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Poincare Conjecture Proof Completed

samzenpus posted about 8 years ago | from the show-your-work dept.

222

Flamerule writes "A New York Times article has finally provided an update on the status of Grigori Perelman's 2003 rough proof of the Poincaré Conjecture. 3 years ago, Perelman published several papers online explaining his idea for proving the conjecture, but after giving lectures at MIT and several other schools (covered on Slashdot) he returned to Russia, where he's remained silent since. Now, mathematicians in the US and elsewhere have finally finished going over his work and have produced several papers, totaling 1000 pages, that give step-by-step, complete proofs of the conjecture. In addition to winning some or all of the $1,000,000 Millennium Prize, Perelman now seems to be the favorite to receive a Fields Medal at the International Mathematics Union meeting next week, but it's not clear that he'll even show up!"

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yay, look at me (-1, Offtopic)

Anonymous Coward | about 8 years ago | (#15916770)

yep

Square Pegs in Round Holes (2, Funny)

Doc Ruby (173196) | about 8 years ago | (#15916775)

Goddamn I love freaky misfit mathematical geniuses. They're even better than their nerdier cousins, the chess geniuses. The ones from Central/Eastern Europe and South Asia always seem to be the most fun.

Re:Square Pegs in Round Holes (-1, Offtopic)

skraps (650379) | about 8 years ago | (#15916788)

Man I have such a boner right now.

Re:Square Pegs in Round Holes (1, Funny)

Anonymous Coward | about 8 years ago | (#15916840)

The ones from Central/Eastern Europe and South Asia always seem to be the most fun.


No kidding. Half of my good math books are Russian translations (and half of my good math professors were Russians). The mathematical ability of Russians must have something to with long Siberian winters. Nothing to do except pee in the snow and write math problems, sometimes both at the same time (especially if you can get some of the 'good' soda machine vodka)!

Re:Square Pegs in Round Holes (1)

Doc Ruby (173196) | about 8 years ago | (#15916953)

I always thought it's their natural advantage in having an "alphabet" much closer to the Greek symbols we have to struggle to even recognize at first.

Re:Square Pegs in Round Holes (1)

nmb3000 (741169) | about 8 years ago | (#15916970)

freaky misfit mathematical geniuses

Make for good stories too... Wait, I saw this coming! There's also something about a black box, a blind guy, passports, and a guy who looks like he spent a little too much time in prison.

Hmm, lost it now.

Grigori Perelman, please give us a sign! (-1, Troll)

reporter (666905) | about 8 years ago | (#15917029)

We should be quite concerned about Grigori Perelman since he returned to Russia. During the last several years, democracy in Russia [washingtonpost.com] and human rights have begun to fade.

If Perelman is truly a genius on par with Albert Einstein, he faces two problems in Russia.

First, the Russian government will want to tap into his genius to improve its weapons systems. In the Russia of today, if he said, "no", then he would be faced with harrassment and, even, trumped-up charges leading to imprisonment.

Second, like Albert Einstein [wikipedia.org] and Andrei Sakharov [wikipedia.org] , I expect that Perelman would be a supporter of human rights and democracy. Their genius enables them to see that freedom fosters the growth of intellect, of which they have much. Unfortunately, in the Russia of today, too much talk about political change to removing the ruling party can cause a tax audit or worse.

Russia, today, is much better than the old Soviet Union, but saying that Russia is a democracy would be an exaggeration.

So, I hope that Mr. Grigori Perelman is okay. If he can read this message, then, I wish that he would, at least, post a message on SlashDot so that we know that he is all right.

Perelman really should come to USA. Here, he can work on neat projects like the new hyperdrive for space travel [newscientist.com] . If this hyperdrive is ever to succeed, we will need the enormous intellect of Perelman to work out the hairy mathematics.

Re:Grigori Perelman, please give us a sign! (5, Funny)

drix (4602) | about 8 years ago | (#15917076)

Haha.. oh that's rich. "Please Mr. Perelman--flee from the military-industrial complex. Come to a sanctum of human rights and democracy. Come to ... [wait for it] ... America!"

The reason they can't find him in Russia is because he's already living in Sweden.

Re:Grigori Perelman, please give us a sign! (3, Funny)

Anonymous Coward | about 8 years ago | (#15917127)

Oh no, not in Sweden! We should send a rescue party before the socialists and insane feminists get to him. He may be taxed to death!

Re:Grigori Perelman, please give us a sign! (2, Insightful)

Anonymous Coward | about 8 years ago | (#15917432)

but at least on the positive side he'll have access to great health-care, low-crime, respectful co-citizens and one of the highest standards of living on the planet

Re:Grigori Perelman, please give us a sign! (1, Insightful)

Anonymous Coward | about 8 years ago | (#15917115)

The USA, instead, is not subject to problems of abuse of the legal system, as the case of Dmitry Sklyarov demonstrated.

Re:Grigori Perelman, please give us a sign! (2, Informative)

ozmanjusri (601766) | about 8 years ago | (#15917444)

We should be quite concerned about Grigori Perelman since he returned to Russia.

Nice bit of jingoistic xenophobia there, but that's about all that's nice about your post.

Gang Tian, who has co-wrote a guide to Perelman's proof, said in 2004: "He certainly has no interest in material things. If he gets the Fields Medal, there is the issue of whether or not he will accept it." He also refused a prize from the European Mathematical Society many years before that.

He is not being threatened, he is simply a person with little interest in material matters.

Re:Square Pegs in Round Holes (0)

Anonymous Coward | about 8 years ago | (#15917131)

hopefully he doesnt turn into another unabomber

Too Many Pages (3, Funny)

tonyr1988 (962108) | about 8 years ago | (#15916787)

Now, mathematicians in the US and elsewhere have finally finished going over his work and have produced several papers, totaling 1000 pages
Someone's going to have to post a printer-friendly on that one.

Re:Too Many Pages (2, Funny)

NotQuiteReal (608241) | about 8 years ago | (#15916896)

Simple - just wave your hands and blather on for a page or so about how obvious the proof is... and in the footnotes reference the 1000 page version.

Trust me, 99.9999% of the folks will never follow the link if your short blather is at all close to an accurite summary.

Re:Too Many Pages (2, Interesting)

G3ckoG33k (647276) | about 8 years ago | (#15917035)

I will wait for the reader-friendly version. Reader's Digest, Simon Singh, Mario Livio where are you all?

I remain skeptical (-1, Troll)

maynard (3337) | about 8 years ago | (#15916796)

1000 pages is a lot of potential for error. Also, Occam's Razor would suggest it to be a ridiculous outcome. If I believed in this I might as well just believe in Santa Clause, the Tooth Fairy, or that crazy man on the moon myth! *shrug* Just let me say, I'm much more partial to the Fields Prize in Philosophy than any esoteric discipline like Mathematics. Sometimes in life, ya just gotta take sides! --M

Re:I remain skeptical (0)

Anonymous Coward | about 8 years ago | (#15916817)

Also, Occam's Razor would suggest it to be a ridiculous outcome. If I believed in this I might as well just believe in Santa Clause, the Tooth Fairy, or that crazy man on the moon myth!

Keep in mind though that some of the easiest problems to solve (in say for instance, graph theory) require multiple steps-- and as is stated in the original post, there's a proof for each step.

So it's not really a 1000 some odd page proof for an entire concept, but a 1000 pages of proof s for each individual component.

Re:I remain skeptical (0, Troll)

maynard (3337) | about 8 years ago | (#15916835)

Yes. But how do you know any one of those steps you've taken is really correct? Whoa. That makes you think twice, doesn't it?

Re:I remain skeptical (0)

Anonymous Coward | about 8 years ago | (#15916842)

Hey dung beetle, it's called peer review. Google it.

Re:I remain skeptical (4, Funny)

maynard (3337) | about 8 years ago | (#15916897)

wait! Don't dung beetles roll their dung into balls? And what does that make it? A sphere! There's some connection here, I swear. Whoa...

Re:I remain skeptical (0)

Anonymous Coward | about 8 years ago | (#15916945)

Actually, they roll the dung of other animals (e.g., large mammals) into balls, which of course are of spherical nature.
Indeed, if you study the field of topology, you would realize that we've proven that you're actually just a morphed ball of elephant dung.

Re:I remain skeptical (1)

althai (992172) | about 8 years ago | (#15917193)

Remember, the proofs that appear in textbooks are very polished, and use many lemmas that were proved earlier. The 1000 page proof includes proofs of all lemmas needed to complete the full proof, and there may be some redundancy as multiple lemmas may have similar proofs. Compare this to the classification of finite simple groups, which is tens of thousands of pages, and known as "the enormous theorem" (although that proof is needfully more complex, as there are many special cases that need to be dealt with).

However, there is definitely some cause for skepticism, as such a long proof is very hard to check, and other similar announcements in the past have had later holes found (such as Andrew Wiles first announcement of the proof of Fermat's Last Theorem, and the above mentions Enormous Theorem.) On the other hand, bost of those proofs have had (in the case of the enormous theorem, probably had) the holes plugged, and I feel confident that if a gap is found in this proof, it will also be bridged.

Re:I remain skeptical (-1, Flamebait)

Anonymous Coward | about 8 years ago | (#15916818)

But then again, you are a fucking idiot, so who really cares what you and your tiny pecker think?

Not I. This is so far beyond your comprehension that attempting to even explain the basics would be like trying
to teach a dung beetle to fly the space shuttle.

Re:I remain skeptical (2, Funny)

tftp (111690) | about 8 years ago | (#15916822)

People who tried to do it on 999 pages or less all failed.

Re:I remain skeptical (4, Insightful)

spuzzzzzzz (807185) | about 8 years ago | (#15917032)

First of all, I highly doubt that all of those 1000 pages are devoted to solving the Poincare Conjecture. Perelman, if I remember correctly, studies Ricci curvature flows which is a large area of mathematics in its own right. In the course of his research, he discovered some things that led to this proof of the Poincare Conjecture. I would expect that the 1000 pages referred to by this article deal with many different consequences of Perelman's work. Mathematicians like to do things in full generality, so they would have studied broader consequences instead of focussing for so long on only one result.

Secondly, I would invite you to write down a complete proof of some well-known mathematical fact, the Stone-Weierstrass [wikipedia.org] theorem say. You must prove this from first principles, starting with axiomatic set theory. I would be very surprised if you even managed to finish and even more surprised if the proof came in at under 1000 pages. This highlights what was mentioned by a sibling of mine: mathematics is divided into small steps and you would never dream of trying to prove something all at once.

Thirdly, this is the first ever proof of the Poincare conjecture. It is quite common in mathematics that a nicer proof of a known fact will be found.

A rabbit is a donut, not a sphere. (4, Insightful)

Vellmont (569020) | about 8 years ago | (#15916799)

What kind of strange rabbits have these topologists seen? The rabbits I've seen have a hole from end to end through them called the digestive tract.

Re:A rabbit is a donut, not a sphere. (2, Funny)

mcc (14761) | about 8 years ago | (#15917030)

What kind of strange rabbits have these topologists seen?

Chocolate ones

Re:A rabbit is a donut, not a sphere. (1)

CubicleView (910143) | about 8 years ago | (#15917337)

It's hardly a redundant if you read all the articles. One of them suggested that rabbits do not have "holes" and could be stretched into a circle without a loss of information. That's wrong on several levels, moral ones for a start. I rather doubt a rabbit is really all that stretchy as well. And anyway, even if they were, as Vellmont quite rightly pointed out, it would be far less futile to attempt to stretch one into a doughnut.

High Mips, Low I/O (1, Insightful)

Anonymous Coward | about 8 years ago | (#15916800)

Most of the freaky genius mathematicians who can do the really wierd stuff are usually (but not always) high MIPS, low I/O types anyway. Spend a week coming up with a partial proof of one percent of a subproof for a much larger problem, no problem. Contemplate going out of the house for bread and milk. See if you can get it delivered, or maybe get someone else to do it (you know, someone you know, someone you won't have to talk to very long...)

a million, a thousand, roundness (4, Funny)

davidwr (791652) | about 8 years ago | (#15916803)

$1,000,000, 1,000 pages, those numbers are apprpriately round for the occasion.

Re:a million, a thousand, roundness (2, Funny)

dabigpaybackski (772131) | about 8 years ago | (#15917583)

You mind proving that?

who cares Fields medal? (1)

helioquake (841463) | about 8 years ago | (#15916809)

If I were known for proving Poincare Conjecture, I wouldn't give a damn to be known as a Fields medal winner. (They'll give it to him anyway, whether he's there personally to receive it.)

Seemed obvious (1, Funny)

Anonymous Coward | about 8 years ago | (#15916814)

Isn't the answer 42?

nytimes is more realistic (2, Informative)

Anonymous Coward | about 8 years ago | (#15916827)

The chinese press distorted the news:
http://news.xinhuanet.com/english/2006-06/04/conte nt_4644754.htm [xinhuanet.com]

Re:nytimes is more realistic (1)

reezle (239894) | about 8 years ago | (#15916982)

That's pretty dang scary.
Did these two guys have ANYTHING to do with solving the proof?

Re:nytimes is more realistic (0)

Anonymous Coward | about 8 years ago | (#15917002)

They did something useful. They rewrote Perelman's notes in such a way that it would be easier for everyone to follow the proof. But nothing really very new.

P.S. Damn... I should really remember to continue to "Post Anonymusly" since I know Cao quite well. ;-)

Hodge Conjecture (1, Interesting)

Anonymous Coward | about 8 years ago | (#15916852)

Talking about 1 million prizes from the Clay Institute, these two people claim they deserve one with 13 pages (>$63k/page)
http://arxiv.org/abs/math.AG/0608265 [arxiv.org]
but of course many of us are a bit suspicious.

Maybe just maybe... (1, Redundant)

Dtyst (790737) | about 8 years ago | (#15916856)

He realized his time is running out and he wants to solve more problems. Maybe he has started solving another problem and dosen't want any outsiders to disturb him. Didn't he do the same with this problem? Maybe that's why no-one can contact him...

How does this relate to string theory? (1)

BlueCoder (223005) | about 8 years ago | (#15916863)

I remember that is was important to string theory, I just don't remember why. I did a search and found nothing. Can anyone elaborate?

Re:How does this relate to string theory? (1)

tftp (111690) | about 8 years ago | (#15916895)

Google is still in business: see here [umich.edu] for example.

Re:How does this relate to string theory? (1, Interesting)

Anonymous Coward | about 8 years ago | (#15916904)

I am in the field, and I am pretty sure that there is no application of this conjecture to any branch of physics at the moment (in particular, for string theory). See also this:
http://www.math.columbia.edu/~woit/wordpress/?p=43 4 [columbia.edu]
(Peter's answer to Cynthia question)

P.S. what is this crap?
"Slashdot requires you to wait between each successful posting of a comment to allow everyone a fair chance at posting a comment.
It's been 10 minutes since you last successfully posted a comment"[...]

Re:How does this relate to string theory? (0)

Anonymous Coward | about 8 years ago | (#15916915)

These days, with the Anthropic Principle and the Landscape, you can make anything relate to string theory. The Poincare Conjecture true. Therefore we must live in a universe w/ constants such that the someone can evolve to prove the Poincare Conjecture. String Theory explains another property of our universe!

Re:How does this relate to string theory? (4, Informative)

S3D (745318) | about 8 years ago | (#15916971)

Google your friend. ANAM (I'm not a matematician), but I'll try.
According to string physicist Lubos Motl [blogspot.com] the proof indeed important to string theory. The proof based on the flow on the manifold (surface), analogous to heat dissipation - Ricci flow [wikipedia.org] . This flow deform metrics (distance between points of the surface). But this process also describe renormalization [wikipedia.org] of worldsheet - how the physics of the worldsheet [wikipedia.org] (surface which string drawing, moving in space and time) change with changing of the observation scale. That is how phisics of string change then the scale of calculation changed.

Re:How does this relate to string theory? (2, Funny)

asifyoucare (302582) | about 8 years ago | (#15917155)

... ANAM (I'm not a matematician) ...

IANAA (I am not an acronymist)

Re:How does this relate to string theory? (5, Interesting)

althai (992172) | about 8 years ago | (#15917269)

I'm not a geometer, but here is my understanding of the proof:

The Ricci Flow [wikipedia.org] was defined by Richard Hamilton in 1981 as a step towards classifying topological compact 3-manifolds. Classifying 3-manifolds would certainly decide The Poincare Conjecture, as it states that all simply connected compact 3-manifolds are homeomorphic to the sphere. This is an important special case: most proofs of the classification of compact 2-manifolds start out by proving the an analogous statement for the 2-sphere. The Ricci Flow is a differential equation which defines how the shape of a manifold changes in time: given an arbitrary manifold M(0), you can apply the differential equation to it to get manifolds M(t) for (some) positive t, which gradually change shape. However, the Ricci Flow is not volume preserving, so you "renormalize" so that M(t) has constant volume.

The Ricci Flow has the useful property that it tends to make manifolds smoother and smoother. For example, if you started out with a lumpy ball, you would eventually get a smooth ball. It was hoped that it could be proved that if the initial manifold was a compact simply connected 3-manifold, then as t increased, the manifold would tend towards a 3-sphere. Unfortunately, while locally solutions to differential equations always exist, they don't necessarily exist for all time, and for some starting manifolds, eventually you would get to a road-block: a t for which M(t) could not be defined. What Perlman (hopefully) showed was that all road-blocks were of certain types, and that a surgery could be formed that would modify the manifold but not it's topological nature, and then you could again apply the Ricci Flow, until the manifold became a sphere.

Note that this method is useful beyond proving the Poincare Conjecture, as it (again, hopefully) describes all road blocks to extending the Ricci Flow, so that the same tools can be applied to any 3-manifold, and not just simply connected ones. In this manner, assuming Perlman made no mistakes (or that any mistakes can be corrected), it is possible to apply the same arguments to prove the Geometrization Conjecture of Thurston, which classifies 3-manifolds.

The tone of the summary is typical (5, Insightful)

blueZ3 (744446) | about 8 years ago | (#15916913)

The incredulity that this mathematician might have been more interested in the challenge of the work than fame and fortune in the Western world practically oozes from each sentence.

I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake? Perhaps he's gone on to other challenges, or he's wrapped up in some research that has his complete attention. Heck, perhaps he just enjoys math for its own sake and doesn't want to deal with all the side-effects of notoriety.

Re:The tone of the summary is typical (1)

maynard (3337) | about 8 years ago | (#15916928)

"I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake?"

Yes.

Re:The tone of the summary is typical (1)

strider44 (650833) | about 8 years ago | (#15917036)

Are you sure it's not just delight rather than incredulousness? Tone is rather hard to pick out with just text so you're assuming a lot in your conclusion...

Re:The tone of the summary is typical (4, Insightful)

smallpaul (65919) | about 8 years ago | (#15917042)

I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake?

It isn't a shock that he did it for its own sake at all. Look at the thousands of open source programmers. The shock is that he's been given a million dollars and seem uninterested. Linus Torvalds does Linux for its own sake but if someone gave him a million dollars, he'd take it. Even someone who is not materialistic might think: "hmmm. A million dollars might help many Russian orphans or deliver AIDS drugs to Africans or ..." It is strange for a single person to be neither greedy, nor ambitious nor altruistic ... merely obsessed.

Yes, that's strange. It's rare and therefore strange.

Re:The tone of the summary is typical (3, Insightful)

aiken_d (127097) | about 8 years ago | (#15917044)

Oddly enough, people tend to form their expectations based on past experiences. Is it so unreasonable for the tone of the article to be incredulous when the situation is unprecedented?

Where you see value judgments and a jaded reporter, I see a pretty reasonable surprise. I don't see anything in the article where the reporter suggests that Perelman "should" do anything other than what he is. Surprise, and remarking on an unusual behavior, is *not* approbation.

-b

Re:The tone of the summary is typical (1)

Threni (635302) | about 8 years ago | (#15917468)

> Is it so unreasonable for the tone of the article to be incredulous when the situation is
> unprecedented?

What's unprecedented? Someone tackling a problem other than for the money? How much money was Wiles' solution to Fermat's problem?

Re:The tone of the summary is typical (1)

greppling (601175) | about 8 years ago | (#15917052)

I'm all for capitalism and the idea of "prizes" to encourage research, but have we really become so jaded that it's a complete shock when someone does something worthwhile merely for its own sake?

Lots of people do things for their own sake (as long as they can pay their bills and get some food). But when someone got a prize of a million dollar as a bonus (for what you enjoyed doing anyway), can you really imagine someone turning this down? Well, Perelman hasn't done this (yet), but lots of people could imagine he will do just that.

Re:The tone of the summary is typical (4, Insightful)

eddy (18759) | about 8 years ago | (#15917061)

I think that never is this more amply examplified than when the people who manage 'rights holders' "explain" how, if it weren't for copyright, there would exist no art.

Maybe he... (2, Funny)

rolandog (834340) | about 8 years ago | (#15917069)

just found a girlfriend? //I keed.

Re:The tone of the summary is typical (5, Insightful)

Thisfox (994296) | about 8 years ago | (#15917087)

Sadly, yes, doing something for it's own sake rather than for monetary gain is frowned apon, and sometimes viewed with fear and confusion, not that I'm saying this review goes THAT far (if you don't believe me, try smiling at someone while in a subway one of these days: the person will generally check that you haven't got someone stealing their wallet while they are distracted. Or busk without a hat out: no one realises that an orchestral musician might just enjoy playing music in the sun in winter, and they search madly for a way to throw a coin into my closed music case). Perhaps he sees the money as a complication rather than a useful item: instead of assuming he could donate it, there would be all the trouble of getting the money into his country, bank balances, taxes, and more questions and papers to fill out to get it donated, and all the rest of it. All of which is time he could have been spending on solving another interesting question, or gathering mushrooms, or whatever. Coming into a fortune is not always fortunate.

Re:The tone of the summary is typical (1)

renoX (11677) | about 8 years ago | (#15917218)

>The incredulity that this mathematician might have been more interested in the challenge of the work than fame and fortune in the Western world practically oozes from each sentence.

That and also while he did the hard work, that he didn't really contribute to the full proof, which is also weird.

TFA is well worth reading (2, Funny)

OldManAndTheC++ (723450) | about 8 years ago | (#15916919)

Quite an interesting character, this Perelman, and his proof could turn out to be a real landmark for mathematics.

I liked this bit:

Asked about Dr. Perelman's pleasures, Dr. Anderson said that he talked a lot about hiking in the woods near St. Petersburg looking for mushrooms.

Whatever he's smoking, I want some!

Re:TFA is well worth reading (3, Insightful)

OldManAndTheC++ (723450) | about 8 years ago | (#15916949)

Side note: the Millenium Prize is a cool million. Which is $24 million less than Adam Sandler makes per movie.

Hurray for the free market! The true value for a personal accomplishment has once again been properly determined and awarded!

Re:TFA is well worth reading (1)

OverlordQ (264228) | about 8 years ago | (#15917134)

Sure he makes $25 million per movie now, but I'm sure he didn't make $1 million for his first movie.

Re:TFA is well worth reading (2, Insightful)

Ibanez (37490) | about 8 years ago | (#15917148)

You know...I think you're trying to be sarcastic, but you shouldn't because you're actually correct.

Want to make a lot of money, do something the generates a lot of money. I can understand your point of view, but get real...

Re:TFA is well worth reading (1, Insightful)

Anonymous Coward | about 8 years ago | (#15917275)

Fair enough -- if making stupid people laugh is considered more important by society than fundamental mathematical discoveries, then it should be more highly compensated. It is. What's your problem with that?

(And BTW mods, how the f*ck is that "insightful" in any way?)

Re:TFA is well worth reading (1)

OldManAndTheC++ (723450) | about 8 years ago | (#15917371)

Fair enough -- if making stupid people laugh is considered more important by society than fundamental mathematical discoveries, then it should be more highly compensated. It is. What's your problem with that?

Simply put, I believe that society is wrong. It is wrong to value the contribution of Adam Sandler as greater than that of Grigori Perelman

One day, probably many years from now, Adam Sandler will be a footnote in some obsolete database, and Perelman will be famous for his contribution to human knowledge. At that point, the relative values of the contributions of Sandler and Perelmen will be clear.

When you take the long view, the opinions of masses of people are worthless. Our social and economic system does not compensate for that failing. It prices things in terms of what people think now. Well most people are wrong, most of the time.

Re:TFA is well worth reading (1)

LucidBeast (601749) | about 8 years ago | (#15917481)

Simply put, I believe that society is wrong. It is wrong to value the contribution of Adam Sandler as greater than that of Grigori Perelma But you have to realize that most of societys concerns are immediate needs. We need food, fuel, sex and something to make the time pass by. These things are valuable because they are needed in huge quantities. Adam Sandler might not be a great comedian, but his skill serves a huge need. Mr. Perelman might be making a great contribution to math and science, which perhaps will solve problems in the future, but in the end his contribution increase need for Adam Sandlers of the future, since most people who benefit from his contribution will have more time to be entertained. There is also a difference between value and monetary value. One could say that Mr. Perelmans contribution goes beyond monetary value, because it is something that most likely money can't buy. Not even million dollar rewards. Mr. Perelman has taken the cat out of the bag and it can't be put back.

Re:TFA is well worth reading (0)

Anonymous Coward | about 8 years ago | (#15917514)

That's trade for you.

What would you propose? Nation building is fun.

You misunderstand free markets (1)

Colin Smith (2679) | about 8 years ago | (#15917505)

From your sarcasm it seems that you have no idea how free markets work... There is no such thing as innate value, the only value that something has is the demand for that thing.

The demand for comedy is higher than the demand for mathematical proofs. The recompense for either has absolutely nothing to do with merit, even if you believe a mathematical proof has more innate merit than comedy. BTW, if you do believe that, please define for us exactly how a mathematical proof is better (has more value or merit) than comedy.

 

Re:TFA is well worth reading (1)

Hal_Porter (817932) | about 8 years ago | (#15917550)

Adam Sandler movies are completely generic, I think we can agree on that.

Now if you compare the average box office take of a generic movie without Adam Sandler and one with him, it's plausible that the difference is more than $25 million. So putting him in a movie may be worth $25 million to the studio.

Whereas these maths prizes are based on some trust fund set up by a rich philanthropist. The economics are completely different. No matter how much money they give away, the prize will still be a success. Also for an unwordly person $1 million is probably just as good as $24 million. Both mean that you can concentrate on work without having to worry about looking for funding for the rest of your life.

Anyhow, you can't prove that solving the Poincare conjecture is absolutely more valuable (in any sense) that making a movie, even a bad one.

Re:TFA is well worth reading (1)

Hal_Porter (817932) | about 8 years ago | (#15917581)

Actually, another argument occured to me.

You could argue that Mozart is 'better' than say Britney Spears because people still listen to Mozart after 200 years, whereas Ms Spears will no doubt be forgotten, and that has some merit. But since most of the popularity of Mozart happened sufficiently long after his death that an investor payoff was unlikely, that doesn't mean that it was rational to invest in his music over the contemporary equivalent of Britney, even if you were one of the few people that understood it immediatly. Listen to it maybe, but investing in it is a bad choice.

So almost by definition truely great works of art will always be underfunded compared to ones which are very popular in the short term, but forgotten in the long term.

Incidentally, one way to fix this economically would be to make copyright perpetual since that would mean that investors, or at least their descendents, would be able to be compensated for recognising genius before eveyone else did.

Re:TFA is well worth reading (1)

dosun88888 (265953) | about 8 years ago | (#15917592)

More people understand Adam Sandler.

Re:TFA is well worth reading (1)

a_ghostwheel (699776) | about 8 years ago | (#15916956)

Here [maps.org] you go :)

Re:TFA is well worth reading (1)

gradedcheese (173758) | about 8 years ago | (#15916963)

Well, huntung for mushrooms is a pretty normal activity in Russia.

Re:TFA is well worth reading (1)

Temposs (787432) | about 8 years ago | (#15916976)

Actually, this going on outtings to find mushrooms is something I'm not surprised by. I have a friend from Russia who tells me stories of his father and a friend taking a long train trip to some wilderness with a couple of huge baskets, and their sole purpose in taking the trip was to collect mushrooms. I believe these are for normal food consumption. Evidently Russia has a good mushroom environment.

Re:TFA is well worth reading (5, Interesting)

Bigos (857389) | about 8 years ago | (#15917151)

In Eastern Europe we don't pick up mushrooms to get narcotic high. It is merely a popular ingredient in our cuisine. The guy got his priorities right. No matter how rich and famous you are, in the West you cant get exactly the same ingredients for East European food. As mushrooms based meals are so delicious, I wouldn't be bothered to travel somewhere to get some stupid price when there is high season for mushrooms.

Re:TFA is well worth reading (0)

Anonymous Coward | about 8 years ago | (#15917267)

In Eastern Europe we don't pick up mushrooms to get narcotic high.

Erm... sure you do, maybe you don't. And in Western Europe we don't exclusively pick psychedelic mushrooms, believe it or not.

And by the way, the mushrooms we are talking about are psychedelic, not narcotic. Big difference :)

Re:TFA is well worth reading (0)

Anonymous Coward | about 8 years ago | (#15917333)

He's not smoking anything. Why do you think he's looking for mushrooms?

Re:TFA is well worth reading (1)

Hitman_Frost (798840) | about 8 years ago | (#15917697)

Eastern Europeans and Russians frequently pick wild mushrooms for fun (and to eat), given that when they are children their parents *explain* which mushrooms are safe to pick, which ones are poisonous, and which ones are easy to confuse with other species and not to pick unless you're really sure.

Compare that to my UK upbringing where all children were warned from the youngest age *never* to pick any wild mushrooms as "you'll probably just poison yourself" and that "even experts can pick the wrong ones sometimes" (must be pretty feeble experts then!). My Polish girlfriend was equally bemused and appalled (as she is by most of these situations in cultural matters) when I recounted to her the differences in Western child raising techniques...

$1,000,000? That's nothing... (0, Offtopic)

1053r (903458) | about 8 years ago | (#15916922)

I can get $1,000,000 by answering 15 questions on "Who wants to be a millionare", or even better yet, by giving money to some poor nigerian who can transfer vast sums of money into my account :)

(Am I the only one who read the title "Porncare conjecture proof completed"?)

Re:$1,000,000? That's nothing... (1)

mathcam (937122) | about 8 years ago | (#15917478)

Well, he did it *one* question, so I guee he wins. :)

Re:$1,000,000? That's nothing... (1)

LiquidCoooled (634315) | about 8 years ago | (#15917588)

It wouldn't exactly make thrilling tv though:

Which of these is the proof of the Poincare conjecture?

a) a fruit

b) a small amazonian tree frog

c) The n==1 case of the generalized conjecture is trivial, the n==2 case is classical (and was known to 19th century mathematicians), n==3 (the original conjecture) appears to have been proved by recent work by G. Perelman (although the proof has not yet been fully verified),

.....1000 pages and several hours later....

n==4 was proved by Freedman (1982) (for which he was awarded the 1986 Fields medal), n==5 was demonstrated by Zeeman (1961), n==6 was established by Stallings (1962), and n>=7 was shown by Smale in 1961 (although Smale subsequently extended his proof to include all n>=5).

d) something we made up

Recognition = Worry (3, Insightful)

BoRegardless (721219) | about 8 years ago | (#15916925)

"Perelman now seems to be the favorite to receive a Fields Medal at the International Mathematics Union meeting next week, but it's not clear that he'll even show up!"

The curse of the gifted is that niggling worry in the back of the mind that if one accepts praise, one may lose his focus, drive or muse, if you will.

Technical comments? (-1, Offtopic)

Cybert4 (994278) | about 8 years ago | (#15916987)

Well I didn't expect any. I guess this is the wrong place. I've decided to learn "the basics" of all aspects of math, physics, and technology. Looking into this, I've discovered manifolds--something I'll look into more. Maybe it'll be as cool as complex numbers!

The prize is important (2, Insightful)

ucaledek (887701) | about 8 years ago | (#15917017)

I think the greatness of the prize isn't the mercenary value people seem to think it holds. The money just shows importance. The prize's value comes from the dialogue and new paths of discovery that are opened up. Remember that in the end Fermat's last theorem (proof of which is what prompted this, at least in part) wasn't important in its result. It was important because the search for a proof resulted in huge new areas of research that are much more fruitful both in the purely abstract mathematical sense and in the practical sense. The fruits of that labor wouldn't have come out without placing such emphasis on the problem. Hilbert's lecture at the beginning of the 20th century was similar. Here was (one of the best minds at the time propising a framework in which to work, goals to look towards. Not even close to all of them have been resolved, but they are smart problems that have led to all sorts of applications and results. It's a goal to work towards. The Clay prize does the same thing. Is the Navier Stokes problem that important? Yes, that's why we have this great initiative for a derivation of classic and not weak solutions, or at least existence. The quest for the solution to the problems and those like it have created real progress. Without this kind of framework, we'd possibly not have the amazing work in PDEs and weak solutions that let us do great composite designs and image processing (to name two areas).

name change? (5, Insightful)

bark (582535) | about 8 years ago | (#15917021)

Now that the conjecture is proved, do they change the name to "theory"? Or does the name stay put because that's what everyone knows and refers to it as?

Re:name change? (1)

Starker_Kull (896770) | about 8 years ago | (#15917071)

In all probability, once it has been vetted and accepted, it will be called a theorEM. Theories are for the inductive sciences. Little nitpick, sorry.

Re:name change? (4, Informative)

Kjella (173770) | about 8 years ago | (#15917320)

Now that the conjecture is proved, do they change the name to "theory"? Or does the name stay put because that's what everyone knows and refers to it as?

Things that are proven, are called theorems. They do depend on axioms, but those are defined as true. Sciences about the real world that can't put up axioms (because that'd require ex facto knowledge about the real world), so they can never be conclusively "proven". Hence well call them theories, like theory of gravity, theory of evolution. A few we've called "laws" as well because they have been so extensively tested, but it is not proven in a strict formal sense.

Ellipse in Highschool (-1, Offtopic)

Kuvter (882697) | about 8 years ago | (#15917050)

In high school I found a quicker way to solve for the area of an ellipse. My teacher checked for 2 weeks to see if there was a quicker way then the one he taught in class, with no luck. 2 weeks later, through the help of my friend I finally explained how and why the formula worked.

Though out that month of time we tested the formula many times and found no conjecture. The teacher told me I could probably get the formula published.

2 week later I completely forgot the formula. Some days I wonder if I could come up with the formula again. I think somehow this relates my actions to Perelman, but on a smaller scale.

Re:Ellipse in Highschool (1)

Kuvter (882697) | about 8 years ago | (#15917104)

Correction it was the circumference not area

Re:Ellipse in Highschool (1)

PatrickThomson (712694) | about 8 years ago | (#15917391)

That's like reading fermat's margin note ... just frustrating.

Re:Ellipse in Highschool (0)

Anonymous Coward | about 8 years ago | (#15917607)

'Frustrating' as in 'outright lying' I hope.
Oh yeah we invented a new method of doing something and we did it for weeks but we forget it now.
Add it to the cold fusion and cloned human pile and fuck off.

Ob Simpson Quote (1)

EuroChild (523969) | about 8 years ago | (#15917095)

Mathematician: "Now watch as I make this remainder diiisaaappearrr"
Lisa: "But seven goes into twenty-eight four times"
Mathematician: "Uh... this is a magic seven"

tifue (-1, Offtopic)

xiaobi (994111) | about 8 years ago | (#15917268)

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1000 pages?! (1)

elFisico (877213) | about 8 years ago | (#15917306)

I don't think there will be a T-shirt with that proof anytime soon... :o)

Math is Art (0)

Anonymous Coward | about 8 years ago | (#15917326)

Did Picasso appreciate his work? Probably not...at least not as much as others do. Sure it was a great challenge, but math is like magic once you know how to get the answer...all the mystery is gone.

-ac

One page (0)

Anonymous Coward | about 8 years ago | (#15917378)

My proof is only 1 page long, but its a really BIG page.

Has anyone read the actual article? (5, Informative)

Anonymous Coward | about 8 years ago | (#15917390)

If any of you had read the article you would have noticed that the 1000 pages is actually a very rough figure for the sum page count of all 3 articles by various people each of which explains Perelmans result in context, thus duplicating the other 2. So in fact the full articles are about 315-470 pages each. Also what Perelman infact did was show that using the Ricci Flow technique on the 3D shapes to solve the Poincare conjecture, an idea of Hamilton's from the 80's, can work. Up till now it was thought that certain structures might degenerate to singularities and fail, but Perelman showed that those singularities would in fact all turn out ok. Poincare's conjecture is for 3D shapes, and higher dimensional generalisations have previously been solved (5+ dim by Smale in 60's, 4 dim by Freedman in 80's, both got Field's medals).

Practical consequences of the proof? (1)

master_p (608214) | about 8 years ago | (#15917411)

It is said that the Poincare Conjecture proof is one of the most important proofs in Mathematics. But I never managed to understand why. What are the practical consequences of this proof? does it have any real-world applications?

He's turned down the money (5, Interesting)

ed_g2s (598342) | about 8 years ago | (#15917447)

According to The Guardian [guardian.co.uk]

After reading TFA . . . (1)

Don_dumb (927108) | about 8 years ago | (#15917462)

I understand
[/lie]

Fields Medal (1)

notjim (879031) | about 8 years ago | (#15917543)

So the other person being tipped is Terrence Tao, anyone else?
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