Is this the end of the Riemann Hypothesis?

[neutrino]

http://www.arsmathematica.net/archives/2007/05/22/latest-on-latest-paper-on-arxiv/

A couple of months ago I linked to Tribikram Pati’s purported proof that the Riemann Hypothesis was false.

Bernhard Krötz has been working his way through the paper and posting periodic updates in the comments of that post. He has completed this project, and in his opinion the proof is correct.

I would still be surprised if this is really how the Riemann Hypothesis meets its doom, but Bernhard deserves recognition for taking the time to read the paper carefully and keeping us updated.

 

[MathematicalPhysicist]

i wonder if the mathematicians, all of whom have tried to prove the RH, how many times have they rechecked it before publishing their proof?
bacuase it seems they haven't done so.

 

[Gib Z]

Well this is actually the first time I've seen a disproof of the RH, true or false. What seems to be the error in their working lqg?

 

[MathematicalPhysicist]

well, gib I am not an expert in RH, or in anything for that matter.
but i read from the link, that some see the representation of this disproof as a poor one, not that it matters if you are right.
but if you look at the amount of people publishing their proof and afterwards take it back, then it makes you wonder why haven't them taken the time to check it for themselves, I am sure if someone can besides you can spot an error so can you, unless you are so vain that you don't see your own mistakes.

 

[Gib Z]

Sometimes its much easier to see other peoples mistakes than you own though. It's not always because of vanity. And anyway, the Reason people put their proofs of Arvix first is to get more eyes on the paper, so as many errors are seen as possible.

 

[Hurkyl]

An important thing to keep in mind is that the ideas the author can be valuable, even if they don't lead to a proof. For a historic example, algebraic number theory spawned from a failed line of attack against Fermat's last theorem.

 

[MathematicalPhysicist]

so if you already found an error, why not write a remark in the absratct that although states that there are some mistakes and the author thinks there's some value to his paper despite the mistakes.

i don't think anyone plans on doing so, cause: 1. they genuinely think that their proof is correct. 2. they haven't double/triple checked their proofs before posting it in arxiv.
there's ofcourse the possibility that mistakes will still be there, but at least you have done your best on checking it, I am not sure that everyone who publish in arxiv check enough their work before publishing, not the majority, but still some of them.

 

[tpm]

I myself wouldn't rely on any 'proof' published at Arxiv.org ... making a simple search you can find more than 100 'proofs' of RH , and about 67 'Unified Theories' and 40 'Quantum gravity theories' (unifying GR and QM) , ..Arxiv is not serious anymore and it's become some kind of 'Bill Cosby Show', i think it should be quitted.

Anyway a good evidence would come from using Post inversion formula calculating high derivatives of :

$$\frac{1}{ s \zeta (s)}$$ evaluated at s=k/t

Since Mertens function $$M(e^{t})$$ is just an inverse Laplace transform

 

[mathwonk]

a remark about arxiv.org.

essentially all papers in algebraic geometry appear there first. That makes it the one universal source for all work in the subject. It makes it unnecessary for professionals to maintain mailing lists of people to send their work to, since everyone can find it there.Thus even if lunatics post crackpot proofs on there, it still serves as a clearing house for all reliable work as well. Its just like a bookstore, Newton's Principia is right there alongside Tammy Faye Bakker's life story or the Philosophy of Eck.

You have to read it and decide its worth yourself. Refereed journals are the place to go for papers that also have been read by at least one person, and even then not necessarily for accuracy.

arxiv is a preprint server, nothing else, and very useful as such.

 

[matt grime]

Indeed, very useful. And those responsible adults who post there should not be tarred by the same brush as the cranks, crackpots, and just idiotic morons who submit preprints to the arxiv like that ex-physics forums poster, eljose, who posted utter ****e here and demeaned the good name of science.

 

[tpm]

Indeed, very useful. And those responsible adults who post there should not be tarred by the same brush as the cranks, crackpots, and just idiotic morons who submit preprints to the arxiv like that ex-physics forums poster, eljose, who posted utter ****e here and demeaned the good name of science.

It's << personal insult removed by berkeman >> to insult anyone who can't defend himself since he was banned and can not reply you...

It's very strange judging anyone with 'crackpot' 'crank' 'troll' just because he/she doesn't publish at Physica Review Letters or Annals of Mathematics ...but if someone publish "I have found God in the Bible" (Bible codes by Rips) or "We live on a 11 dimensional universe but we can't realize of it because the extra dimension are wrapped up" (String Theory) and you consider these men to be respectable , it's some another kind of Racism (legal) which we could call "elistism" , you judge only the name not the article.

 

[CRGreathouse]

It's very strange judging anyone with 'crackpot' 'crank' 'troll' just because he/she doesn't publish at Physica Review Letters or Annals of Mathematics ...but if someone publish "I have found God in the Bible" (Bible codes by Rips) or "We live on a 11 dimensional universe but we can't realize of it because the extra dimension are wrapped up" (String Theory) and you consider these men to be respectable , it's some another kind of Racism (legal) which we could call "elistism" , you judge only the name not the article.

Where do you get the idea that matt judges eljose because of where he publishes? In fact matt wrote that we should be tolerant of people who use those sources despite the crackpots who sometimes use them also.

 

[tpm]

then..why you both judge him (eljose) as a 'crackpot' ?? .. for example from historical perspective nowadays Euler and Ramanujan would be considered as crackpots, in facts Ramanujan without Hardy's help would have been starving on India, whenever you say 'you argument/idea is wrong' you must give objective arguments , not only say 'since the journal is not very known..it's clear that the author is a crackpot'

 

[DeadWolfe]

Have you read an of his stuff?

He was banned with very good reason. He was one of these people who had created an excellent quantum gravity theory, and solved multiple millenium prize problems, but every mathematically literate person in the world was consipering to keep his work hidden.

 

[CRGreathouse]

then..why you both judge him (eljose) as a 'crackpot' ?? .. for example from historical perspective nowadays Euler and Ramanujan would be considered as crackpots, in facts Ramanujan without Hardy's help would have been starving on India, whenever you say 'you argument/idea is wrong' you must give objective arguments , not only say 'since the journal is not very known..it's clear that the author is a crackpot'

Hmm, let's break this down.

Claim 1: matt grime and CRGreathouse both think eljose is a crackpot.
Claim 2: Euler and Ramanujan would be considered as crackpots.
Claim 3: Ramanujan without Hardy's help would have been starving on India.
Claim 4: Objective arguments must be given when a person is said to be wrong.
Implicit claim: matt grime was saying 'since the journal is not very known..it's clear that the author is a crackpot'

1. I certainly got this impression, though it's hard for me to tell -- eljose seemed to be more of a physicist than a mathematician, and I know little about physics. (I can't speak for matt.)
2. I dispute this. Hardy did have his initial doubts about Ramanujan, but it didn't take him long to conclude that he really knew his stuff -- less time, certainly, than it took PF to ban eljose. I can't imagine the circumstances under which Euler would have been considered a crackpot... couldn't you have at least picked Cantor or Cardano or someone like that?
3. Probably true, though he may well have lived longer like that. What has this to do with the other points?
4. I don't generally agree. This puts too much of a burden on the 'establishment' and too little on the potential crackpot. I feel rather the reverse: for a potential author to publish s/he must give compelling arguments for why s/he should be published and why h[ei]r work is correct.

I most especially contest the implicit claim about matt, as it is almost completely the opposite of what he wrote.

 

[Hurkyl]

then..why you both judge him (eljose) as a 'crackpot' ??

Because his attitude and the content of his postings satisfied the definition of crackpot.