## Russian May Have Solved Poincare Conjecture 527

nev4 writes

*"Reuters (via Yahoo News) reports that Grigori Perelman from St. Petersburg, Russia appears to have solved the Poincare Conjecture. The Poincare Conjecture is one of the 7 Millenium Problems (another is P vs NP, also covered on /. recently). Solving a Millenium Problem carries a reward of $1M, but apparently Perelman isn't interested..."*nerdb0t provides some background in the form of this MathWorld page from 2003.
## He'd post AC (Score:5, Insightful)

Take the case of Paul Erdos [wikipedia.org] who was essentially homeless, but published over 1500 papers and is considered one of the all time greats in the field.

Perelman just casually posted his solution out to the web in much the same way that some of the most brilliant posts on

## Re:He'd post AC (Score:5, Funny)

Yeah, it's broadband.

## Re:He'd post AC (Score:5, Insightful)

"A musician must make music, the artist must paint, a poet must write, if he is to be ultimately at peace with himself. What a man can be, he must be. This need we may call self-actualisation. (Motivation and Personality, 1954)". This happens after the various esteem needs, love needs, safety needs, and physiological needs are met. I think the average person gets stuck dealing with the "safety needs" (thus easy 9/11 manipulation). And the average reasonably-successful-slashdotter-guy gets stuck with the "esteem needs" stage aiming for Karma.Only us self-actualized "Anonymous Coward" guys rise above this with insightful and informative posts such as this one without whoring for karma.

## Re:He'd post AC (Score:4, Funny)

And the average reasonably-successful-slashdotter-guy gets stuck with the "esteem needs" stage aiming for Karma.But the geeks are all kept equal with hatchet, ax, and 50-point karma cap.

## Re:He'd post AC (Score:3, Insightful)

"A musician must make music." I'd strike the "If

Regarding the "homeless" Paul Erdos, who wouldn't go to more than a little trouble to have him as a house guest? Seems like he'd have the advantages of the

## Except... (Score:3, Insightful)

heirarchy. In other words, it's all well and good to be self-actualized, but you need to have your rent and food bills coveredfirst## Re:He'd post AC (Score:4, Insightful)

Anyone that brilliant would see how pointless it is to worry about money. When will the rest of us learn?Oh please. What is this? The 60s? Apparently the guy is able to find enough time to work on these problems. That kind of freedom is what money buys. If he didn't have enough money to do that then it would suddenly become much more important.

"Money" is not some stack bills in your wallet. It represents some tangible effort that had value, and that value is now stored in a convenient form, ready to be exchanged for something else of value.

## Re:He'd post AC (Score:5, Interesting)

Apparently the guy is able to find enough time to work on these problems. That kind of freedom is what money buys.It probably would only take $15K in the US to rent a small apartment in a cheap city and buy food for a year, allowing him to work on his problems. I think the point is that this guy may have been able to make a significant contribution to human knowledge and maybe centuries of notoriety with what it cost to live for a few years. Most of the rest of us would have taken the same amount of money and just dumped it into buying an upscale SUV.

## Re:He'd post AC (Score:3, Informative)

I agree that Ricci flows are very specialized; I believe Hamilton and Perelman are the experts (with possibly Yau, Tian, Donaldson, or a few others). Many mathematicians get a lot of enjoyment from "solving a di

## Re:He'd post AC (Score:2, Insightful)

I meant to say is that we'd all be happier if we didn't have to worry about money. However, a lot of people are living paycheck to paycheck and the little things in life (broadband, it's a joke) make the effort meaningful.

Your reply was dead on though, and insightful.

## Re:He'd post AC (Score:2, Insightful)

In truth, money is a loan from a central bank to a government, that due to interest can never be repaid. Think about it a moment, if you get a $100,000 home loan, you don't walk away with a brief case of bills (and even if you did, they can't be exchanged for gold), the bank assigns some numbers to your account briefly, which gets assigne

## Re:He'd post AC (Score:3, Insightful)

All money is, is slavery to a bank, which gives permission for someone to transfer real property to you.Humm, but what if the loan has been paid off, for long enough you've forgotten that you once made house payments?

You see, I wasn't about to be scratching to make a mortgage payment when my income was reduced to the social security (gawd, what an oxymoron that is for some folks) levels in my old age, so the house has been paid off for 8 years now, and I've been almost-retired for 2.5 years.

That little

## Re:He'd post AC (Score:4, Interesting)

Let's say that there is a small economy. I am a central bank. Right now, there is no money. Therefore, you take a loan out for $10, and I charge $1 interest. Frank takes out a loan for $10, and I charge him $1 interest. The whole economy has $20 in it, but they owe $22. There's no way this can be paid off. Now, one of you could handle their money better than the other, and get a $1 advantage to pay off their loan, but that would leave only $9 in the economy to pay off a remaining $11 loan. One of you would be fine, but there is no way in this system for everyone to pay back their debts. So, eventually, the banks own nearly everything.

This is why the founders of our country hated central banks, and was one of the primary reasons for the revolutionary war.

## Re:He'd post AC (OT) (Score:3, Interesting)

## Re:He'd post AC (Score:2)

## Re:He'd post AC (Score:3, Informative)

## Re:He'd post AC (Score:3, Insightful)

nothing. You don't need any special equipment or a formal higher education.This means you can do it on welfare from your trailer park home, or from a cardboard box under a bridge if that's your thing. Significant mathmatical breakthroughs have, in the past, been made by incredibly poor persons with little schooling to speak of. Admittedly this is rare, but not unheard of.

You really just need access to a library of some sort and that

## Re:He'd post AC (Score:2)

There are more than enough needy causes that could do with such a boost to their funds.

## Re:He'd post AC (Score:5, Insightful)

## Re:He'd post AC (Score:5, Insightful)

However, I've seen many intelligent people work hard without stopping because it was the right thing to do, not because of the monetary gain. That is what I'd hope to highlight.

## Re:He'd post AC (Score:3, Insightful)

However, the last couple of years since I finished, I have lived very close to the official poverty limit of my city, and I know that is bad.... So, I need to do something to get a higher influx of cash. I find no motivation in doing it, though, to the contrary, it feels like I have to abandon the pursuit of interesting things to get it.

I just need to be fed, kept clothed when it is col

## How do you get your jollies? (Score:3, Interesting)

If you're a sex fiend, you'll spend your time in the gym, and maybe convincing people to pay you hefty consulting fees to tell them things they already know.

If you're a musician, you'll be in a band, even if you'll never make more thana hundred bucks a gig.

If you want to be the richst man in the world, well, if I knew the answer to that I'd be the richest man in the world.

But if you're a guy who actually does like solving

## Computer Time (Score:3, Insightful)

(Ok, in reality, that's kinda short-sighted, as you could buy $1 million of computer time, but maybe he doesn't like computers.)Computer time will only help with P problems, or P elements of NP problems. Great mathematicians seem to be NP-solving machines. A hundred years of computing time on the best computer might releive some of their tedium but would actually have an insignificant impact on their ability to solve problems.

The rest of us lesser beings might consider spending out time building a supe

## Re:He'd post AC (Score:4, Funny)

You're completely correct; I think my comment was mistaken.Woah, that's weird! I thought I was reading Slashdot but it must actually be some other site.

## Re:He'd post AC (Score:5, Funny)

There's more to life than money.Yes, but he could reinvest the money into rubber bands and apples and solve thousands of Poincaré conjectures at once and thus gather even more money to buy apples for the hungry children in the world and rubber bands for their trousers. Well, if this business model isn't patented yet, of course...

## Re:He'd post AC (Score:2, Insightful)

It makes sense. Anyone that brilliant would see how pointless it is to worry about money.Perhaps all of these years of fertilizing your organic garden with human feces has lead to some sort of spongiform encephalitus.

Money IS important. It may not be the most important thing in the world, but we all need to eat and have a safe place to sleep at night. Those things take money.

LK

## Re:He'd post AC (Score:5, Insightful)

Einstein's original paper on Special relativity was named "On the electrodymanics of moving bodies".. It was not named "Revolutionary new discovery by me, Albert Einstein which will revolutionize the world of physics".

I guess there are several reasons for this.. one is simply manners. Boasting is unpolite. Scientific papers rarely have exciting titles, even when the results are exciting.

The second is of course, that a good scientist realizes the if a result may be revolutionary. A good scientist also always leaves room for doubt.

So the natural behaviour would of course to be careful and discreet, and not go confidently telling the world of your revolution until it has been verified. Otherwise, you'll end up with a lot of egg on your face.

Conversely, most scientists are highly sceptical of 'revolutionary' results which are announced in the press before being published. In fact, most pseudoscientists are very good at publicizing themselves and their 'revolutions', probably because they are totally convinced of their own theories, and are lacking the 'self-doubt' bit.

## Re:He'd post AC (Score:3, Interesting)

"On the electrodynamics of moving bodies"

is exceedingly boastful.

In computer science, an analogy might be to publish a paper titled:

"On datastructures, in general"

What an oddly broad topic to choose, unless

you are claiming to be saying something

rather profound.

## Re:He'd post AC (Score:4, Insightful)

So it would be like publishing a paper called "on datastructures" if you were the person that invented datastructures....

## Re:He'd post AC (Score:3, Funny)

## Re:He'd post AC (Score:4, Insightful)

I guess there are several reasons for this.. one is simply manners. Boasting is unpolite. Scientific papers rarely have exciting titles, even when the results are exciting. The second is of course, that a good scientist realizes the if a result may be revolutionary. A good scientist also always leaves room for doubt.Contrast this lack of fanfare with another recent publication, Stephen Wolfram's A New Kind of Science [amazon.com]. This 'new' science seems to have been met with mixed reviews at best, and not the paradigm shift that the author seems to have been hoping for. Of course only time will tell who is right... But in the event that Perelman's is incorrect, his humility and lack of hubris regarding his solution definitely earns him my respect, and undoubtedly that of many others in the field.

## He wouldn't care to post (Score:2)

## dammned practical? (Score:2)

maybe we should be looking for the monomania gene in all these 'idee fixee' folks...

## Re:He'd post AC (Score:2)

some of the most brilliant posts on /. come form "anonymous cowards" sitting in their offices at MIT.Really? I've read a few interesting posts from AC's, but not a single one that I would consider brilliant. We may be using different units of measure, but I'd certainly be curious to read a few of these brilliant AC posts.

Provide links, please.

## Re:Getting Maried Bad for Math? (Score:3, Insightful)

## The "free" internet bubble never burst (Score:5, Funny)

But there's a snag. He has simply posted his results on the Internet and left his peers to work out for themselves whether he is right -- something they are still struggling to do.

"There is good reason to believe that Perelman's approach is correct. But the trouble is, he won't talk to anybody about it and has shown no interest in the money," said Keith Devlin, Professor of Mathematics at Stanford University in California.

I'm always amazed how much free stuff is on the internet. Free million dollar solutions! Good luck with em!

## Math? (Score:5, Informative)

## Re:Math? (Score:3, Funny)

GBP (George Bush Pound) - The dollar unit associated with the search for WMDs.

## Re:Math? (Score:4, Funny)

## Re:Math? (Score:4, Funny)

I think you misspelled sourted.

## Look at his method for solving this!!! (Score:5, Funny)

Just kidding! I have no clue what the hell this is. I got lost after the word conjecture.

## Re:Look at his method for solving this!!! (Score:5, Funny)

## Re:Look at his method for solving this!!! (Score:2)

## So tell the truth... (Score:5, Funny)

## Damn... (Score:5, Funny)

(I wonder if this is what some of my non-engineering clients think of my work sometimes)

## Yes but... (Score:5, Funny)

- Greg

## Re:Yes but... (Score:4, Funny)

## Re:Yes but... (Score:5, Informative)

Makes sense, as I have no idea what the question is.Hm... Let's see what the article tells us about it:

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.Ah. Poincaré understood to ask a simple question like "what is six multiplied by seven" in such a profoundly stupid way that it puzzled the world ever since if and why the answer was 42...

## Re:Yes but... (Score:2)

## $1 million USD? (Score:5, Informative)

A reclusive Russian may have solved one of the world's toughest mathematics problems and stands to win $1 million (560 million pounds) -- but he doesn't appear to care.Heh. Last I checked, $1 million dollars was not quite equal to 560 million (British) pounds. (560 thousand, sure

In an article on mathematics. Of all things.

## Re:$1 million USD? (Score:5, Funny)

## Re:$1 million USD? (Score:3, Funny)

## Billions - Spanish / English (Score:3, Informative)

Cheers

## Re:Billions - Spanish / English (Score:3, Informative)

## The Whocares conjecture (Score:5, Funny)

## An apple is simple connected a donut is not. (Score:2, Funny)

However you stated 'We say the surface of the buttocks are "simply connected"' buy that do you mean to ignore all the plumbing associated with the butt while recognizing the thru and thru nature of the mouth/nose hole.

I NEED more information. I'm strangely fascenated by the topography of butts. Perhaps I can get a grant.

## Riemann hypothesis reportadly also solved (Score:5, Interesting)

This particular problem has big implications for online cryptography as it deals with the distribution of prime numbers. Apparantly.

(I'm no mathematics person BTW.)

## Re:Riemann hypothesis reportadly also solved (Score:5, Informative)

For those too lazy to click:

## Riemann was covered this summer on Slashdot (Score:2)

## meh, important, but not that important. (Score:2)

Just because the hypothesis hasn't been proven doesn't mean someone can't start working on an application that only works if it is true. I'm pretty sure there's guys already working under this assumption. Don't know anyone personally, but that's what I'm told.

Quantum computing is a nice, related example. When Shor came up with a factoring algorithm, no one had proven that quantum computing was possible. But tha

## The Millenium Problems (Score:5, Informative)

- sm

## Just like Linux configuration forums (Score:3, Insightful)

But there's a snag. He has simply posted his results on the Internet and left his peers to work out for themselves whether he is right -- something they are still struggling to do.Okay, so tell me how this is any different from every l33t user that tells me how to get my dual flat panel setup working under Xandros without editing the X files manually? Sounds like these kids just tried their hands at mathematics, too.

## Mr. President... (Score:2, Funny)

## Re:Mr. President... (Score:2)

## Hopefully he has better luck than de Branges (Score:5, Informative)

It is not that de Branges is unqualified: he settled Bieberbach's Conjecture [wolfram.com]. Interestingly, much of the validation of de Branges work on Bieberbach's Conjecture was done by a team at the Steklov Institute, referred to in the MathWorld link in the article.

## Re:Hopefully he has better luck than de Branges (Score:5, Interesting)

## Re:Hopefully he has better luck than de Branges (Score:3, Insightful)

No, Branges needs to prove that the counterexample does not apply to his theory.It's not a court, Branges doesn't need to do anything - someone needs to prove it one way or another for the science to progress.

## Re:Hopefully he has better luck than de Branges (Score:3, Insightful)

Yeah, I skimmed his paper, and noticed that as well. Apparently, "apology" in this context means a proof that has not yet been subjected to peer review, but which the author is deeply convinced is correct. Pasting some output from a

dict apology, it seems:## One thing he overlooked... (Score:4, Funny)

## Re:One thing he overlooked... (Score:5, Funny)

Just like the joke about the mathematician who woke up and discovered a fire in his room. After working out exactly how much water to use and what direction to throw it, he said "There is a solution" and went back to sleep (without putting out the fire - that's a job for the physics/engineering folks).

## Wake me up when it's peer reviewed and accepted (Score:2, Insightful)

Editors, I'm talking to you.

## Racist title (Score:4, Insightful)

## Re:Racist title (Score:3, Funny)

## Re:Racist title (Score:2)

No harm in that. Now if they said "Pinko May Have Solved..." or better yet "Whitey May Have Solved..." (or Honkey, etc), there could have been a slight problem. (No insult intended, perhaps I'm a white guy from Russia.)

Would it have be

## Re:Racist title (Score:3, Informative)

Chill out. It was a

joke.So, to quote Trek, "Double dumbass on you."

## Paincare conjecture (Score:2, Funny)

A Christian Scientist from Theale

Said, "Though I know that pain isn't real,

When I sit on a pin

And it punctures my skin

I dislike what I fancy I feel".

Oh! It's poincare... forget it...

## tr/Russian/Grigori Perelman/ ..? (Score:5, Insightful)

"

Grigori PerelmanMay Have Solved Poincare Conjecture"I've noticed that these kinds of announcements often make a point of appending a nationality to the name of the person involved in the discovery. Surely this proof builds on mathematical knowledge from around the world. Or was Grigori Perelman standing solely on the shoulders of "fellow Russian" mathematicians? I highly doubt it...

## Re:tr/Russian/Grigori Perelman/ ..? (Score:2)

I suspect it's the long winters.

## Interesting View (Score:2, Interesting)

## Perelman and the prize (Score:5, Interesting)

So think about his perspective: he's a complete loner who was ignored by the mathematical community for 10 years! Now that he's going to be a "certified" genius (with the $1M prize) why exactly should he care.

Also, it's worth pointing out that like Wiles (who solved the Fermat Conjecture), Perelman's work develops a theory that has the Poincare conjecture as a corollary which is interesting but not of central importance.

## Re:Perelman and the prize (Score:5, Interesting)

Perelman was unemployed for 10 years while he worked on the problem. His last job was in the States in the early 90s, where he saved enough money to live in Russia for the whole time he worked.What I find particularly interesting is that this guy was able to devote 10 years of his life to solving a problem so complex that there was no intermediate output. The same happened to Wiles, who took 7 years to get hold properly of the Fermat theorem.

Obviously, in both cases it would have been impossible to reach such great results if the authors had had to keep a steady pace of lesser publications. But this is the rule in the academic world: "publish or perish". You must prove yourself "productive" year by year, otherwise you're out.

I've always thought that applying industrial methods of prouctivity measurement to research is utter madness (I am an academic myself). IMO, Perelman's and Wiles' cases show it clearly.

## Any relation to Yu Perelman (Score:2)

which made learning mathematics as a kid absolutely wonderful ? Wonder if Grigori Perelman

is of any relation to the author of that book Yu Perelman ?

## Time (Score:3, Interesting)

The main problem with all of these solutions especially in math is that time is the largest factor in determining if the solution is correct. Give you 2 years and its marginally okay. Give you 40 and its accepted as a standard etc...## Russian may have proved Poincare Conjecture (Score:4, Funny)

they prove conjectures.

## My Solution to Number 5 (Score:5, Funny)

5 Riemann hypothesis Involving zeta functions, and an assertion that all "interesting" solutions to an equation lie on a straight line. It seems to be true for the first 1,500 million solutions, but does that mean it is true for them all?Answer:

NOit doesn't mean it's true for all of them. You would have to prove that.Where do I get my money?

## Why aren't proofs verifiable via software? (Score:3, Interesting)

I am not talking about having a computer generate the proof itself, which can be difficult of course, I am just talking about verifing a given proof.

## some terminology (Score:5, Insightful)

The n-sphere (which mathematicians generally denote by S^n) can be thought of as `all points in (n+1)-dimensional space which are at unit distance from the origin'. So S^2 is the

surfaceof a solid 3-dimensional ball. This sometimes surprises people, who expect this to be S^3 but the key observation here is that the 2 refers to theintrinsicdimension of the object, rather than theextrinsicdimension of any space you might happen to put (`embed') the object in. The fact that we often think of the 2-sphere as being embedded in 3-dimensional space doesn't change the fact that it's inherently a 2-dimensional object. An ant wandering around on it still only has two degrees of freedom.The 3-sphere (S^3) locally looks like ordinary, flat, Euclidean 3-space, but on a larger scale it kind of doubles back on itself - if you keep walking (or floating) in a `straight line' (well, actually the 3-dimensional analogue of a `great circle', but never mind) in any direction, then you'll eventually get back to where you started.

The Poincaré Conjecture says

This, by itself, isn't particularly enlightening to the non-topologist, but what it actually boils down to is:

What does this mean?

Well, an `n-manifold' is a space which

locallylooks like ordinary, flat, Euclidean n-dimensional space. So a 3-manifold is a space (like S^3) which locally looks like ordinary 3-space (but which might twist back on itself in a peculiar way on a larger scale).`Closed' means that the 3-manifold doesn't have a boundary - no matter how far you walk, you're not going to run into a brick wall, or fall off the end. `Compact' is a bit more technical, but in this context essentially means you don't get odd shooting-off-to-infinity stuff you have to deal with.

And `simply-connected' means that the first homotopy group (the `fundamental group' of the space) is trivial. What

thatmeans is that any closed loop (of string, if you like), in the manifold, can becontinuouslyshrunk down to a point. Here `continuous' means that you're not allowed to cut or glue the string while you're doing it.To use a 2-dimensional analogy, the 2-sphere (the surface of the 3-dimensional ball, remember, or alternatively a British doughnut) is simply-connected, because given any closed loop in the surface, you can shrink it down to a point without it getting snagged on anything. Whereas the 2-torus (the surface of an American doughnut) isn't, because you can't shrink all closed loops down to a point - one which goes all the way round the central hole, for example, can't be shrunk.

Finally, `homeomorphic' is basically a technical word for `topologically equivalent' - we allow continuous deformations (stretching, twisting, etc, but not cutting or pasting), rotations, reflections, or any combination of these.

So, the (classical) Poincaré Conjecture is essentially a technical way of saying ``If it looks like a 3-sphere then, basically, it is''. (For certain definitions of `is', and `looks like'.)

The analogous conjecture in n-dimensional space is known to be true for n=1 (trivial), 2 (pretty simple), and 5 and above (the 5-dimensional case was proved by Zeeman, who is my PhD grandsupervisor - my supervisor was one of his students). The 4-dimensional case is weird, and there are three different forms to consider - the `piecewise linear' and `topological' cases have been proved, but the `smooth' case is still unproven.

As I understand it, what Perelman claims to have done is prove Thurston's Geometrisation Conjecture, which implies the Poincaré Conjecture as a special case - rather lik

## Re:Duplicate? (Score:4, Informative)

## Re:Duplicate? (Score:5, Funny)

Think nothing is impossible? Try slamming a revolving door.Place a 2 by 4 on the floor in the door.

Slam the revolving door.

Another impossible problem solved.

## Re:Duplicate? (Score:3, Funny)

## Re:Duplicate? (Score:2)

## Re:Duplicate? (Score:2, Informative)

Maybe what we have here is just the impending lapse of the Clay Math. Inst.'s required two years of scrutiny...

## Re:Duplicate? (Score:2, Informative)

## Re:Problems with the Millenium Problems (Score:5, Funny)

I'm joking, but you're still an idiot.

## Re:Problems with the Millenium Problems (Score:2)

There are a number of reasons why these problems should have prize money attached to them without direct practical applications that are curreently known. First, their results are important from a pure

## Re:Problems with the Millenium Problems (Score:3, Interesting)

How? There are many branches of mathematics and mathematicians who deal in practical work and will decry the relevance of this type of work.The results of different mathematicians, some big and some small, are put together by the next generations of mathematicians to derive new results. Many people who deal with the practical are content to buil on fairly old results. They can decry all they want, but most likely even they use somee result which was initially a solution waiting for a problem. General r

## Re:Wake me... (Score:4, Informative)

## Re:Wake me... (Score:2)

That was in April 2003. It's now over a year later again and it hasn't been disproven.What we need is a 1 Million $ prize for the person that disproves the proof.

## Re:Poincare Conjecture link sucks! (Score:4, Insightful)

The Poincare Conjecture involves hypothetical 4-dimensional shapes with the same properties, and isn't very easy.

## Re:Confused (Score:5, Informative)

It's pretty easy to see that all simply connected 2-manifolds (in 3 dimensions, at least) are homeomorphic to the shell of a sphere, i.e. they may be stretched and contorted to look like it. The question answered here is whether the same is true in the next dimension.