
On Norbert Blum’s claimed proof that P does not equal NP - cschmidt
https://lucatrevisan.wordpress.com/2017/08/15/on-norbert-blums-claimed-proof-that-p-does-not-equal-np/
======
spaceseaman
> I am confident that by the end of the week we will hear substantive comments
> on the technical claims in the paper.

I am amazed by the speed with which mathematicians are able to quickly
congregate and debate such things like this. It makes me excited to enter a
graduate program knowing that people take academia so seriously. Their love
and devotion to purely intellectual pursuits should really be appreciated
every once in awhile.

~~~
solomatov
> Their love and devotion to purely intellectual pursuits should really be
> appreciated every once in awhile.

It's not purely intellectual pursuit. I am sure, eventually, there will be
some applications of it.

~~~
OtterCoder
> It's not purely intellectual pursuit.

I feel like you don't really understand theoretical mathematicians.
Application is a side effect of the highest maths, not a goal of its
practitioners.

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naturalgradient
Some interesting ongoing discussion (last post an hour ago):

[https://cstheory.stackexchange.com/questions/38803/where-
is-...](https://cstheory.stackexchange.com/questions/38803/where-is-norbert-
blums-2017-proof-that-p-ne-np-being-discussed#comment88798_38817)

In particular someone claimed to have found a flaw (which I can not comment
on, not a complexity theory person):

'Tardos' function is a monotone function which is 1 on k-cliques and 0 on
complete (k-1)-partite graphs. As far as I can tell, Berg and Ulfberg use ONLY
these properties in their CNF-DNF approximation proof for CLIQUE, which hence
prove that Tardos' function has exponential monotone complexity. Blum's
Theorem 6 says that monotone complexity lower bounds by CNF-DNF approximation
for monotone functions, give the same NON-monotone lower bound. Hence, Tardos'
function have exponential complexity according to Theorem 6 (which is false)'

~~~
crb002
I'm 90% sure the first paper proving P!=NP will either use a Kolmogorov
complexity argument, or an exact enumeration involving a semigroup problem
that is exponential.

~~~
Ar-Curunir
Any clarification on how you expect such arguments to be used? Otherwise your
claims are completely out of left field, because most approaches are not
anything along those lines.

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weinzierl
Scott Aaronson is confident that it will be refuted by the end of the week:

> I’d again bet $200,000 that the paper won’t stand [...] and if the thing
> hasn’t been refuted by the end of the week, you can come back and tell me I
> was a closed-minded fool.

[http://www.scottaaronson.com/blog/?p=3389](http://www.scottaaronson.com/blog/?p=3389)

On the other hand, his original post contained an short explanation (one or
two sentences) what he believed to be a flaw in the paper, which he has
removed since then.

~~~
naturalgradient
FWIW,

I think Aaronson's dismissive attitude is unbecoming and disrespectful amongst
colleagues.

'Unrelated Update: To everyone who keeps asking me about the “new” P≠NP proof:
I’d again bet $200,000 that the paper won’t stand, except that the last time I
tried that, it didn’t achieve its purpose, which was to get people to stop
asking me about it. So: please stop asking, and if the thing hasn’t been
refuted by the end of the week, you can come back and tell me I was a closed-
minded fool.'

Quick-copy pasting a Facebook comment as reason not to want to deal with it,
betting a large sum of money almost tauntingly is not good scholarship.

A serious researcher made a serious effort to solve a problem. Say you have
not verified it and don't want to comment.

It almost seems like he does not want P/NP to be proven because he has made a
reputation by becoming an authority on dismissing attempts.

~~~
Analemma_
I don't think his dismissiveness is aimed at his colleagues, but rather to the
commenters on his blog. Aaronson's public persona has resulted in him getting
mobbed by requests-for-comment from the general public every time there's some
news about theoretical CS (or D-Wave), which I'm sure is what happened here. I
imagine it gets tiring after a while, like actors constantly being asked to
repeat some catchphrase.

I think he could respond to it better (once you're a public-enough figure
online, a good skill to learn is knowing when to step away from the keyboard
instead of saying something grumpy you'll probably later regret), but I see
where he's coming from.

~~~
naturalgradient
As a researcher, I think he is dismissive of Blum's work.

Let's take a moment to change perspective:

Imagine you worked for years on something and finally uploaded it on ArXiv,
waiting for the community to weigh in. The following characters appear:

1\. Someone known in the field does not bother reading it but says you are
probably wrong, bets money on you being wrong and says he does not want to be
bothered with it. How would you feel?

2\. Someone else known in the community starts collating information/comments
to help verify the proof or find instructive mistakes.

3\. Another mathematician also believes Blum is wrong just because it is
statistically likely, and does not want to spend time on something that will
most likely lead nowhere. She keeps this opinion to herself and simply does
not engage with the material. If approached, she declines to comment because
she says he did not have time to check the proof.

Aaronson went for option 1 and in my highly _personal_ opinion, it's the worst
of the ones listed. It's standing at the sidelines being snarky. Just because
he may as well be right does not make this behaviour any better.

It is the equivalent of laughing in an undergrad lecture when someone asks a
naive question.

~~~
Analemma_
I think we're talking past each other and don't actually disagree. To clarify
my last post: I don't approve of what Aaronson did. I think it was a dumb
thing to say and (assuming my hypothesis is correct that he did it out of
frustration at constantly being pestered to comment on CS news) he instead
should've cooled off and, as you say, taken option 3. I think he was aiming
his statements at his fans, not academia, and in his frustration forgot that
there's no such thing anymore as a message only directed at one group.

I just want the problem with his behavior to be accurately diagnosed, because
I think (again, I could be wrong) the solution is "better manage your temper
with your non-academia fans" and not "rethink your relationship with other
academics".

~~~
naturalgradient
Thank you for clarifying this

------
brudgers
Knuth on why he believes P = NP _and_ what it means [see question 17]:

[http://www.informit.com/articles/article.aspx?p=2213858](http://www.informit.com/articles/article.aspx?p=2213858)

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crsv
I read these things and I wish I could understand it with a cursory knowledge
of mathematical theory, but alas, I'm left longing for understanding, because
it seems like a really interesting debate.

------
crb002
I've been convinced P!=NP ever since I started studying semigroup lower
bounds. Even black box group membership is exponential in the largest prime
less than or equal to N. [https://oeis.org/A186202](https://oeis.org/A186202)

~~~
jmcgough
P!=NP seems to be the general sentiment, though we're still waiting on the
proof :)

~~~
tachyonbeam
I share the same sentiment, but I think it could be that P!=NP is an
unprovable statement. Could be that there's something fundamental about the
nature of computing which makes it impossible to prove or disprove it.

~~~
sacheendra
Maybe that could be a thing to prove.

Is it possible to prove that something is not provable?

~~~
emmab
> Is it possible to prove that something is not provable?

It's possible to prove that something is not provable within some axiom set.
See:
[https://en.wikipedia.org/wiki/List_of_statements_independent...](https://en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC)

