anybody with a time machine (3, Funny)

## LadyLucky (546115) | more than 12 years ago | (#3298433)

## Re:Pah, anybody with a time machine (0)

## Frank.B.Parker (520642) | more than 12 years ago | (#3298466)

## I gave up being a math major (0)

## Anonymous Coward | more than 12 years ago | (#3298436)

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

## Anonymous Coward | more than 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 | more than 12 years ago | (#3298471)

Athankyou

## The homosexual spelling correction conspiracy. (0)

## Anonymous Coward | more than 12 years ago | (#3298630)

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) | more than 12 years ago | (#3298487)

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

## Beautyon (214567) | more than 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) | more than 12 years ago | (#3298509)

## proof has been announced (5, Insightful)

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

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 | more than 12 years ago | (#3298579)

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).

Liam.

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

## p3d0 (42270) | more than 12 years ago | (#3298692)

## books on this stuff (2)

## danny (2658) | more than 12 years ago | (#3298589)

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?

Danny.

## Re:books on this stuff (0)

## Anonymous Coward | more than 12 years ago | (#3298627)

Try M.A.Armstrong's

Basic Topologypublished 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) | more than 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) | more than 12 years ago | (#3298667)

The old one was Spanier's "Algebraic Topology".

(which is also quite nice).

## Re:books on this stuff (1)

## Pepeee (233622) | more than 12 years ago | (#3298674)

## English please! (2, Interesting)

## prestwich (123353) | more than 12 years ago | (#3298603)