

Graph Isomorphism update: quasipolynomial claim restored - tejtm
http://people.cs.uchicago.edu/~laci/update.html
This is _NOT_ the retraction update of several days ago.<p>http:&#x2F;&#x2F;people.cs.uchicago.edu&#x2F;~laci&#x2F;update.html<p>previous posts to same link are for the retraction so unable to just link directly as they take precedence.
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jwtadvice
I remember the same thing originally happened with Wile's proof of FLT. It's
heartwarming to know that scholars continue to skeptically check each other's
work for factual correctness.

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williamstein
Even better -- this situation is much more public and open than the situation
with Andrew's FLT proof. I remember when Wiles proof was announced, when there
was a gap, etc. only a select few got to actually look at the proof. It was
only published after it had been very carefully checked. I started studying
number theory exactly during this strange period of secrecy in 1993.
Incidentally, exactly at that time, I used to play around writing computer
games with Harald Helfgott, who is the guy who just found the mistake with
Graph Isomorphism a few days ago... (He's a fantastic mathematician.)

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saalweachter
I can't help but wonder if the qualitative difference in the problems -- graph
isomorphism is an important, active area of applied mathematical research in
search of a better algorithm, FLT was a multi-century abstract mathematical
puzzler -- makes for a difference in the groups of people working on the
problems and their attitudes.

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JCzynski
Wiles was weird at the time. Math is done in public, he just really wanted to
be the one to have the final valid proof of Fermat's Last Theorem.

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jacobolus
Saying you’re working on FLT in the late 20th century is a good way to make
everyone think you’ve gone nuts and are wasting your time. It makes some sense
to make sure you have something solid before you mention it.

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bonzini
Technically he was working on the Taniyama conjecture (now known as the
modularity theorem), not on Fermat's last theorem.

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CJefferson
I don't think this is finished yet. The paper is very complex, and not
completely checked yet. Other issues will possibly arise. That's part of any
large maths proof.

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tomrod
I don't know this work, about I appreciate the candor and honesty this
academic presents. Thanks for posting.

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masalax
Great news!

>I am working on an updated arXiv posting.

I sure hope this isn't the new "I have discovered a truly marvelous proof of
this, which this margin is too narrow to contain"!

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cvoss
Babai commented that the new work-around requires a 2-page proof and makes 10
existing pages obsolete. So, a net savings of 8 pages, in theory! We'll see
how it turns out.

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pmiller2
Makes me wish it was possible to write a -8 page paper. :)

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SixSigma
I would have written a shorter letter, but I did not have the time. - Blaise
Pascal, Provincial Letters: Letter XVI (4 December 1656)

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WhitneyLand
This is so cool, the guy (among other things) beat an important algorithm that
had stood as the fastest for decades.

~~~
wolfgke
Luks worked together with Babai on the previous fastest algorithm. Babai is
just very modest when he only mentions Luks when reffering to it.

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heinrichf
It should be noted that Helfgott (who found the issue in the proof) is
scheduled to talk about Babai's work at the famous Bourbaki seminar next
saturday:
[http://www.bourbaki.ens.fr/seminaires/2017/Prog_janv17.html](http://www.bourbaki.ens.fr/seminaires/2017/Prog_janv17.html)
The seminar is broadcast live on youtube, notes and video are available
afterwards.

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raverbashing
It's the retraction of the retraction, basically

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oh_sigh
Not exactly - Helfgott's initial analysis pointing out the flaw was(and still
is) correct - it's just that Babai found a way to work around it.

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xiphias
Does this also mean that Bitcoin mining time is quasipolynomial with the
difficulty parameter?

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drdeca
I don't think bitcoin's work function is based on graph isomorphism?

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xiphias
Yeah, I read more about it, only subgraph isomorphism is known to be NP-
complete...of course the complexity of that will remain a mystery for a long
time.

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wolfgke
And finding a nonce that makes the block have a SHA256 with many leading
zeroes is probably not an NP-hard problem.

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xiphias
It is, some people also tried SAT solvers for mining:

[http://jheusser.github.io/2013/02/03/satcoin.html](http://jheusser.github.io/2013/02/03/satcoin.html)

~~~
wolfgke
Please look up the definition of NP-hardness again. If the problem

(#) := "finding a nonce that makes the block have a SHA256 with many leading
zeroes"

was NP-hard, it would be an interesting idea to use a solver for (#) to solve
e.g. SAT (not the other way round!).

TLDR: You talked about the wrong inclusion.

