7 ms·

How Grigori Perelman solved one of math's greatest mysteries

112 points by phacks 12y ago

legohead 12y ago
He solved the Poincaré Conjecture in 7 years. It has been nearly 13 years since.. wonder what he will do next!
- xxxyy 12y ago
  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.
  - mythealias 12y ago
    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-destiny http://www.newyorker.com/magazine/2006/08/28/manifold-destin...
  - this_user 12y ago
    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.
xxxyy 12y ago
For those interested there is a good Russian documentary on Perelman's life: https://www.youtube.com/watch?v=Ng1W2KUHI2s https://www.youtube.com/watch?v=Ng1W2KUHI2s
eamsen 12y ago
Here is some info and a great explanatory video for William Thurston's geometrization conjecture, which laid down some of the work for the proof: http://terrytao.wordpress.com/2012/08/22/bill-thurston/ http://terrytao.wordpress.com/2012/08/22/bill-thurston/
deuill 12y ago
The New Yorker also published an excellent piece on Perelman and the solving of the Poincaré back in 2006: http://www.newyorker.com/magazine/2006/08/28/manifold-destiny http://www.newyorker.com/magazine/2006/08/28/manifold-destin... It's interesting to see the political implications behind breakthroughs like this.
guard-of-terra 12y ago
"Stekhlov Institute" It should be "Steklov Institute" because there's no х to be found in "Стеклов".
- endgame 12y ago
  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'!".
  - phacks 12y ago
    Author speaking, I corrected those typos, thanks. I'm French, hence the quite frequent mistakes. As for the "'s" thingy, I did laugh out loud on your comment.
    - endgame 12y ago
      Now I feel like a huge grouch. Thanks for taking it well.
sirbetsalot 12y ago
good guy, doesn't give a shit about the corpo-academic kleptocracy. For the love of math, that is all.
misiti3780 12y ago
really great article - i had read a lot about him before and never come across the fact that he was jewish and didnt believe anti-Semitism existed.
- phacks 12y ago
  If you'd like to read more, I highly recommend "Perfect Rigour: A Genius and the Mathematical Breakthrough of the Century" by Masha Gessen. I mainly refered to this book while writing this article.
general_failure 12y ago
Anyone know how he makes a living?
- ky3 12y ago
  In America, you live off the fat of the land. In Soviet Russia, the fat of the land lives off you.
  - hyperbovine 12y ago
    Thanks for clearing that up.
  - omonra 12y ago
    In Soviet Russia joke downvotes you!
- adamnemecek 12y ago
  Supposedly he lives off his mother's pension.
- mlvljr 12y ago
  His sister sends him some money (she lives in Sweden now), as far as I've heard. The man actually lives within a walk distance from me (or used to at the moment of hype), you can both pay for your water / electricity / etc, and not starve by any means with a monthly income of $600, roughly.
privong 12y ago
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.
- n09n 12y ago
  That's science, not math.
  - dalke 12y ago
    The quote from the article does start "As we know, the process of submitting to a scientific journal ...", not "math journal".
    - raverbashing 12y ago
      Maybe it would be better to call it an Academic/Research Journal
      - dalke 12y ago
        To include history, philosophy, musicology and other academic fields? I don't see how that's better.
- jdoliner 12y ago
  > 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.
rdtsc 12y ago
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-destiny 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.

112 points by phacks 12y ago

legohead 12y ago

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

xxxyy 12y ago
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.
- mythealias 12y ago
  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-destiny http://www.newyorker.com/magazine/2006/08/28/manifold-destin...
- this_user 12y ago
  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.

xxxyy 12y ago

For those interested there is a good Russian documentary on Perelman's life: https://www.youtube.com/watch?v=Ng1W2KUHI2s https://www.youtube.com/watch?v=Ng1W2KUHI2s

eamsen 12y ago

Here is some info and a great explanatory video for William Thurston's geometrization conjecture, which laid down some of the work for the proof: http://terrytao.wordpress.com/2012/08/22/bill-thurston/ http://terrytao.wordpress.com/2012/08/22/bill-thurston/

deuill 12y ago

The New Yorker also published an excellent piece on Perelman and the solving of the Poincaré back in 2006: http://www.newyorker.com/magazine/2006/08/28/manifold-destiny http://www.newyorker.com/magazine/2006/08/28/manifold-destin... It's interesting to see the political implications behind breakthroughs like this.

guard-of-terra 12y ago

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

endgame 12y ago
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'!".
- phacks 12y ago
  Author speaking, I corrected those typos, thanks. I'm French, hence the quite frequent mistakes. As for the "'s" thingy, I did laugh out loud on your comment.
  - endgame 12y ago
    Now I feel like a huge grouch. Thanks for taking it well.

sirbetsalot 12y ago

good guy, doesn't give a shit about the corpo-academic kleptocracy. For the love of math, that is all.

misiti3780 12y ago

really great article - i had read a lot about him before and never come across the fact that he was jewish and didnt believe anti-Semitism existed.

phacks 12y ago
If you'd like to read more, I highly recommend "Perfect Rigour: A Genius and the Mathematical Breakthrough of the Century" by Masha Gessen. I mainly refered to this book while writing this article.

general_failure 12y ago

Anyone know how he makes a living?

ky3 12y ago
In America, you live off the fat of the land. In Soviet Russia, the fat of the land lives off you.
- hyperbovine 12y ago
  Thanks for clearing that up.
- omonra 12y ago
  In Soviet Russia joke downvotes you!
adamnemecek 12y ago
Supposedly he lives off his mother's pension.
mlvljr 12y ago
His sister sends him some money (she lives in Sweden now), as far as I've heard. The man actually lives within a walk distance from me (or used to at the moment of hype), you can both pay for your water / electricity / etc, and not starve by any means with a monthly income of $600, roughly.

privong 12y ago

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.

n09n 12y ago
That's science, not math.
- dalke 12y ago
  The quote from the article does start "As we know, the process of submitting to a scientific journal ...", not "math journal".
  - raverbashing 12y ago
    Maybe it would be better to call it an Academic/Research Journal
    - dalke 12y ago
      To include history, philosophy, musicology and other academic fields? I don't see how that's better.
jdoliner 12y ago
> 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.

rdtsc 12y ago

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-destiny 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.