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Grigory Perelman and the Poincare Conjecture 241

Posted by kdawson
from the another-tortured-genius dept.
EagleHasLanded writes "Russian mathematician Grigory Perelman doesn't talk to journalists. Actually, he doesn't talk to anyone anymore. So we'll have to settle for insights via his biographer, Masha Gessen, who, strangely enough, has never talked to him either. But she has spoken with just about everyone who has ever had any significant interaction with Perelman, and the result is the book Perfect Rigor, which more than adequately explains why Perelman has gone into self-imposed exile, and why he probably won't collect the million dollars he won by solving the Poincare Conjecture."
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Grigory Perelman and the Poincare Conjecture

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  • by jonnat (1168035) on Sunday December 20, 2009 @07:44PM (#30507632)
    Sylvia Nasar, also the author of "A Beautiful Mind", wrote a great piece [newyorker.com] about Perelman shortly after the publication of his proof. Deeply moving, in my opinion.
  • by macraig (621737) <mark...a...craig@@@gmail...com> on Sunday December 20, 2009 @08:14PM (#30507774)

    There seems little doubt, based on this interview with the biographer, that he is indeed firmly entrenched somewhere on the higher end of the autistic Spectrum.

    I feel a stronger connection with people like Perelman than the vast majority of my alleged peers, though still not an emotional one. People like Perelman have a more instinctive grasp of ethics than any neurotypical types. Another rather well-known person who I would consider very similar (if just a bit more social) is Craig Newmark, of Craigslist.org fame. Wired Magazine had what I thought was a very telling article [wired.com] about Newmark and his Aspie "eccentricities".

    Eccentricities or not, if the rest of the world were to (voluntarily) take lessons from the ethics of those two men, the Earth would be a dramatically different place, indeed.

  • Mathematicians (Score:2, Interesting)

    by Guido del Confuso (80037) on Sunday December 20, 2009 @08:26PM (#30507816)

    Perelman has a mind that is capable of taking in more information than any mathematical mind that has come before. His brain is like a universal math compactor. He grasps complex problems and reduces them to their solvable essence. The problem is that he expects human beings to be similarly subject to reduction.

    This is a universal affliction among mathematicians I've known. They tend to look at the world mathematically, and aren't really able to understand things they can't reduce to an equation. This leads to a very black and white view of the world, where things must be a certain way, and anything that doesn't fall into that worldview is just wrong. Everything that people do must have a rational reason, and if they can't find one they will construct a reason that seems rational to them--regardless of how simplistic it is, or how dim a view of their fellow human beings it leads them to.

    Mathematicians, by and large, tend to be very unhappy people in my experience. Not all of them, of course. Some mathematicians have a certain "spark" that allows them to abandon mathematics temporarily and give themselves over to the pleasure of an interpersonal relationship; but even so it is still against their nature to do so, and they will always slip back into the comfort of a mathematical outlook sooner or later.

    I suspect that extraordinary skill in mathematics is not the cause of such a personality, but rather they are both common effects of some psychological variation that simply causes such people to perceive the world in a particular way.

  • by macraig (621737) <mark...a...craig@@@gmail...com> on Sunday December 20, 2009 @08:48PM (#30507914)

    You have a lot to learn, then, my young Padawan. It was the context in which he refused it that was significant.

  • Re:Mathematicians (Score:5, Interesting)

    by Pixie_From_Hell (768789) on Sunday December 20, 2009 @08:54PM (#30507942)

    I'm a mathematician, and I'm afraid I really don't know what you're talking about.

    Mathematics is often pictured as a very isolated practice -- a person sitting alone at a desk. But it's surprisingly social, and while there is a fair amount of desk time, there's a lot of interpersonal relationships (as you put it) in the actual doing of math. Asking questions, explaining your results, mentoring students, even teaching classes -- a lot of math involves other people.

    Anyway, I know lots of mathematicians, and I think generally they're pretty happy people.

  • by jjohnson (62583) on Sunday December 20, 2009 @09:04PM (#30507988) Homepage

    Well, I did RTFA. His view that the commercialization of math is somehow wrong, that money is an offensive form of compensation for mathematical success, is idiosyncratic but not especially insightful ethically (if it's not outright mistaken); I wouldn't call it genius of moral philosophy. People will study and try to understand his proof, regardless of whether or not he takes a position teaching it; there's even a good argument to be made that he, the one person who clearly understands his proof, could do much good by accepting a position at a prestigious university because then he can help others to study and understand it.

    I'm not saying he's a bad person. I'm saying his position on money and math is very narrow and eccentric. I don't see how this corresponds to ethical genius. You clearly do. Please explain it to me.

  • by guacamole (24270) on Sunday December 20, 2009 @09:12PM (#30508022)
  • by Kjella (173770) on Sunday December 20, 2009 @09:18PM (#30508046) Homepage

    Lots of people refuse to give public interviews yet don't end up with stories like this. He's turned down a major prize and a million dollars, meaning he doesn't want recognition or money. It's one thing to not talk to journalists or a big conference, but if you're not talking to anyone you have and will develop major issues. All it'd take to dismiss this is for some good friends and colleagues to come forward and say he's a nice guy who doesn't want attention and would like to keep his personal life private, so thanks but no thanks.

    Instead, he really does sound like the kind of obsessive shut-in who isn't coping very well with the world not working like mathematics. I remember seeing a TV show about people with heavy OCDs, it was quite amazing how stuck they could be because they couldn't decide or needed perfection or just spent all day going through rituals to the point of doing nothing else. This might be one of those persons that in a very few ways are not just functional but exceptional while otherwise just like them. I'm not saying there's proof to say that, just that I believe it to be possible.

  • Re:Logic (Score:5, Interesting)

    by selven (1556643) on Sunday December 20, 2009 @09:19PM (#30508048)

    Want not to read = you have a desire to leave the book unread
    Not want to read = you don't have a desire to read the book

    So if you're feeling neutral about the whole thing, the second one fits but not the first.

  • by macraig (621737) <mark...a...craig@@@gmail...com> on Sunday December 20, 2009 @09:57PM (#30508234)

    Just in that limited context that you mention, that could seem plausible, but the larger context of his life screams otherwise: his limited social engagement, his obsession with both math and music, his social and moral rigidity, his inability to adapt... those are all trademark clues. It's the sum of his behaviors that gives it away, not any one of them taken singularly.

    Another person I'd suggest is a close parallel: John Draper, aka Cap'n Crunch.

  • Re:Maybe .... (Score:3, Interesting)

    by iluvcapra (782887) on Sunday December 20, 2009 @10:09PM (#30508302)
    Because he didn't have a good agent... And he is motivated by a self-destructive personal ethics, as opposed to Garbo, who didn't want to be alone as much as she simply wanted to be let alone, and pursued seclusion as a conscious strategy to maintain a certain lifestyle. As the TFA states, he got offers from all over the world to be paid handsomely to teach and do maths, but he rejected them all, because he thinks getting paid to do work is some sort of prostitution.
  • Humankind Cares (Score:4, Interesting)

    by reporter (666905) on Sunday December 20, 2009 @10:39PM (#30508456) Homepage
    Eccentric people are people who think in ways that are not constrained by societal norms. Such people are the source of geniuses who, unconstrained by conventional thinking, discover breakthrough technology or scientific principles that ultimately improve the human condition.

    Albert Einstein is the most well-known example of an eccentric genius. Grigory Perelman is another example. So is Claude Shannon, the "father" of communications theory.

    Yet another example will likely be Burkhard Heim [newscientist.com]. He formulated the mathematics for warp-drive, and the Department of Defense is actively studying his work in an attempt to build a prototype of a warp-drive engine.

  • Re:Maybe .... (Score:5, Interesting)

    by Anonymous Coward on Sunday December 20, 2009 @10:40PM (#30508466)

    Because the field of mathematics has too many toxic personalities (such as the Chinese maths guy who tried to defraud Perelman of credit) and because the maths should be an object of beauty in itself, the personalities who uncover it are merely the instruments by which the maths is revealed. If you go to a museum, do you look with amazement at the ancient works of wonder, or do you look at the collection of 1920s trowels? If you are willing to accept that a modern digging tool is nothing compared to what the tool has discovered, then accept Perelman's view that he is nothing compared to the discoveries he has made.

    Having said all that, it's b* obvious to anyone with half a brain that Perelman is showing classic signs of Geek Syndrome (Asperger's Syndrome). Personally, I'd suggest he goes to a Buddhist monastary in another country, as meditation alters brain chemistry to reduce the feelings of stress and anxiety. It would also likely be much healthier than living in an environment as chemically polluted as Russia. It'll also keep his brain reasonably agile, should he ever decide to return to maths.

    Probably the worst thing he could do is nothing. Sir Conan Doyle's view of a stagnant mind designed to work at high power is that it'll rip itself to shreds. History concurs, for the most part.

  • by Anonymous Coward on Sunday December 20, 2009 @11:15PM (#30508646)
    Why to children already gifted in Math? Wouldn't it be better spent helping children who are struggling with Math? Or, heck, even adults who struggle with Math?
  • by colfer (619105) on Monday December 21, 2009 @12:13AM (#30508922)

    More to the point, he is willing to speak out on bad ethics in math, and VERY few mathematicians do so. Whether it is due to conformity, as he says, or a more complex reason, I cannot say. But he is correct that the open nature of math goes along with a lot of questionable crediting of work. Sometimes it is just people trying to make a difficult academic situation function. The subject has become so vast that students have a hard time reaching competence by the end of their PhD's. (Physics has a more regularized system of post-docs.) And full supervision of dissertations becomes lax: other faculty are too specialized and too busy and too lazy. Add to these more or less well-meaning types of lapses actual greedy chicanery and it all becomes rather unpleasant.

    There have been worse times in math. The competition for jobs in the 1930s was brutal, and professors were expected (to some extent) to appear mean, not nice as now. But our period has its peculiar frustrations. You almost cannot exaggerate the vastness of published work these days, something which has happened across academia, but causes its own particular stresses in math. You will hear mathematicians complain about that, but not so much the ethical problems of which they are well aware.

    Maybe it is under control, relative to other disciplines, who knows. But keeping problems in proportion is not a strong suit for many math types!

  • Re:Mathematicians (Score:1, Interesting)

    by Anonymous Coward on Monday December 21, 2009 @12:36AM (#30509064)

    I am a (Ph.D.) mathematician that does not teach at a university, instead I work for an investment firm. I also have a degrees in CS and Engineering.

    I find your observations to be interesting and maybe a little true.

    I definitely look at the world mathematically. My other mathematician friends do not apply mathematics to almost everything the way I do.

    "They tend to look at the world mathematically, and aren't really able to understand things they can't reduce to an equation. This leads to a very black and white view of the world, where things must be a certain way...."

    I do love reducing things to equations. I am quite good at that. A number of people have risked millions of dollars on projects where I estimated the probability of success. (We made millions of dollars on those projects.) I often think that many things like love, beauty, and even religion may be amenable to a mathematical approach. I don't think I see the world in black and white. I tend to categorize assertions as either 1) Mathematically Proven (True/False), 2) Scientifically "proven", 3) Possibly True or False, 4) not possible to prove but possible to define, or 5) statements that refer to ambiguous concepts.

    Here are three examples: I think that the world is warming due to man made CO2 emissions, but I don't think there is enough valid scientific evidence to be sure. I don't think that long distance telepathy is possible, but I really don't know. I know my children love me and my understanding of that love does not seem to have much to do with mathematics or science.

    I think you are very correct to think that mathematics changes the way that you think. I was an engineer before I went to grad school for math. After I got my math Ph.D., I took some engineering and science classes. I had to change my thinking to be successful in those classes. I was so used to mathematically precise objects that, during the first few weeks of class, I had a lot of difficulty with ambiguity in the homework problems. After the first few weeks, I did quite well in the classes, but I did need to change my thinking.

    "anything that doesn't fall into that worldview is just wrong"

    My wife has religious views that I cannot understand and I tend to think that she is mostly wrong. She thinks she can communicate with God and get answers about questions like "What should I wear today?" Statistically, the answers she gets are true about 60% or the time when the question is verifiably true or false. That makes me think that she is wrong when she says she is talking to God.

    "Everything that people do must have a rational reason, and if they can't find one they will construct a reason that seems rational to them--regardless of how simplistic it is, or how dim a view of their fellow human beings it leads them to."

    This statement does not apply to me. I really don't understand people well and many times I can't think why they behave the way they do. On the other hand, one of my mathematician friends did try to figure out the rational motivations of other people. He was very upset when he finally realized at age 40 that many if not most of our human motivations are not based in reason.

    "Mathematicians, by and large, tend to be very unhappy people in my experience."

    Three of my best friends are mathematicians and I am on a first name basis with about 20 other mathematicians. My friends seem to be about as happy as most of the other people I know. I will occasionally struggle with mild depression, but I think that would be normal for any parent facing the challenges I face. (My son was in the hospital for a significant portion of his life.) Most of my mathematician acquaintances seem happy, but maybe they are just happy to see me because I like and respect them all so much.

    "Some mathematicians have a certain "spark" that allows them to abandon mathematics temporarily and give themselves over to the pleasure of an interpersonal relationship; but even so it is still against their nature

  • by Anonymous Coward on Monday December 21, 2009 @12:50AM (#30509138)

    Please mod parent up. I am an assistant professor in a university and this is what I have observed. The dishonesty in science has reached unprecedented level, especially because today's scientific work is so associated with politics and money.

    There are professors in high places who claim authorship to papers that are way beyond their capability (thanks to their post-docs). There are faculty members who place the ability to obtain grants above all other research qualities. There are dubious papers being published in good venues simply because authors of the papers "know people".

    These things happen because today scientists are more into personal gain than scientific truth. The point is, scientific truth often conflicts with personal gain. (Compare this to economy, where a market where everybody is driven by personal gain resulted in an extremely dishonest system.)

    Perelman's position makes perfect sense in such a backdrop.

    As for the reward he wants? All post-docs to rise and revolt against their dishonest professors, and take back science from those who are not interested in it.

  • Re:Maybe .... (Score:5, Interesting)

    by silentcoder (1241496) on Monday December 21, 2009 @05:03AM (#30510090) Homepage

    >You do know that the "high power" mind of Sir Conan Doyle believed wholeheartedly in fairies? "History concurs", my ass!

    That's a bit of a bad juxtaposition. Conan Doyle only started believing in mysticism in his old age, after the death of his wife - and it is widely believed that his "conversion" was a reaction to severe depression and PTSD.
    That is a very different time in his life compared to the man who practically invented the idea of using science to solve crimes. Just reread chapter one of "A study in scarlet" sometime and remember that this was written several decades before the first forensic department opened it's doors, not to mention that his character's habit of deducing details about people from their appearance and mannerisms has a striking parallel to modern criminal profiling.

    So yes, Conan Doyle was a highly intelligent and scientifically minded person, who also happened to be a skillfull and entertaining author - sounds like a pretty high-powered mind to me. That he abandoned this out of a desperate longing for dead person, and with it a desperate desire to believe that there was some way to contact her does not change this. Such things happen to the best.
    Newton became a mystic in his older years too - and dedicated much of his last years to the study of alchemy, at a time when the rest of the world were already quite busy abandoning it. The man who set us on the route to understanding the universe as obeying laws which can be explained in maths more than anybody else, genuinely believed that the combination of elements can be affected by spirits.

    Houdini, after a similar personal loss, went to see a "psychic". Being an expert illusionist, he recognized her fraud quite easily and in anger spent the greater part of his remaining life on an unprofitable and unpopular quest to find and expose fraudulent spiritualists. In this case, his disillusionment ripped him towards a new path of logic, but he only got on it because he was about to abandon it first.

    In short, the philosopause happens - it does not negate the work done in a man's life that, being only human, old age can weaken old resolves.

  • by macraig (621737) <mark...a...craig@@@gmail...com> on Monday December 21, 2009 @05:10AM (#30510116)

    The other Anon Coward who replied to you did a fine enough job dissecting your arguments; I wouldn't have even bothered. Do you honestly find your arguments valid? They sound to me like the result of someone trying to hang onto a few cherished delusions. I do wanna respond directly to this bit of self-delusion, though:

    (And it would not have been unethical to spend it all on gold-plated violins and ping pong paddles, either; there is nothing unethical about earning, having, or spending your own money)

    You're incorrect. "Earning money" can be grossly unethical. Do you not understand that we live on a planet with finite resources, and that it is those resources that underwrite money? If someone is getting wealthy, he's doing it at the expense of a certain number of others: he's hoarding resources and depriving others of the use of those resources. In getting wealthy, that person is disadvantaging others. The wealthier the person is, the more people he had to disadvantage to achieve it. Warren Buffet understands and acknowledges this dynamic... why don't you?

    In an ethical economy, the goal is for every transaction to be an equal exchange of value; I was actually taught this concept in Business 101, as best I can recall.

    By contrast, in a capitalist economy, the goal - as its very name suggests - is to create as much inequality as possible in every transaction. Does that sound fair or ethical to you? Do you have even a modest mental inventory of the manipulative tactics that people employ to that end? Virtually all capitalist tactics used to disadvantage others fall into one of three classes:

    • manipulation of the other party's emotions;
    • deliberate attempts to mis-educate; or
    • deliberate attempts to deny information.

    That's the capitalist playbook, right there; does that sound ethical to you?

    *sigh* And here I thought I had nothing in reply.

  • by Mathinker (909784) on Monday December 21, 2009 @09:03AM (#30511100) Journal

    I was sure you were joking until I checked the WP article. Oops, forgot to check the article history. Ah, yup, you're OK (or clairvoyant)....

    Someone should invent a word for the weird feeling you get when you do research to understand a joke and it turns out not to be one.

  • by moeinvt (851793) on Monday December 21, 2009 @10:02AM (#30511532)

    That was interesting. Thank you. I especially liked the following part:

    " . . .along the highway between Beijing and the airport there were "billboards with pictures of Stephen Hawking plastered everywhere."

    Now that's cool. I've never had the pleasure of seeing a lecture by Hawking in person. Is it common for someone like him to get this type of publicity ANYWHERE in the U.S. ? Apart from a few tiny posters stapled on campus bulletin boards and taped to light poles, I don't recall seeing any type of real publicity for a public appearance by a scientist, mathematician or engineer. Sad reality.

  • by khallow (566160) on Monday December 21, 2009 @10:53AM (#30512054)

    These things happen because today scientists are more into personal gain than scientific truth. The point is, scientific truth often conflicts with personal gain. (Compare this to economy, where a market where everybody is driven by personal gain resulted in an extremely dishonest system.)

    It's amazing how ignorant of ethics and economics, an educated person can get. Sure, the academic environment is a remarkably dishonest environment these days, even compared to the business world (which is where the ignorance comes in). I don't question Perelman's desire to leave the environment. What I questioned in my original post is the mythology surrounding his choice. It doesn't take a lot of brain power to see that there is a fairly rigid class structure in most of academia: tenured professors, non-tenured professors and lecturers, various classes of students, and the rest of the staff. There's also considerable stagnation and silly politics making the environment rather limiting. The environment can be rather stressful, especially if you don't like public speaking or teaching. You can't make a lot of money either. There are plenty of good reasons not to enter that mess that have nothing to do with ethics.

    Remember this whole thread started because someone boasted that Perelman had a "more instinctive grasp of ethics" than normal people. Ignoring the minor contradiction that ethics is a reasoned approach to morality not an instinctive one, this still seems a bizarre claim to make. My take is that any ethical logic that Perelman pursues is much easier due to his relative isolation. He has fewer conflicts and distractions to dissuade him from whatever he wants to do. What that means is that while he can still serve as some sort of ethical or moral inspiration for us, it remains that most of us we have difficulties and conflicts in our lives that he doesn't have. I resent the confusion of those issues with some sort of mental inadequacy on our part.

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