
How Grigori Perelman solved one of math's greatest mysteries - phacks
https://medium.com/@phacks/how-grigori-perelman-solved-one-of-maths-greatest-mystery-89426275cb7
======
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...](http://www.newyorker.com/magazine/2006/08/28/manifold-destiny)

(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.

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xxxyy
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)

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deuill
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-
destin...](http://www.newyorker.com/magazine/2006/08/28/manifold-destiny)

It's interesting to see the political implications behind breakthroughs like
this.

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eamsen
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/)

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general_failure
Anyone know how he makes a living?

~~~
ky3
In America, you live off the fat of the land.

In Soviet Russia, the fat of the land lives off you.

~~~
omonra
In Soviet Russia joke downvotes you!

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misiti3780
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
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.

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

~~~
xxxyy
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
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...](http://www.newyorker.com/magazine/2006/08/28/manifold-destiny)

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

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guard-of-terra
"Stekhlov Institute"

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

~~~
endgame
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
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
Now I feel like a huge grouch. Thanks for taking it well.

------
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.

~~~
jdoliner
> 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.

~~~
dalke
Quoting from [http://www.lib.uni-bonn.de/PhiMSAMP/Data/Book/PhiMSAMP-
bk_Ge...](http://www.lib.uni-bonn.de/PhiMSAMP/Data/Book/PhiMSAMP-
bk_GeistLoeweVanKerkhove.pdf) :

> Mathematicians disagree about the amount of detail checking that has to be
> done by the referees. While some (few) mathematicians think that checking
> the correctness of the proofs is the main task of the referee, others
> disagree with this and consider mathematical correctness the problem of the
> author rather than that of the referee.

It later quotes an editor:

> There are situations where almost nothing needs be checked (e.g., the
> results come from a seminar where the results were checked, or I see the
> paper is not too good and then it is useless to check details, or the author
> is well-known and it is his concern to submit a correct paper). There are
> situations when I insist to check all the procedures (e.g., when it concerns
> good results from a less known author).

See how it's assumed that the author's reputation is used as a proxy for the
quality of the paper?

It also quotes an opinion piece by Nathanson:

> Many great and important theorems don't actually have proofs. They have
> sketches of proofs, outlines of arguments, hints and intuitions that were
> obvious to the author (at least, at the time of writing) and that,
> hopefully, are understood and believed by some part of the mathematical
> community. But the community itself is tiny. In most fields of mathematics
> there are few experts. [. . .] In every field, there are `bosses' who
> proclaim the correctness or incorrectness of a new result, and its
> importance or unimportance. Sometimes they disagree, like gang leaders
> fighting over turf. In any case, there is a web of semi-proved theorems
> throughout mathematics.

and it reports questionnaire results sent to math journal editors asking if
they require verification of all of the proof, or only partial verification:
"six editors thought that the referee should check all proofs in detail; five
thought that the referee should check some proofs in detail", and one of he
six actually commented "but to be reasonable, I am happy when I find a referee
doing [the latter]."

These comments seem to contradict the statement that "peer review is actually
where you verify results".

Also, not all non-math/science papers involve "verification through
experimentation." It's hard to verify through experiment a report of the
neutrino interactions observed from supernova 1987A.

