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Grigory Perelman and the Poincare Conjecture
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."
By not buying or reading this book, I am doing what Perelman surely would have wanted.
Sylvia Nasar, also the author of "A Beautiful Mind", wrote a great piece about Perelman shortly after the publication of his proof. Deeply moving, in my opinion.
I guess I have to be more than a little skeptical of the opinion of someone who's only built up a view of someone based on hearsay. Trying to spin this like it's an advantage is at best self deception. Maybe it's an advantage because you get to make more stuff up, but it's certainly no advantage in actually trying to understand the person, or honestly convey who they are.
I don't really blame the guy for not wanting to talk to journalists. With few exceptions, journalists don't represent the interests of the truth, (and most certainly not YOUR interests). Generally they're trying to sell some eyeballs, and you're the bait. Gessen talks about how the when you interview someone you're always fighting their own perception of them self. That may be true (though I'm not sure it's exactly a negotiation as much as it is an integration). When you read a journalists biography, you're constantly fighting what the journalist might have thought was the most interesting story to tell, (as opposed to the most accurate one).
AccountKiller
Perelman's proof is fairly skeletal, though most/all now agree it contains all the required components and enough of a sketch of the missing details. However,some Chinese mathematicians (Cao and Zhu) filled in some of the details in a massive 300-page journal article. A famous Chinese mathematician, Shing-Tung Yao, was accused of promoting the Cao-Zhu article as the real proof, and taking away credit rightfully due to Perelman. There were other shenanigans alleged on both sides.
To some extent it comes down to a question of insight vs. work, with some on the Chinese mathematicians' side claiming that Perelman basically came up with the high-level breakthrough, but didn't follow through with the work to actually prove the theorem, which they claim is non-trivial--- and so the credit for the proof should go to Cao-Zhu, while Perelman gets credit for coming up with the major ideas that inspired the proof. Others view Perelman as essentially coming up with the proof.
Here's a brief bloggy summary with some links.
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
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.
Yeah, and I think C (and all its derivatives) went the wrong route. The single "=" should have been comparison, and something else (like ":=") should have been assignment. I think that's logically cleaner, and gets along nicer with mathematics.
Well, by all means then, master, please enlighten me. How is refusing either lucrative positions or the prize in his particular context somehow ethically praiseworthy rather than simply eccentric?
From an article on the New Yorker, I think it sums it up better than TFA:
Perelman repeatedly said that he had retired from the mathematics community and no longer considered himself a professional mathematician. He mentioned a dispute that he had had years earlier with a collaborator over how to credit the author of a particular proof, and said that he was dismayed by the discipline’s lax ethics. “It is not people who break ethical standards who are regarded as aliens,” he said. “It is people like me who are isolated.” We asked him whether he had read Cao and Zhu’s paper. “It is not clear to me what new contribution did they make,” he said. “Apparently, Zhu did not quite understand the argument and reworked it.” As for Yau, Perelman said, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.”
Then another bit at the very end of The New Yorker:
Mikhail Gromov, the Russian geometer, said that he understood Perelman’s logic: “To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”
If you still do not understand why his refusal to accept the money, I'm not sure I can help you. Somethings are greater than any amount of money.
-Tynin
http://englishrussia.com/?p=998
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.
Even with qualification, this seems like a very rash generalization. I attended a doctoral program in Logic at the University of California Berkeley, where the names on the office doors were pretty much the same as the names of the most significant theorems. What struck me was the incredible diversity of how the best mathematicians' minds worked. Some saw mathematics as a meaningless game with symbols. Others had a vivid imagination for platonic realities that they captured in their work. Some were multi-talented, outgoing, and verbally and socially skilled . Others were introverted and poor communicators. I don't know what mathematicians you know, but your generalization that mathematicians tend to be unhappy makes no sense to me at all. I personally knew, and in a few cases worked for, a number who solved important problems. An example would be Julia Robinson (Hilbert's Tenth Problem) who certainly suffered from poor health and did have some difficult times earlier in her life, but at the time I knew her (1986-1972) could not be described as an unhappy person.
If nothing else he could give it to a charity that helps children who have a gift in Math.
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.
Who said anything about understanding?
Actually I was responding to jjohnson, who in his question asked for enlightenment.
He stated his reasons, we understand them.
If you understood them, why are you still asking questions about them?
Instead, I too am curious what makes his refusal ethically significant to you.
Because he refuses to work in a system he feels has been driven by cut throat politics. Because he, with all his eccentricities, was able to reach above all of that and find comfort in a life not dictated by men with agenda's who'd smile while sticking a dagger in your back for a place in history.
While your selected quotes indicate a consistent and logical approach to ethics (barring that Perelman's characterization of mathematics as a dishonest culture isn't nuanced and may even be self-serving), we also have a quote from another reply at your level:
The commercialization of mathematics offends him. He was deeply hurt by the many generous offers he received from U.S. universities after he published his proof. He apparently felt he had made a contribution that was far greater than any amount of money--and rather than express their appreciation in appropriately mathematical ways, by studying his proof and working to understand it--they were trying to take a shortcut and basically pay him off. By the same token, the million dollars will probably offend him. I don't think we will be hearing from Perelman again.
That quote is taken by the author of TFA who admittedly has never spoken with Perelman. What I've read from Perelman was taken by sources with whom he did speak with, and in them I found nothing about his disdain over the perception of being bought off. Perhaps that is just creative writing on the part of TFA, or maybe it is the truth, but I cannot tell. From my readings I took from it that it was his belief that math isn't something that should need a monetary reward, that the simple discovery of a new proof and the recognition that automatically goes with it are more than enough. It is a rare day we get to advance the knowledge of mankind, and he did so in a noble fashion, all the while his peers (Yau, Cao, and Zhu) worked hard to take the credit.
Assuming that characterization is correct, then it's not fair on Perelman's part to dictate what other peoples' perception of a reward should be.
I don't believe he tried to push his views on the world. When they tried to give him the Fields metal, they spent weeks trying to talk him into it, they even gave him three options; accept and come; accept and don’t come, and they'd send the medal later; third, I don’t accept the prize. From the very beginning, he told them he didn't accept. He didn't tell them that the prize and those that accept it were his lessers, just that he did not want it. He felt that if the proof was correct, that was all then he needed with no further recognition.
For example, what sort of communication did he make with the outside world to curb those job offers? How are they supposed to read his mind and determine what he wants for recognition?
This sounds a lot like a problem that will work itself out naturally. Why should a winner of a contest/prize have to announce to the world their intentions and how they'd like to be recognized? These people, companies, universities came to him, he has no responsibility to anyone to even return their calls as it were.
This sounds a lot like spite (as a strategy of altruism, I apologize for the connotation), sacrificing benefits both to yourself and others in order to harm someone in particular. While there can be ethical versions of spite, this seems more driven by pride than by some ethical standard. Finally, I don't have the ability to distinguish between an eccentric ethical system wh
Ah, and how about we use \/ for OR and /\ for AND. Oh the world will be a better place! || and &&, we spit on you!
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.