
Claimed proof of Riemann Hypothesis - japaget
http://www.researchgate.net/publication/285720971_An_asymptotic_Robin_inequality
======
tokenadult
Is there someone here who follows Riemann Hypothesis research closely enough
to comment on whether there is any there here?[1] The Riemann Hypothesis is a
sufficiently complicated and famous problem that I think it must be easy for a
wishful thinker to suppose he has found a solution when he actually hasn't.

[1] This is a reference to a famous quotation from Gertrude Stein's
autobiography, "anyway what was the use of my having come from Oakland it was
not natural to have come from there yes write about it if I like or anything
if I like but not there, there is no there there."

[https://en.wikipedia.org/wiki/Gertrude_Stein#.22There_is_no_...](https://en.wikipedia.org/wiki/Gertrude_Stein#.22There_is_no_there_there.22)

~~~
gragas
That quote makes me feel like I'm having a stroke.

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dooglius
On page 4, it says "Now by Robin criterion d(n)<0 for n large enough, yielding
lim sup (n->infinity) (d(n)) <= 0". If I understand the criterion from page 1
right, assuming RH is false only implies that d(n) <= 0 for some n > 7! -- not
for all n sufficiently large, so the limit superior is not constrained as
claimed. In fact, on page 2, the paper claims "Thus, if m is bounded and
n->infinity, we see that d(n)->infinity", which, if the falsity of RH did
imply lim sup (n->infinity) (d(n)) <= 0, would make for an even shorter and
simpler proof.

Disclaimer: I've only got an undergrad in math and don't know much about the
specifics of the cited papers, so I might be missing something.

~~~
contravariant
Apparently the negation of RH is enough to state that there needs to be
infinitely many numbers such that d(n)<=0. That would imply that you can find
arbitrarily large n such that d(n)<=0, but I don't think that's enough to
claim that "lim sup (n->infinity) (d(n)) <= 0".

I think it's enough to claim "lim inf (n->infinity) (d(n)) <= 0" though, but
for some reason they proved that in a different way, that I don't quite
understand yet.

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erostrate
There are dozens of papers attempting to prove the Riemann Hypothesis. Here is
a list [1]. A joke from the author of the list: "It's easier to prove the RH
than to get someone to read your proof".

[1]
[http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproo...](http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproofs.htm)

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silentvoice
Coming from a PhD in math I can give this good trick for assessing grand
mathematical claims:

Google the authors.

Maybe unfair to intelligent amateurs, but based on my decade of experience you
find out from this whether to take something seriously.

Might need some adjustment of Google terms for hard-to-google names, just use
common sense.

~~~
chx
Except Patrick Sole is a real mathematician who has been working in this area
for some years now
[http://www.emis.de/journals/JTNB/2007-2/article03.pdf](http://www.emis.de/journals/JTNB/2007-2/article03.pdf)
and so it's not easy to dismiss it just based on a name.

The most plausible explanation is
[https://www.reddit.com/r/math/comments/3vnrqj/two_authors_cl...](https://www.reddit.com/r/math/comments/3vnrqj/two_authors_claim_a_proof_of_rh_using_an/cxpg7b9)
here: "Zhu sent Sole some questions about his Robin inequality paper,
including Zhu's ideas for proving RH. Sole responded, but there was some
communication breakdown that led to Zhu thinking Sole endorsed his ideas. Zhu
typed up his idea and added Sole's name to it in order to get the paper read.
This is of course unethical, but given that Zhu thought his proof was correct,
in his mind he was doing Sole a favor."

This was published on Saturday so my best guess is Patrick Sole on Monday will
either post a refute or will claim it is true and everyone will shit a brick
(unikely).

~~~
silentvoice
I wasn't clear enough. I was responding to the flow of comments of the form:
"Riemann hypothesis is hard, this is unlikely to be true." Sure it's true, but
doing a little more research could inform that opinion well past the zeroth-
order approximation of "it's a hard problem."

I didn't actually take my own advice, I just wait for Terence Tao to write a
post then I know it's true :)

~~~
chx
I think the average HNer will hear when a proof happens for real in just the
everyday channels of theirs: Twitter, Facebook, Reddit, HN etc will be FULL of
it (with good reason). Remember the Higgs boson?

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wbhart
The description on researchgate says "work in progresswork in progresswork in
progresswork in progresswork in progresswork in progresswork in progresswork
in progresswork in progress". It seems unlikely that the author would write
that if they really believed this was a complete work. It's just not worth
posting purported proofs of the Riemann Hypothesis. There are dozens of them.
Until someone serious comes forward and says, "we think this is a proof", it's
not.

------
powera
I'm just going to say "no way". No way that a 4-page document is the proof,
and no way it's on any site other than a university or Arxiv.

~~~
logicallee
Arxiv detracts from, does not add, to credibility. it's an open preprint
platform after all. This is like saying "No way such an important project
would be anywhere other than github." That's not much of an argument.

As for flaws, it's four pages. They can be written up in an afternoon, if the
paper makes sense to its intended audience. Of course, that's not exactly HN.

EDIT: Very interesting replies. I'll leave this up, though apparently quite
wrong.

~~~
Certhas
There are vast areas of research where every credible paper gets posted to the
arxiv. So even though being on the arxiv does not imply credibility, not being
on the arxiv implies lack thereof.

~~~
logicallee
I'm incredulous of:

>There are vast areas of research where every credible paper gets posted to
the arxiv

due to your word "every" which from context you mean literally; no exceptions.
So, what would these vast areas of research be? The statement would not be
true for any areas of research I know about.

EDIT: Thanks for the replies - fascinating. That in certain fields, no paper
is worth reading if not on arxiv.

~~~
Certhas
For the areas I used to work in for many years, high energy physics and
quantum gravity, I can't think of a single exception.

Of course I don't have total knowledge of these fields, only my corner of
them, and I'm sure you'll find a counterexample if you dig deep enough, but if
counterexamples are remarkable and rare, then the heuristic: "Not on the
arxiv, not likely to be credible" stands.

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Estragon
At the end of Lemma 2, "[9, Th. 8, (39)]" seems to be referring to corollary 1
of Theorem 8 on page 70 of [1], equation (3.30). Maybe "(39)" is meant to be
"(30)".

Their argument for Theorem 1 seems not-crazy, and quite accessible.

[1]
[https://projecteuclid.org/download/pdf_1/euclid.ijm/12556318...](https://projecteuclid.org/download/pdf_1/euclid.ijm/1255631807)

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cgrubb
The paper uses results from "Grandes valeurs de la fonction somme des
diviseurs et hypothèse de Riemann" by Robin, which is not available online, as
far as I can tell.

