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How Grigori Perelman solved one of math's greatest mysteries

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Re: How Grigori Perelman solved one of math's greatest mysteries

#11

Post by privong »

A quibble with the author's impression of peer review:

As we know, the process of submitting to a scientific journal has, besides the diffusion of one’s results to the community, the aim of verifying those results. Here, such an approach was made impossible by Perelman, so some independent groups of scholars set at the highly difficult task to understand, complete, verify, and explain his work.

Peer review does not "verify results"; peer review is there to make sure there are no serious and obvious flaws. Duplication of studies and collection of additional data / use of other techniques is what verifies results.

It is possible Perelman's papers received a more rigorous review because they were not peer reviewed – giving people incentive to dig into the details, perhaps more than they would have if the papers had appeared in a journal. But, given the signficance of the problem he was attacking, I suspect the papers not being in a peer-reviewed journal made little difference, in terms of how much effort was expended to check his proofs.

Re: How Grigori Perelman solved one of math's greatest mysteries

#12

Post by mythealias »

xxxyy wrote: post #5
legohead wrote: post #2

He solved the Poincaré Conjecture in 7 years. It has been nearly 13 years since.. wonder what he will do next!

It is perhaps unfortunate, but it is possible that Poincare will be the biggest and final work of Perelman. He has shut down his professional connections, and it is rumored that he has simply burned out. I hope to be wrong. Either way he is a remarkable person, and will be remembered.

It might be he is burned out with all the politics surrounding the claim of his work but not with the work in general. People who enjoy doing something rarely get burned out doing it lifelong.

From the newyorker article linked by deuill:

    The prospect of being awarded a Fields Medal had forced 
    him to make a complete break with his profession. “As
     long as I was not conspicuous, I had a choice,” Perelman 
    explained. “Either to make some ugly thing”—a fuss about 
   the math community’s lack of integrity—“or, if I didn’t do
     this kind of thing, to be treated as a pet. Now, when I 
    become a very conspicuous person, I cannot stay a pet and 
    say nothing. That is why I had to quit.” We asked 
    Perelman whether, by refusing the Fields and withdrawing 
    from his profession, he was eliminating any possibility 
    of influencing the discipline. “I am not a politician!” 
    he replied, angrily.
http://www.newyorker.com/magazine/2006/08/28/manifold-destin...

Re: How Grigori Perelman solved one of math's greatest mysteries

#14

Post by n09n »

privong wrote: post #11

A quibble with the author's impression of peer review: As we know, the process of submitting to a scientific journal has, besides the diffusion of one’s results to the community, the aim of verifying those results. Here, such an approach was made impossible by Perelman, so some independent groups of scholars set at the highly difficult task to understand, complete, verify, and explain his work. Peer review does not "…

That's science, not math.

Re: How Grigori Perelman solved one of math's greatest mysteries

#16

Post by jdoliner »

privong wrote: post #11

A quibble with the author's impression of peer review: As we know, the process of submitting to a scientific journal has, besides the diffusion of one’s results to the community, the aim of verifying those results. Here, such an approach was made impossible by Perelman, so some independent groups of scholars set at the highly difficult task to understand, complete, verify, and explain his work. Peer review does not "…

> Peer review does not "verify results"; peer review is there to make sure there are no serious and obvious flaws. Duplication of studies and collection of additional data / use of other techniques is what verifies results.

What you're saying is true of Science than Math. There's a fundamental difference between Math research and Science research. Math research doesn't involve hypothesis and verification through experimentation. Perelman's paper is purely logical it starts with axioms and derives its conclusions from them. For research like that peer review is actually where you verify results.

Re: How Grigori Perelman solved one of math's greatest mysteries

#17

Post by endgame »

guard-of-terra wrote: post #7

"Stekhlov Institute" It should be "Steklov Institute" because there's no х to be found in "Стеклов".

The author managed to get the name of the prize wrong in the title, as well.

Specifically: the apostrophe doesn't mean "LOOK OUT HERE COMES AN `S'!".

Re: How Grigori Perelman solved one of math's greatest mysteries

#18

Post by rdtsc »

This is not quite complete as far as explaining the reasons why he didn't accept.

The key quote can be found in the New Yorker article

http://www.newyorker.com/magazine/2006/08/28/manifold-destin...

(someone else already posted 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.”
He was disillusioned with the mathematics community not just with Cao and Zhu's dishonesty. It was more crushing and dissapointing that others didn't rise up to speak against it.

Re: How Grigori Perelman solved one of math's greatest mysteries

#19

Post by this_user »

xxxyy wrote: post #5
legohead wrote: post #2

He solved the Poincaré Conjecture in 7 years. It has been nearly 13 years since.. wonder what he will do next!

It is perhaps unfortunate, but it is possible that Poincare will be the biggest and final work of Perelman. He has shut down his professional connections, and it is rumored that he has simply burned out. I hope to be wrong. Either way he is a remarkable person, and will be remembered.

According to his Wikipedia article citing a French source he may be working on at least one of the other six problems. Seems like he mainly wants to be left alone so his withdrawal from the world is not surprising and may just be a way to fade back into obscurity so he can focus on his work.

Re: How Grigori Perelman solved one of math's greatest mysteries

#20

Post by dalke »

n09n wrote: post #14
privong wrote: post #11

A quibble with the author's impression of peer review: As we know, the process of submitting to a scientific journal has, besides the diffusion of one’s results to the community, the aim of verifying those results. Here, such an approach was made impossible by Perelman, so some independent groups of scholars set at the highly difficult task to understand, complete, verify, and explain his work. Peer review does not "…

That's science, not math.

The quote from the article does start "As we know, the process of submitting to a scientific journal ...", not "math journal".
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