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The Almighty Buck Science

Russian May Have Solved Poincare Conjecture 527

Posted by timothy
from the he-said-to-forward-the-prize-money-to-me dept.
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.
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Russian May Have Solved Poincare Conjecture

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

    by SYFer (617415) <syfer&syfer,net> on Monday September 06, 2004 @08:55PM (#10172924) Homepage
    True math genius and the desire for money (and fame and babes, etc.) seem to be mutually exclusive traits and I think that's rather inspiring (and damned practical).

    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 /. come form "anonymous cowards" sitting in their offices at MIT. What a god.

    • by Stevyn (691306) on Monday September 06, 2004 @08:59PM (#10172961)
      It makes sense. Anyone that brilliant would see how pointless it is to worry about money. When will the rest of us learn? There's more to life than money.

      Yeah, it's broadband.
      • Re:He'd post AC (Score:5, Insightful)

        by Anonymous Coward on Monday September 06, 2004 @09:16PM (#10173074)
        This observation of Stevyn and the answer to his question "When will the rest of us learn?" is well explained by Maslow's heirarchy of needs [wikipedia.org]. The was Maslow would havd put it is that this guy and other brillian people are 'self actualized' "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.

        • by Anonymous Coward on Monday September 06, 2004 @09:28PM (#10173152)
          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)

          by Tony-A (29931)
          One thing I've learned is that if I can stand to live with myself, if I like myself, nothing else really makes that much difference.
          "A musician must make music." I'd strike the "If ...". It's essential, but probably has little to do with being at peace with oneself. In fact, the drive toward getting it right is very much not being at peace with oneself.

          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)

          What's often overlooked in Maslow's heirarchy of needs is the fact that it is a heirarchy. In other words, it's all well and good to be self-actualized, but you need to have your rent and food bills covered first . You can't just skip from "poor starving genius huddled in an alley scrawling your brilliance in feces on the walls" to "self-actualized."
      • Re:He'd post AC (Score:4, Insightful)

        by Paradise Pete (33184) on Monday September 06, 2004 @09:17PM (#10173085) Journal
        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)

          by Waffle Iron (339739) on Monday September 06, 2004 @09:38PM (#10173202)
          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:2, Insightful)

          by Stevyn (691306)
          I appologize, my comment was mistaken.

          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)

          I'm confused, you're clueful enough to realize money (in it's ideal form) is an abstract of work/effort... but you fail to see what it is in it's more corrupt actual form.

          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)

              by johnnyb (4816) <jonathan@bartlettpublishing.com> on Tuesday September 07, 2004 @12:51PM (#10178431) Homepage
              I think what he was saying was that the ONLY way money comes into circulation is through loans. Therefore, although some can pay back there loans, it is physically impossible for the entire country to ever pay back their loans, because not only are we responsible to pay back the loans, but we also have to pay back interest! But the banks only created enough money for the _principle_ of the loan, not for the interest. So, while you and me can pay back our individual loans, it is physically impossible for the whole country to pay off its debt, because the money supply would be gone, and there would be nothing left to pay with.

              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.
        • Erm, perhaps you missed the joke? GP said "there's more to life than money... it's broadband"
        • Re:He'd post AC (Score:3, Informative)

          by NonSequor (230139)
          If we weren't talking about Erdos, I'd agree with you. The thing about him, is that he wasn't just a great mathematician, he was a great collaborator. In addition to that he was generally good natured and his many quirks were (mostly) endearing. He brought out the best in the people he worked with. Erdos didn't need money because he was held in such high esteem that he could go anywhere and people would be willing to pay for his meals and give him a place to sleep just for the opportunity to work with him.
        • Re:He'd post AC (Score:3, Insightful)

          by CaptainCheese (724779)
          The thing about pure mathmatics is, it's a pastime that essentially costs 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
      • What would be nice I think would be if he is not interested in the money at all, then he could still take the money anyway and donate it to a charity.

        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)

        by SYFer (617415) <syfer&syfer,net> on Monday September 06, 2004 @09:50PM (#10173253) Homepage
        We don't need to "learn" from this, really. it's perfectly OK in our society to take pride in our achievements and to try to gain from them. Unless you're truly self-actualized (as another poster astutely pointed out), we're all subject to certain realities and desires. After all, monetary reward can enhance your ability to do more good. As Hunter S. Thompson once said, "feed the body or the head will die." There's no shame in that. I find it interesting though, that some artists and scientists seem to exist on another plane altogether.
        • Re:He'd post AC (Score:5, Insightful)

          by Stevyn (691306) on Monday September 06, 2004 @09:57PM (#10173290)
          You're completely correct; I think my comment was mistaken. Without the reward of money at the end of the tunnel, I probably wouldn't be in school now working towards a goal. There is no shame in working for money because it represents a reward for an invaluable effort.

          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)

            by KjetilK (186133)
            That's an interesting comment. I find no motivation in money at all, and I did go to University for close to 9 years...

            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

          • If you're a math geek, you'll do things that let you sit down and work on problems.

            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
          • by kahei (466208) on Tuesday September 07, 2004 @04:48AM (#10175226) Homepage
            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.

      • by spektr (466069) on Monday September 06, 2004 @09:51PM (#10173265)
        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)

        by Lord Kano (13027)
        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)

      by k98sven (324383) on Monday September 06, 2004 @09:12PM (#10173048) Journal
      Well.. I think it's kind of a general thing for all good Science too.

      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)

        by tlord (703093)
        Actually, the title:

        "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)

        by mbw314 (609450) on Monday September 06, 2004 @10:26PM (#10173454)
        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.
    • oh well.. he wouldn't care to post here, I guess. There are more interesting things around to do, for a methamatical genius, than to hang around with nerds. (btw, I love his books)
    • perhaps true math genius is, as you mention, an exclusive trait from womanizing and acquisition mentality..

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

    • 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.
  • by poofyhairguy82 (635386) on Monday September 06, 2004 @09:01PM (#10172967) Journal
    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)

    by hunterx11 (778171) <`hunterx11' `at' `gmail.com'> on Monday September 06, 2004 @09:03PM (#10172982) Homepage Journal
    1,000,000 USD is about equal to 560,000 GBP, not 5.6 million GBP.
  • by Anonymous Coward on Monday September 06, 2004 @09:04PM (#10172988)
    He's trying to integrate homeomorphic convergence using a Baxter-Bates supermodality, which Krause clearly explained is impossible for T(s) in a non-linear progression. Fantastic thought process on this complex differential geometric problem.

    Just kidding! I have no clue what the hell this is. I got lost after the word conjecture.
  • Damn... (Score:5, Funny)

    by Overzeetop (214511) on Monday September 06, 2004 @09:05PM (#10172997) Journal
    I read all the links, and I'm pretty sure they were all in english, but I didn't understand a word of it. No wonder all the mathematicians are nuts.

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

  • Yes but... (Score:5, Funny)

    by gbulmash (688770) * <semi_famous@yaho ... m minus math_god> on Monday September 06, 2004 @09:06PM (#10173003) Homepage Journal
    His answer to the problem was "42".

    - Greg
    • by dynayellow (106690) on Monday September 06, 2004 @09:07PM (#10173015)
      Makes sense, as I have no idea what the question is.
      • Re:Yes but... (Score:5, Informative)

        by Anonymous Coward on Monday September 06, 2004 @09:22PM (#10173122)
        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...
    • Aw, I was going to guess that!
  • $1 million USD? (Score:5, Informative)

    by Anonymous Coward on Monday September 06, 2004 @09:06PM (#10173007)
    From the article:

    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.
  • by Neo-Rio-101 (700494) on Monday September 06, 2004 @09:07PM (#10173013)
    Whocarés Conjecture If we stretch a g-string around the surface of somebody's buttocks, 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 g-string has somehow been stretched in the appropriate direction around someone's face, then there is no way of shrinking it to a point without breaking either the g-string or suffocating the person. We say the surface of the buttocks are "simply connected," but that the surface of the person's face is not. Whocares knew almost hundred years ago, knew that a well shaped pair of cheeks is essentially characterized by this property of simple connectivity, and asked the corresponding question for the rest fo the people still reading this, as to why they were doing so. This question turned out to be extraordinarily difficult, and slashdotters have been struggling with it ever since.
    • Therefor a butt is not simply connected.

      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.

  • by jm91509 (161085) on Monday September 06, 2004 @09:11PM (#10173038) Homepage
    According to the Guardian [guardian.co.uk] another clever Maths dude has proposed a solution to another of the 7 "million dollar" problems.

    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.)

    • by Anonymous Coward on Monday September 06, 2004 @09:26PM (#10173136)
      That's a great link, with a wonderful human-readable summary of the 7 problems.

      For those too lazy to click:

      Seven baffling pillars of wisdom

      1 Birch and Swinnerton-Dyer conjecture Euclid geometry for the 21st century, involving things called abelian points and zeta functions and both finite and infinite answers to algebraic equations

      2 Poincar&#233; conjecture The surface of an apple is simply connected. But the surface of a doughnut is not. How do you start from the idea of simple connectivity and then characterise space in three dimensions?

      3 Navier-Stokes equation The answers to wave and breeze turbulence lie somewhere in the solutions to these equations

      4 P vs NP problem Some problems are just too big: you can quickly check if an answer is right, but it might take the lifetime of a universe to solve it from scratch. Can you prove which questions are truly hard, which not?

      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?

      6 Hodge conjecture At the frontier of algebra and geometry, involving the technical problems of building shapes by "gluing" geometric blocks together

      7 Yang-Mills and Mass gap A problem that involves quantum mechanics and elementary particles. Physicists know it, computers have simulated it but nobody has found a theory to explain it
    • The purported proof of the Riemann conjecture was reported and discussed in June 2004 here on slashdot [slashdot.org]. Incidentally the comments contain what I feel is the funniest math-related lines I've ever heard: Riemann-chu, I prove you! [slashdot.org] (credit to foidulus [slashdot.org]).
    • Not really. There are already a lot of people who believe that the RH is likely to be true.

      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
  • by shadowmatter (734276) on Monday September 06, 2004 @09:17PM (#10173087)
    Since a great deal of discussion and awe comes up anytime one of the millenium problems is mentioned (solved?) on Slashdot, I'd just like to say that any layman interested in learning more about the millenium problems should run to his/her library/bookstore and pick up The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time [amazon.com]. Although, perhaps, for the layman, the end may become a bit tricky (the problems are explained simply in order of increasing difficulty), it's a book worth sticking with, and ultimately worth a read.

    - sm

  • by Brento (26177) * <brento.brentozar@com> on Monday September 06, 2004 @09:19PM (#10173104) Homepage
    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.
  • ...we must not have a poincare conjecture gap!
  • by DeepRedux (601768) on Monday September 06, 2004 @09:25PM (#10173132)
    A few months ago Louis de Branges published his proof of the Riemann Hypothesis [purdue.edu] on the internet. This is also a Millennium problem. Apparently, no mathematician has read it [lrb.co.uk].

    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.

    • by agentpi (787696) on Monday September 06, 2004 @11:37PM (#10173899)
      I go to Purdue, and de Branges is unable to explain himself at all. He has attempted to explain his process to other professors at a seminar here, and has only confused them. He also kicked first year grad students out of his seminar, stating they were to inexperienced. From these grad students, I have learned that he is pretty much and hotshot and an asshole. I'm thinking about going to his seminar on wednesday just to see how long it takes him to kick me out. (I'm a first year undergraduate). A note about his proof of the Bieberbach Conjecture. While de Branges did prove the conjecture, he overcomplicated it, as he does many things, and everybody and their thesis advisor has simplified his proof in some way. Mathworld really discredits his "proof" for one, it contains no proof, and his method was proven flawed by counterexample in 1998.
  • by HoldmyCauls (239328) on Monday September 06, 2004 @09:28PM (#10173151) Journal
    Solving a Millenium Problem carries a reward of $1M, but apparently Perelman isn't interested...
    He does realize that's as good as *money*, right???
    • by TheLink (130905) on Monday September 06, 2004 @10:47PM (#10173617) Journal
      He was working on "A special theory on winning a million dollars with math". Being a real mathematician since he has proven to himself he can get the reward, he is satisfied.

      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).
  • by Anonymous Coward
    I'm tired of seeing these 'please make me famous even though I didn't really prove it' threads. The little boy has cried wolf too many times. We don't care unless it's really solved.

    Editors, I'm talking to you.
  • Racist title (Score:4, Insightful)

    by Fjornir (516960) on Monday September 06, 2004 @09:46PM (#10173233)
    I can't believe slashdot would run a story with that title. "Perelman May Have Solved Poincare Conjecture" would have been much more dignified. You would never see "Muppet May Have Solved Poincare Conjecture" would you? Please, Perelman is a mathematician first, Russian second.
    • by Anonymous Coward
      Oh, good, now Russians are Muppets. You've helped.
    • I don't see where there's a problem. The guy lives in Russia, right? You know, people go to work (non-tech people let's say, defnintely not slashdot-fodder), and gather around the watercooler and say "Hey, did you hear about that Russian guy who solved that math thing?".

      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
  • Wow! Someone finally solved the paincare conjecture... wait, didn't morphine do that? and the Christian Scientists [wikipedia.org]?

    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...

  • by etheriel (620275) on Monday September 06, 2004 @10:15PM (#10173384)
    Why doesn't this article's title read:

    "Grigori Perelman May 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...

    • Russian mathematicians are a special breed. If you ever do any original mathematical research, especially a high powered area like analysis, the chances are some Russian did it in the 60s.

      I suspect it's the long winters.
  • Interesting View (Score:2, Interesting)

    by a3217055 (768293)
    This is all very interesting and I like the way Perelman has gone about working out this whole genius and fame, and money. I wonder what if movie stars ever found out or the RIAA or the music industry, they might license him. Interestingly there was also a breakthrough in the Riemann Hypothesis, I wonder if anyone has ever heard of Louis de Branges de Bourcia at Purdue and his paper on the Riemann Hypothesis [purdue.edu]. The person who posted the news article did not tell use what Poincaré Conjecture is? Well
  • by NimNar (744239) on Monday September 06, 2004 @10:30PM (#10173480)
    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.

    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.
    • by doublegauss (223543) on Tuesday September 07, 2004 @02:47AM (#10174798)
      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.

  • Does anyone remember the book "Mathematics can be fun" maybe published some 40 years ago
    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)

    by r2q2 (50527) <zitterbewegung@gm[ ].com ['ail' in gap]> on Monday September 06, 2004 @11:10PM (#10173740) Homepage
    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...
  • by Eric119 (797949) <eric41293@comcast.net> on Monday September 06, 2004 @11:32PM (#10173877) Journal
    In Soviet Russia...

    they prove conjectures.
  • by JohnPM (163131) on Tuesday September 07, 2004 @03:40AM (#10175017) Homepage
    I've solved it:

    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: NO it doesn't mean it's true for all of them. You would have to prove that.

    Where do I get my money?
  • by grumbel (592662) <grumbel@gmx.de> on Tuesday September 07, 2004 @06:55AM (#10175564) Homepage
    One thing I don't get is why isn't there some software out there to verify the proofs? I mean math follows rules and these rules should be convertable into a piece of software, shouldn't they? So why do I always read that somebody might have proofed this and that, yet nobody has yet verified it and often there are even just a few people with enough knowledge to verify the proof at all so it takes quite some time until a proof get verified.

    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)

    by njj (133128) on Tuesday September 07, 2004 @07:52AM (#10175748)
    I'll try and explain what the Conjecture is, because it's not entirely obvious. First of all, I need to explain what the 3-sphere is.

    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 surface of 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 the intrinsic dimension of the object, rather than the extrinsic dimension 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

    Any homotopy 3-sphere is homeomorphic to the 3-sphere

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

    Any closed, compact, simply-connected 3-manifold is homeomorphic to the 3-sphere

    What does this mean?

    Well, an `n-manifold' is a space which locally looks 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 that means is that any closed loop (of string, if you like), in the manifold, can be continuously shrunk 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

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