
Blum: “The proof is wrong. I shall elaborate precisely what the mistake is.” - chx
https://arxiv.org/abs/1708.03486v2
======
DrBazza
And this what science is about. I'm wrong and I'll say so. I've been proved
wrong, because I _was_ wrong.

~~~
dekhn
math, not science

~~~
alexanderstears
They both share the view that explanations/hypotheses can either be retained
or rejected (and better explanations can retained).

Math is unique in that the standard of proof is more comprehensive and the
domain is bounded but this is a good example of someone employing the
scientific method and exhibiting good scientific community values.

~~~
xyzzyz
No, mathematics works completely different than science. In both math and
science, you do some observations, and then formulate theory that explain some
of these observations. However, in science, you then design experiments and
predict the results based on your theory, taking care to ensure that the
experiments distinguish between the reality in which your theory holds, and
the one where it doesn't.

In math you might also do that as a sanity check, but that's not the point. In
math, the point is to actually _prove_ your theory to be correct, something
which is absolutely impossible to do in science, where you can only prove
theory to be _wrong_.

~~~
alexanderstears
>taking care to ensure that the experiments distinguish between the reality in
which your theory holds, and the one where it doesn't.

I get the impression that you're thinking of specific domains within science.
Many theories are contextualized within something (e.g a theory of why there's
lightning might be more domain specific than a theory of electromagnetism).

I don't disagree that things are proved within mathematical systems and
scientific claims / hypotheses are categorically different (and weaker, I
suppose).

But the author made a claim, discovered an error in their claim, and alerted
the community to his mistake and signaled their intention to address it.
That's not behavior that's exclusive to mathematics. Many scientists have made
claims that they think the evidence supports, and then they realize that
something wasn't correct, and they make the correction.

Cartographers / mariners used to think that California was an island:
[https://en.wikipedia.org/wiki/Island_of_California](https://en.wikipedia.org/wiki/Island_of_California)

They had solid evidence to think that's the case but then eventually they
realized the mistake and they've corrected it.

~~~
thaumasiotes
> They had solid evidence to think that's the case

Why do you say this? It is not supported by the link you provide.

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exikyut
For anyone dense like me:

\- The author has uploaded a [v2] with file size 0 bytes (see bottom of page);
this constitutes retraction of the publication

\- [v2] has a comment, shown approximately partway down the page, which is
what this post's subject cites

You can click the [v1] link to get a PDF link to the now-retracted
information. I really like arXiv's versioned publishing.

------
herodotus
Is the comment that "the proof is wrong" from the author himself?

~~~
Etheryte
Yes, both the article ( _" A Solution of the P versus NP Problem"_) and the
comment on it ( _" The proof is wrong"_) are written by Blum. It's both very
nice and honorable that the author is pointing out his own errors publicly.

~~~
molyss
In retrospect, I think the initial abstract of the paper ("Berg and Ulfberg
and Amano and Maruoka have used CNF-DNF-approximators to prove exponential
lower bounds for the monotone network complexity of the clique function and of
Andreev's function. We show that these approximators can be used to prove the
same lower bound for their non-monotone network complexity. This implies P not
equal NP.") was also a way to have as many people as possible double check the
proof, due to the very strong result of the paper.

In other words, he might not have been building up the hype but instead was
making sure he wouldn't have to retract a paper with a (more or less) obvious
mistake in it. That's how science should be done rather than behind closed
doors !

~~~
quantdev
I don't understand what you're trying to say. How would his abstract be
different if he wasn't trying to get as many people to look at it?

Many results in math establish a famous theorem by proving something more
abstract that "easily" implies the famous result, like with Fermat's Last
Theorem.

~~~
colanderman
Perhaps by leaving off the last sentence, "this implies P not equal NP", and
changing the title. That sentence does not change the meaning of the paper; it
just adds an eye-catching (and already accepted as true) implication.

~~~
quantdev
I suppose, though it would be very strange and disingenuous to leave off the
most important implication.

~~~
munificent
Well, Turing called his famous paper "On computable numbers, with an
application to the Entscheidungsproblem" without really state that the
"application" is that he _solved_ it.

------
sova
What a fantastic person to point out such a subtlety once it has come to
light. Easily steer your fellow scientists right!

~~~
xrange
Here's an utterly trivial question. Do most people working on computational
problems like this consider themselves mathematicians or scientists?

~~~
jdoliner
Mathematicians, despite the fact that the field is called "Computer Science"

~~~
sova
Dijkstra say Computational Scientist

~~~
_kst_
Dijkstra is alleged to have said:

"Computer science is no more about computers than astronomy is about
telescopes."

but that's disputed.

[https://en.wikiquote.org/wiki/Computer_science#Disputed](https://en.wikiquote.org/wiki/Computer_science#Disputed)

~~~
icebraining
He has said something to more or less the same effect:

 _it was firmly implanted in people’s minds that computing science is about
machines and their peripheral equipment. Quod non [Latin: "Which is not
true"]. We now know that electronic technology has no more to contribute to
computing than the physical equipment. We now know that programmable computer
is no more and no less than an extremely handy device for realizing any
conceivable mechanism without changing a single wire, and that the core
challenge for computing science is hence a conceptual one, viz., what
(abstract) mechanisms we can conceive without getting lost in the complexities
of our own making._

------
willvarfar
The homepage Blum is referring to is presumably [http://theory.cs.uni-
bonn.de/blum/blum.var](http://theory.cs.uni-bonn.de/blum/blum.var) but I can't
find an explanation of the flaw there yet.

~~~
technofire
The flaw is shown here:

[https://cstheory.stackexchange.com/questions/38803/is-
norber...](https://cstheory.stackexchange.com/questions/38803/is-norbert-
blums-2017-proof-that-p-ne-np-correct/38823)

~~~
komali2
Welp looks like I have a whole new set of things to learn before I can read a
thing :P

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avs733
Thank you for the title update.

I know there was a pool on how long till it was disproved. Who had 19days?

~~~
technofire
It was known long before 19 days, actually within a week of publication:

[https://cstheory.stackexchange.com/questions/38803/is-
norber...](https://cstheory.stackexchange.com/questions/38803/is-norbert-
blums-2017-proof-that-p-ne-np-correct/38823)

~~~
viksit
Does anyone know who wrote that answer?

~~~
chx
Check
[https://cstheory.stackexchange.com/a/38832/5630](https://cstheory.stackexchange.com/a/38832/5630)
Alexander Razborov was the first to prove it wrong by providing a
counterexample. He got a Nevanlinna Prize in 1990 for a result in this field,
it's not a surprise at all he was the one.

------
foota
He sounds crushed, I hope he's doing okay. Must be hard to have something be
wrong after working on it for what I imagine was a very long time.

------
mastazi
That's why when you share Arxiv links you should never ever share direct links
to the pdf.

E.g. If someone shared v1 before the author retracted, by visiting that link
(even today) you would know nothing about what happened.

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deepnotderp
Awesome, this is science and math working as it should be, kudos to Blum!

