Talk:Lindelöf hypothesis

Arxiv is not a reliable source

No matter how "highly reputable", and "internationally renowned" the author of a paper can be, Arxiv is definitely not a reliable source just by itself. Wikipedia is not "USA Today" or the "New York Times", and we will wait until a paper is accepted and published by a peer-reviewed mathematical journal before we mention it in an encyclopedia. Sapphorain (talk) 20:29, 21 April 2018 (UTC)

Moreover, a simple claim on the proof of a famous conjecture, anywhere, not backed by an actual sound proof, published in a reliable mathematical journal, does not deserve to be mentioned in wikipedia. Sapphorain (talk) 20:41, 21 April 2018 (UTC)

You are ignoring my point that there is a difference between being a reliable source for the statement that an internationally renowned mathematics professor has made a claim (which is the case here) and being, on its own, a reliable source for the statement that the said professor has proved the Lindelof hypothesis (which nobody is suggesting). You are just shouting statements without making proper arguments. Of course a claim about a proof can be encyclopaedic, and a claim that is presented as what it is - a claim - does not have to be "backed" by its accuracy. I am applying for this page to be protected to stop your vandalism.

 AlexanderTrampton (talk) 21:21, 21 April 2018 (UTC)

Rationale: user "Sapphorain" has repeatedly reverted the edit in which I referred to the claim by internationally renowned mathematics professor Athanassios Fokas that he has proved the Lindelof hypothesis. This user keeps repeating that "Arxiv is not a reliable source", ignoring the point I spelled out that there is a big difference between a) a statement that a professor has made a claim and b) a statement that his claim is true. It is obvious that the latter statement would require peer review. The former statement does not require peer review, and it is the former statement that is made here.AlexanderTrampton (talk) 21:24, 21 April 2018 (UTC)

I should clarify that Prof Fokas really is an internationally renowned professor, who is a winner of the Naylor Prize for applied mathematics and is at Cambridge University. According to his Wikipedia page, he holds at least seven honorary doctorates. We are not talking of an otherwise unknown mathematician who appears as if from nowhere to post on a website saying they have proved a famous hypothesis. The system at Arxiv is reliable enough for us to say with sufficient certainty that he has really claimed to have proved the Lindelof hypothesis and the claim was not falsely made in his name by an impostor. The issue is whether or not his making of this claim should be included here. Contrary to what user "Sapphorain" has said, there is no issue as to whether the statement that he has made the claim is itself "reliable" or not. Nor does the statement that he has made the claim need to be backed by a statement that the claim is true. Nobody is arguing that this article at Wikipedia should contain the assertion that the claim is true. For all I know, it may happen that his claim fails the peer review process, which, given his status and the importance of the Lindelof hypothesis, may itself be encyclopaedic if it occurs. AlexanderTrampton (talk) 21:57, 21 April 2018 (UTC)

 Not done: Not protected page.. Galobtter (pingó mió) 05:16, 22 April 2018 (UTC)

Galobtter - Well the vandalism has stopped for the moment, but for all we know it may soon start again, given that the page is not protected, in which case a managerial button-click yielding the words "Done. Protected page" will be required, preferably with typed words showing an understanding of the issue raised, rather than a managerial button-click yielding the words "Not done. Not protected page". AlexanderTrampton (talk) 09:18, 22 April 2018 (UTC)

To have as the first section of the page an exclusive mention of Fokas’s claim is both giving undue weight to this particular claim and giving undue weight to such claims altogether. It is I think quite sufficient to have a small section near the end of the page, mentioning that several claimed proofs have been published over the years. I wrote such a section, in which a note provides a link to some of these claims (on ArXiv), including Fokas’s. Sapphorain (talk) 19:01, 22 April 2018 (UTC)

It is patently obviously absurd to put a claim by such an internationally renowned professor on the same level as the numerous claims of proof by mathematicians who have previously been known for little or no peer-reviewed work. This claim should rightly be given more weight than previous claims. If you can find a single claim of proof of the Lindelof Hypothesis made by any other professor of mathematics at one of the world's top 10 universities, or even the top 1000, who has won so many prestigious awards, then please do edit to give their claim the same prominence as Fokas's claim. I have restored the section, but moved it to the end of the article.AlexanderTrampton (talk) 00:05, 23 April 2018 (UTC)

It is premature and inappropriate that the page convey such an information, devote a whole section to it, stresses the fact that the claimer is famous, and adds pleonastic verbiage about the hypothesis loosing its hypothesis status if and when it is verified. I understand your enthusiasm but Wikipedia is not a tabloid, it is an encyclopedia. Sapphorain (talk) 06:52, 23 April 2018 (UTC)

My point was not that the claimant is "famous". And explaining that a proven hypothesis becomes a theorem, which would be inappropriate in a scholarly journal, is highly appropriate for this website in which articles are written for the lay reader. If there is pleonasm, it is in your use of the phrase "if and when", although I understand that you may wish to emphasise what you are typing. I have learnt that you frequently participate in spats at Wikipedia; please can you desist now. It is not the accepted rule here that claims of proof should not be referenced in articles (which you imply when you use the word "premature"); nor is it a rule that claims by all persons must be given equal weight. I have taken on board your opinion that the reference should not go at the beginning, and I have therefore moved it to the end. AlexanderTrampton (talk) 09:56, 23 April 2018 (UTC)

Unfortunately Sapphorain has again edited without giving an explanation here, posting material that mentions Professor Fokas's work but only in the context of previous claims that have not been accepted. The point for which I have offered support and to which Sapphorain does not respond, namely that the Fokas 2017 claim should be given much more weight than previous claims - even if it is found to be unsound - still stands. I have amended this section accordingly, and hopefully there will be no need for further edits.AlexanderTrampton (talk) 13:29, 23 April 2018 (UTC)

I have just seen the ill-toned comment Sapphorain supplied with his edit. I am trying to suppress my irritation at being told what should and should not be included by a poster who misuses apostrophes, posts run-on sentences, calls an explanation for lay users of how a hypothesis becomes a theorem "useless verbiage" (despite having had the reason for its appropriateness explained to him in simple language), types "Fokas" as "Focus", and needed to be taught that whereas the accuracy of a claim requires acceptance by peer review, the existence of a claim does not - advice for which he has not even shown the courtesy of saying "thank you". But anyway I have amended his latest edit, am aware that I will not get the time back that I have spent dealing with the vandalism, and hope that this will be an end to the matter, while fearing that it will not be.AlexanderTrampton (talk) 14:18, 23 April 2018 (UTC)

I have reverted your edit for the following reasons. (1) «  while several proofs and disproofs have been claimed » is not sourced anymore, and as such it is weasel words; in fact only « severals proofs » is sourced so far, in the version I restored. (2) «  most of which have been found faulty » is probably true, but not sourced. (3) «  the first claim of a proof to be made by a world- leading… » etc, is vague and not sourced (what is « a world-leading mathematician »?). (4) In fact «  a world-leading mathematician » is another weasel word. It should be avoided here; it is quite sufficient to mention Prof. Fokas is at Cambridge University. Sapphorain (talk) 15:12, 23 April 2018 (UTC)

Not every statement needs to be sourced, and in fact not a single one of the statements in your own edit are sourced, except for the fact that Prof Fokas has claimed to have proved the hypothesis, for which I was the one who provided the source. "World-leading mathematicians" may not be capable of precise definition, but I assure you that nobody would use a definition that does not include a professor at Cambridge University who is so highly cited, has won the Naylor Prize, and so on. I will now revert. Please leave it be now. You may have time on your hands, but there is no need for an edit war. You are misusing the term "weasel words" and your actions suggest a lack of good faith. "Weaselling" might be defined so as to include certain types of specious reasons offered in justification of unhelpful edits. I am not going to explain at length to you the relevance of why "not accepted" is just as unsourced as "found faulty".AlexanderTrampton (talk) 16:24, 23 April 2018 (UTC)

Rationale: user "Sapphorain", ignoring advice, persists in trying to minimise the importance of the fact that in 2017, for the first time in the history of mathematics, a leading mathematician has claimed to have proved this hypothesis.AlexanderTrampton (talk) 16:28, 23 April 2018 (UTC)

I have no idea what you're trying to do with this (do you understand what a protected page is?). If you want the page protected go to WP:RFPP. Both of you, AlexanderTrampton and Sapphorain stop edit warring over this! And Alexander, stop calling his edits vandalism. Galobtter (pingó mió) 16:36, 23 April 2018 (UTC)

Sorry - I got as far as your insolent question. I won't read any further. Stick this website up your arse. Please delete my account. My time is valuable. Goodbye.AlexanderTrampton (talk) 16:47, 23 April 2018 (UTC)

Outside comments

As someone with a lot of experience in the math project and no stake in this article:

1. Many famous mathematicians claim to prove things. Many of these claims turn out to be wrong, and many turn out to be right. The fame of the mathematician is not on its own a deciding factor - there is also the question of whether other mathematicians comment online to say the proof is flawed, as happened with the recent claim of P ≠ NP. [1] These may lead us to not mention a preprint even if the author is famous.

2. When there is a preprint on an open problem that is of unusual interest, we usually just say "XXX has claimed to prove YYY" with a link to the preprint. There is little benefit from us editorializing about preprints.

3 Arxiv is not a reliable source for claims about math directly, but it is a reliable source for claims like the one quoted in the previous sentence; cf. WP:PRIMARY

— Carl (CBM · talk) 16:49, 23 April 2018 (UTC)

I made a few edits to achieve a similar thing on this page and integrate the reference into the style of the other references. — Carl (CBM · talk) 17:01, 23 April 2018 (UTC)

Thanks. Sapphorain (talk) 17:05, 23 April 2018 (UTC)

For what it's worth, I'm happy with the section as it currently stands. Note that Fokas first claimed to have proved the Lindelof Hypothesis in what is described as the second version of his article at Arxiv, published in November 2017. It is the third version that is from the current year, 2018. The first version contains a proof not of the Lindelof hypothesis but of a close variant of it, as stated in its title. The second and third versions also contain that proof, but in those versions he states that he has got from there to a proof of the Lindelof hypothesis itself. So far he has not stated in detail how he gets from the proof of the variant to the proof of the hypothesis, and he indicates that he will show that step in a subsequent article, written with co-authors, already at Arxiv but under preparation and not for public view.AlexanderTrampton (talk) 17:17, 23 April 2018 (UTC)

So in short: he claims he has a proof, but didn’t write the details, and is now working on it with colleagues. Why in the hell do we have to mention this in Wikipedia?! Sapphorain (talk) 18:52, 23 April 2018 (UTC)

It's a balance, but our common practice has been to mention "particularly prominent" claims about proofs of important problems. But our pattern has been to mention these claims in a very brief and neutral way - just a short sentence linking to a paper. The reader is then able to evaluate the overall situation independently of us.

At the same time, we do not normally mention someone's affiliation when we name them - we let the link to their biography handle that. So we should follow the same here, rather than going out of our way to mention the affiliation that Fokas holds. Anyone who wants more info can click to get it. — Carl (CBM · talk) 11:01, 24 April 2018 (UTC)

The current version of that section is fine by me. The reason I put in the reference to Cambridge University was because Sapphorain was not taking on board that a proof claim made by someone of Fokas's stature is worthy of mention whereas many of the claims to have proved famous hypotheses that are made by mathematicians who have published little or no previous influential work are not. But as you say, if people wish to know why Fokas's claim is worthy of mention then all they need to do is click. AlexanderTrampton (talk) 18:19, 24 April 2018 (UTC)

Please do not delete the section on Fokas's claimed proof

This was removed again by the same user who kept removing it earlier. I have restored it. — Preceding unsigned comment added by AlexanderTrampton (talk • contribs) 22:30, 8 June 2018 (UTC)

While I agree with Carl's comments above, I don't think this case yet rises to the level where we should even mention it. I have seen too many papers by prominent mathematicians making claims "to be fleshed out" in a follow-on paper, only to have no such paper ever appear. I think that Sapphorain correctly removed the comment for reasons that are in accordance with Wikipedia policies and we should wait on this until an actual paper exists.--Bill Cherowitzo (talk) 22:52, 8 June 2018 (UTC)

Were any of those papers by mathematicians as prominent as this one with claims to have proved theorems as important as this one? Sapphorain's action was not correct. He had removed the section several times before and the matter was ironed out in talk. If he had anything new to say he should have said it in talk, not just done the same action again and given the same reason that he gave before. Matters concerning Arxiv and peer review have already been explained to him but he has not listened. AlexanderTrampton (talk) 00:20, 9 June 2018 (UTC)

So I am asking for examples of those papers matching or exceeding this one on the two prominence criteria, and for references to what Wikipedia policies would be breached if this section stays. There is no policy that bans all mention of claimed mathematical proofs or proofs that have not been peer-reviewed. Grigori Perelman published his proof of the Poincaré conjecture in the Arxiv. AlexanderTrampton (talk) 00:24, 9 June 2018 (UTC)

Why do you say you agree with Carl's comments? How about "we usually just say 'XXX has claimed to prove YYY'"? Can you please justify your opinion about this claim being at too low a level to justify being mentioned. AlexanderTrampton (talk) 00:29, 9 June 2018 (UTC)

As is easy to check, I did not in any way remove the section on this alleged proof by Fokas. This was already done before by another contributor. I only removed a reference to an ArXiv paper which, being all by itself, was not acceptable in the article. Sapphorain (talk) 06:40, 9 June 2018 (UTC)

I stand corrected and I apologise, and I realise now that you removed only the reference and not the section. The reason I wrongly thought you had removed the section itself was that I saw that it had been removed and I saw your comment when removing some text that "Arxiv is not a reliable reference; it may become a convenient source, but only after the paper is published in a reliable journal", and I assumed that the text you had removed was the section. Only I am at fault for that. Nonetheless your comment goes against what was agreed. It would have been better after the section was removed to restore it rather than to remove the reference. I have restored both the section and the reference. Arxiv is a reliable reference for the assertion that a claim of proof has been made. It is unfortunate that one is having to repeat that. AlexanderTrampton (talk) 18:12, 9 June 2018 (UTC)

Fokas' paper has been updated on June 19 with a new title. The new version no longer claims to have proven the conjecture. As a result, I have simply removed all references to Fokas' claims from this wikipedia article. For what it's worth, let me add that I don't think these claims should have appeared on wikipedia in the first place. If the claim had been prominent, it would have generated at least some interest from the mathematical community which could be objectively deduced, other than the presence of the preprint itself, i.e. there would be references to the preprint in other papers, talks, reading groups, etc. As far as I can see, both claim and retraction basically passed unnoticed. 94.66.58.97 (talk) 03:14, 26 June 2018 (UTC)

You're mistaken. The 19 June update not only contains a repetition of his claim to have proved the hypothesis; it also contains further information about his proof. How come you thought otherwise, and you were so sure as to remove material from an encyclopedia on that basis? Next time you think you might be justified in removing material, please ensure that your premise is actually correct - especially if you hold a minority view that the original inclusion was unjustified for some other reason.AlexanderTrampton (talk) 02:16, 29 June 2018 (UTC)

A claimed mathematical proof is of little interest, Prof. Albeverio made similar claim

In https://arxiv.org/pdf/1010.3374.pdf Prof. Albeverio (http://www.hcm.uni-bonn.de/people/profile/sergio-albeverio/) has claimed as well to have proven the Lindelöf hypothesis. And he has more credentials. I believe we shouldn't mention neither Albeverio, nor Fokas. I am a mathematician. Albeverio has substantially more credentials than Fokas by the following criterium: number of peer-reviewed publications in the area of number theory or complex analysis. Also, calling Fokas "world-leading" is a mistake. He is not. In mathematics, there should not be given a lot of value to claims. A Google search, for example, reveals numerous claimed proofs, both FOR and AGAINST the validity of the Riemann hypothesis. — Preceding unsigned comment added by 2A02:586:3909:B400:6518:EE93:1959:9397 (talk) 07:59, 28 June 2018 (UTC)

That someone else made a claim does not mean claims are of little interest. It will come as no surprise to those working on the Riemann or Lindelof hypotheses if one or both of them are proved by those who have hitherto been working in one or more areas of mathematics previously thought to be unrelated to those hypotheses. Three days ago the University of Southern California formally announced the proof in a press release, which I will cite when I amend the article. AlexanderTrampton (talk) 01:57, 29 June 2018 (UTC)

The proof of the hypothesis has now been formally announced by the University of Southern California

...in its press release of 26 June 2018. Despite this, we have certain users of Wikipedia

• who are suggesting that the 19 June 2018 version of the paper at Arxiv, which actually contains further information about the proof, in fact provides grounds for removing the reference to Fokas's work;
• who have wrongly claimed that Fokas no longer claims to have proved the hypothesis;
• who have claimed that Fokas has won most of his prizes in Greece as if that makes him non-notable;
• who claim that Fokas is not "world-leading", appearing to be ignorant of the fact that he has appeared on the ISI's Highly Cited Researchers list;
• and who have even removed a reference here to the USC's press release in which the proof was formally announced.

I am finding it difficult to understand what good cause there could be for such actions. Please stop vandalising this article and posting specious justifications. AlexanderTrampton (talk) 02:11, 29 June 2018 (UTC)

I disagree. There are a couple of red flags, which should make us wait to mention Fokas' claim, until it is supported by experts (e.g. via a peer-reviewed publication).

• Red flag 1: He says in his abstract's first sentence that Lindelöfs Hypothesis is "one of the most important open problems in the history of mathematics". This is simply untrue, and sounds like someone wanting to push his own fame. I have never seen a successful mathematician do this. By the way, the true statement would be "an important and likely extremely difficult problem in the area of analytic number theory".
• Red flag 2: He himself says in his paper "The completion of the rigorous derivation of the above results will be presented in a companion paper." So we have simply a mathematician stating that he proved something, but has not provided the full proof yet, so verification is not even possible.
• Red flag 3: Lack of papers in related areas
• Regarding your claim that he is "world-leading": Can you provide a link to this ISI list? It would be helpful to know in which place he is, among how many people, and with regards to which subarea of mathematics. — Preceding unsigned comment added by 2A02:586:3909:B400:F00F:8C70:E730:19C8 (talk) 07:23, 29 June 2018 (UTC)

These aren't red flags at all. If you dislike Fokas for some reason, you should stand aside or try to put your personal feelings aside. You are implying he is not a successful mathematician because you personally are not aware of any successful mathematician who has referred to a problem as being among the most important in the history of mathematics. That is absurd, and I will not discuss the matter on that level. Similarly with your previous assertion that Fokas is not world-leading because most of his prizes have been Greek and also with your innuendo regarding pure and applied mathematics. The ISI publishes a list of Highly Cited Researchers each year. I do not know the exact years when they have included Fokas, but the fact that he has been included on an ISI HCR list is widely referenced by numerous reliable sources on the web. The lists for years other than the latest year seem not to be so easily downloadable since Thomson Reuters sold Thomson ISI to Clarivate in 2016. If you believe that the distribution by nation of Fokas's many prizes, your apparent lack of familiarity with his work in complex analysis, your apparent lack of familiarity with the work done in the field of asymptotics and elsewhere in "applied" mathematics to increase understanding of the Riemann zeta function, and so on, taken together, constitute a basis for suspecting that in fact he has never actually been included on any ISI Highly Cited Researchers list, despite the numerous references in apparently reliable sources to the contrary, you should try to get hold of the lists for all available years, search for the name "Fokas", then report your findings back here.

There may well be a reasonable case for referring only to the claim of proof, given that the full proof has not been published. So why not amend to that affect? Perhaps we will then reach consensus. Please stop removing all reference to Fokas from this article. Thanks. AlexanderTrampton (talk) 11:32, 29 June 2018 (UTC)

V3 of Fokas paper stated that « It is possible to obtain the Lindelöf hypothesis ».

V4 doesn’t anymore claim a proof of the hypothesis, but proofs of an asymptotic identity that only « suggests the validity of Lindelöf hypothesis » . Moreover, the abstract also informs us that « The completion of the rigorous derivation of the above results will be presented in a companion paper ». So in fact the paper only contains results suggesting that the Lindelöf hypothesis might be true, and the said results are not even rigorously proved in it. And in top of that, we don’t even know if this companion paper already exists.

As of the so called « Press release », it is by the School of Engineering of USC, and not by the Mathematics Department, which doesn’t even mention the issue.Sapphorain (talk) 11:12, 29 June 2018 (UTC)

In mathematical work, "suggest" without "may" does not mean what you think it means. What relevance do you wish to give to the fact that the press release was issued by the university's School of Engineering rather than its Department of Mathematics? It is at the former that Fokas currently holds his USC chair. AlexanderTrampton (talk) 11:32, 29 June 2018 (UTC)

I am a mathematician, working in number theory, and I have a pretty good idea of what the verb suggest means when used by a mathematician: if one comes up with a reasoning suggesting some assertion is correct, it at best means that the reasoning provides a heuristic argument towards the truth of the assertion, and not a rigorous proof of it. Sapphorain (talk) 12:00, 29 June 2018 (UTC)

The statement by one of the universities where this professor holds a chair and his own statement that "the completion of the rigorous derivation of the above results will be presented in a companion paper" make clear that he is not using the word in the sense you are familiar with. The word "will" coming from the pen of a mathematician of Fokas's stature is a restatement of the claim. The sheer amount of effort put into minimising the importance of this claim that has now been amplified by a formal satement by a university is extraordinary. A number of famous proofs by leading mathematicians have been announced first elsewhere than in peer-reviewed journals. Consider for example Andrew Wiles and Fermat's Last Theorem, and Grigory Perelman and the Poincaré conjecture. AlexanderTrampton (talk) 12:26, 29 June 2018 (UTC)

You are (deliberately ?) mixing up two different statements in the abstract of version 4 of Fokas paper. The results for which Fokas announces a rigorous derivation in a companion paper does not imply the Lindelöf hypothesis. It it an assertion that will at best (even if and when rigorously proved) be a good heuristic argument in favour of the validity of the Lindelöf hypothesis. Sapphorain (talk) 14:04, 29 June 2018 (UTC)

In private communication to me, Fokas confirmed Sapphorain's understanding. @AlexanderTampton: You understood it wrongly (just ask him). There is no proof yet. Fokas is precise in his paper. He says "suggests". You are doing a disservice to Fokas, by putting words in his mouth. The press release is not correct. You somehow got very involved into that - I don't know why. I have done analytic number theory, and the way you talk about it (and mathematics) suggests that you have no understanding on that topic. You should better go edit some other places on Wikipedia, where you better understand what is going on. — Preceding unsigned comment added by 2A02:586:3909:B400:F00F:8C70:E730:19C8 (talk) 14:06, 29 June 2018 (UTC)

Thanks for this. But I was not going just by my reading of it, which may well have been wrong. (By the way, if you assumed that my personal view was that the proof was correct, or that Fokas would ever prove this hypothesis, or even that the hypothesis was true, you would be mistaken.) I was also going by the fact that in March 2018 Fokas published an article entitled "A Formal Proof of the Lindelöf Hypothesis". Despite what some have suggested, so far he has not publicly rowed back to say that further to what he said in March he has now realised that he was mistaken and that he has yet to reach a proof. If that had happened, it would be sufficiently noteworthy for mention here: "Prominent mathematician Fokas claimed to have proved the Lindelöf hypothesis. Then he withdrew his claim. He says he made a mistake and is still working on it. (Or he says he realises he was barking up the wrong tree and has given up.)" In fact, his department said only a few days ago that he HAS proved it. You are some guy on the internet who says you have a good private source for the contrary. That's fine. You may well have. But that's not the kind of source that gets encyclopedia articles written. Statements by universities are. I am not putting words into anybody's mouth. This guy has been quoted by his own department! You may be aware that it is actually very rare for a mathematics department to say that one of its professors has proved a famous hypothesis and then for him to say privately otherwise. If you are an associate or acquaintance of his, and you are posting in good faith, I suggest you advise him to instruct a withdrawal of the press release. The press release is causing a lot of the confusion here. My use of it is perfectly in keeping with policies here at Wikipedia. Until it is withdrawn, we should not assume it is misleading and based on a misreading just because you say so. Ask Fokas to instruct its withdrawal for reason of inaccuracy or, if appropriate, to instruct the issue of a followup notice saying what the exact score is: he hasn't proved it, he hopes to at some point, he has given up, he thinks he has proved it but is still checking, he no longer cares whether it is true or false, he is retiring and leaving the work to others, he may make a further statement in a year's time, or however else he wishes to phrase or explain the actual position. Until that time, we go by the press release, OK? We do not go by your interpretation citing a private source. AlexanderTrampton (talk) 16:33, 29 June 2018 (UTC)

Fokas's claimed proof

I have now edited back so that Fokas's claimed proof is referenced and the USC statement is cited. There is insufficient cause to describe the proof as correct: that will have to wait for peer review, which may find it correct or incorrect. But ample grounds are marshalled above for mentioning its existence. AlexanderTrampton (talk) 15:05, 29 June 2018 (UTC)

Once again: Fokas is not claiming anymore a proof of the conjecture; all what peer-review can provide (about this yet non existent article) is the correctness of a related result which will not be the verification of the conjecture. Sapphorain (talk) 15:17, 29 June 2018 (UTC)

Can we attempt to reach a consensus please, based on publicly verifiable sources? Can we start at the beginning. Fokas claimed in a paper to have proved the Lindelöf hypothesis. Fokas's department a few days ago then issued a statement saying he had proved it. Do you accept that those two sentences are accurate? There was a consensus here that his claim was sufficiently noteworthy, for reasons including his prominence, for mention here. Subsequent events cannot affect that. What are we disagreeing about? If he publicly says he no longer believes he has proved it, that should be mentioned here. What are you trying to argue? Wikipedia works on the basis of publicly verifiable sources. In view of the confusion, if anybody taking part in these squabbles really is in touch with Fokas, and if it is true that he does not believe he has proved the hypothesis, then they should ask him to have the press release withdrawn. That's the least he can do. It will be better still if he gets a followup issued. We should go by the publicly verifiable sources we have got. AlexanderTrampton (talk) 16:43, 29 June 2018 (UTC)

The article as it is says that Fokas says he proved the hypothesis, and that the USC said he said that. That is wholly accurate, impartial, neutral, without a point of view. Your interpretation may well be right that in the latest version of the Arxiv paper he does not say he has proved it. That is of course different from saying that contrary to what he first said he now believes he has not proved it. But interpretations are not what Wikipedia is meant to be based on, any more than private sources are. I have been spoken to here in a patronising way by a few individuals who are clearly in an arrogant mood or have their backs up for some reason, but please just leave the article as it is until further clarification is available in public sources. That this guy said he proved it does not stop becoming noteworthy because of later events, but the later events may well themselves be noteworthy. AlexanderTrampton (talk) 16:56, 29 June 2018 (UTC)

There is a thread at Math Overflow which some here may find of interest. AlexanderTrampton (talk) 16:59, 29 June 2018 (UTC)

In the Wikipedia text it should be mentioned that Forkas replaced his initial statement of having proved Lindelöf, by saying that he has proved something which suggests that Lindelöf is true. It would be unfair, if we sticked to what he said in the past, as he has come now to a different conclusion. -DX — Preceding unsigned comment added by 2A02:586:3909:B400:F00F:8C70:E730:19C8 (talk) 18:30, 29 June 2018 (UTC)

When Wiles announced the proof of Fermat's theorem, this was a huge event, written about in the New York Times. When Perelman posted his papers on the arxiv containing his proof of Poincare, this immediately attracted the attention of many mathematicians. Nothing remotely analogous happened here. As far as I can see, (1) the posting of Fokas' paper in August, (2) its reposting in November with a new title, where it first claimed in its abstract to contain a proof of Lindelof, and finally, (3) its reposting as v4 on June 19 with yet a new title and where the claims of containing a proof were removed from the abstract, all these events remained essentially completely unnoticed. The only thing that generated any discernible noise (some chatting on online discussion sites) is a press release from the USC engineering school. I don't believe that these type of press releases, which experienced people immediately recognize as self-generated publicity, are of themselves sufficient to discuss the work on wikipedia. Moreover, the press release claims that a solution has been published on the arxiv, something we all agree is manifestly false. No one currently claims that the arxiv preprint in its current form contains a claimed solution to the Lindelof hypothesis. At best, Fokas may currently be claiming that in a future paper, he plans to give a solution, but even here, it is not clear that he is referring to the full conjecture. It would be unfortunate (for Fokas especially) if this messy situation had to be spelled out in detail in this wikipedia article. That's why it is really preferable to simply delete.131.111.185.9 (talk) 19:38, 29 June 2018 (UTC)

Can you explain why you call a paper entitled "A formal proof of Lindelöf's hypothesis" a "reposting" of a paper entitled "A formal proof of a slight variant of Lindelöf's hypothesis", as if the titles did not suggest that they were momentously different papers, rather than the second being a "reposting" of the first? And please can you cite the exact place where you think the abstract of the November 2017 version claims that that document contains a proof of Lindelöf. (It does not claim any such thing). Whether anybody likes it or not, the press release ADDS to the reliability of the statement that Fokas claims to have proved Lindelöf.

But I agree with much that is in the second part of what you write here. The situation is indeed messy and the press release is not at all well written and it contains the error that you point to. But articles here at Wikipedia must be based on reliable public sources, not on private information. It is true and it is verifiable from public sources that Fokas has claimed to have proved Lindelöf. The only question then is his stature, which is sufficient. There has been no publication of the full proof, and no peer review as far as we know. That's all that I'm saying should go in the article. Fokas may find it embarrassing, but so what? At Wikipedia we should not remove statements that meet all the usual criteria simply in order to save a person from mild embarrassment or indeed to cause them embarrassment. Everybody makes mistakes sometimes. Andrew Wiles was mistaken when he first announced he had proved Fermat's Last Theorem. In this case I have no idea why Fokas did it publicly in writing before a successful peer review, but he did it. I can appreciate that your motives are good, but you are missing something about Wikipedia and I suggest you might achieve something that helps improve things from your point of view AND that also helps improve Wikipedia if you devote your efforts to encouraging Fokas to get Daniel Druhora or the USC to pull that press release. At the moment - I know I keep repeating this - it is a reliable source for the statement that Fokas claims to have proved Lindelöf. He has not withdrawn his claim anywhere in public. If a retraction appears in a reliable source - perhaps another press release - that too will be worthy of mention here. It is not every day that a mathematician of his stature claims to have proved a hypothesis that is so well known, or retracts his claim. But Wikipedia is not a crystal ball and in Wikipedia terms it matters little NOW what happens next. AlexanderTrampton (talk) 21:09, 30 June 2018 (UTC)

I strongly suggest you spend your energy about something else than Lindelöf’s hypothesis, and in fact, if possible, in a subject having nothing to do with mathematics. This will be better for you, for the other contributors, and for wikipedia in general. Sapphorain (talk) 21:28, 30 June 2018 (UTC)

I believe it's you who could do with some personal advice. I realise you find it hard to back down from your original misunderstanding that "Arxiv is not a reliable source", even after it had to be explained to you multiple times that the document was being cited as a source for the making of a claim and not for the truth of the claim. Now you repeatedly act in bad faith, including by removing a section from the article ostensibly for the reason that "everything" in the edit that added it was "wrong" because you wrongly thought a link to a front page for a collection of versions of articles at Arxiv was a link to one of the versions. You have wasted so much time. I would advise you to go elsewhere for personal development reasons, but many places that have better rules regarding behaviour wouldn't want you. Stop fouling up this article for specious reasons. If you want to improve your contributions, address points made in the discussion like a serious adult. AlexanderTrampton (talk) 00:34, 1 July 2018 (UTC)

 Administrator note This page is not currently protected. — xaosflux ^Talk 00:49, 1 July 2018 (UTC)

Sorry but I thought I had applied for protection. How do I do that?

Users Sapphorain and some others who may be the same as each other keep removing the section on the claim by Professor Athanassios Fokas to have proved this theorem. Sapphorain's grounds are clearly specious. Other users seem to be motivated by a wish not to cause Fokas embarrassment. But there are verifiable and reliable sources for his having claimed to have proved this theorem. What will happen next - he finds that he hasn't proved it, or a peer-reviewed proof is published and a report appears on the front page of the New York Times, or something else - I have no idea, but Wikipedia is not a crystal ball and so that question is not relevant. AlexanderTrampton (talk) 00:42, 1 July 2018 (UTC)

Edit: to judge from Sapphorain's talk page, he or she appears to indulge in frequent disputes, often accusing others of vandalism, and has been warned to desist from attacking other editors. The antisocial behaviour hasn't reached the threshold of meriting exclusion but it has continued for years. AlexanderTrampton (talk) 01:19, 1 July 2018 (UTC)

I have now applied for semi-protection. Could the administrator who reviews the dispute please take a look at the users who have removed the section. As well as Sapphorain they include the following users:
2a02:586:3909:b400:f00f:8c70:e730:19c8 (Athens)
94.71.132.212 (Athens)
131.111.184.3 (Cambridge)
131.111.185.9 (Cambridge)
31.221.56.70 (Southeast England)
109.176.95.172 (Southeast England)
132.205.229.213 (Montreal)
My guess is that investigation as to whether some of these are socks might be fruitful. AlexanderTrampton (talk) 02:06, 1 July 2018 (UTC)

I am a bit miffed that you have omitted my revert of your addition on June 8 (and comment on this talk page above). You have provided a perfect example of why we should not and do not consider ArXiv preprints to be reliable sources from (and here I disagree with Carl) anyone. The claim has been withdrawn, the press release has been modified to reflect that and this is no longer of any interest to anyone. You have been one of the most disruptive editors that I have seen in a while. This nonsense has to stop. --Bill Cherowitzo (talk) 03:41, 1 July 2018 (UTC)

Why do you persist in not acknowledging the difference between accepting an article at Arxiv as a verifiable source for a claim and accepting it as a verifiable source for a statement's veracity? The claim has not been withdrawn, and even if it had been withdrawn that would not make it without interest. Moreover, I was the one who suggested that some people might wish to encourage the amendment of the press release, and I was also the one who amended the section so that it mentioned the amendment.

The claim is of interest to many people, including mathematicians at Math Overflow, Fields Medal winner Terence Tao and a number of contributors to the highly-regarded comments section at his blog, and some contributors at Reddit

I did not mention your reversion because I did not notice it among all the one-off blankings by IP contributors and I have not got time to ensure that my contributions here are fully comprehensive. However I have made some serious points which are in keeping with standard Wikipedia policies (for example concerning reliability, verifiability and prominence) and which are not getting addressed by the trigger-happy blankers. Practically all of my points have been rubbished, including by contributors who have speciously claimed that Fokas is not particularly prominent, or that most of his prizes have been Greek, who claim he may withdraw his claim (which is irrelevant) or that he has withdrawn it (which is not true), or who paint his claim as comparable to the dozens that have been made by mathematicians who are poorly known. Please set out a proper argument using premises, logical reasoning and conclusions and not using words such as "nonsense" and "disruptive" or taking sideswipes at those who disagree with you in such a way as to convey that you yourself believe that you have insufficient skills at argument to participate. That is how we should reach a consensus. Argue properly and you may be persuasive. Address your opponent's points. If you wish to be taken seriously, to raise your game, please contribute below in the section I have created entitled "Proposed section on claimed proof by Fokas". Thank you. AlexanderTrampton (talk) 11:05, 1 July 2018 (UTC)

Article protected

I have protected the article from editing for a month since the content dispute over if/how to present Fokas' claim has led to recent edit-warring. Though the discussion in the above sections has turned somewhat heated and personalized, as an external viewer I see all the involved editors (including the ones contributing anonymously) acting in good faith. Therefore I'd recommend them to try to arrive at a consensus among themselves as to what the current Fokas claim is, and if/how it should be included in the article. If needed, drop a note at WT:WPM, or use one of the dispute resolution processes, to get outside opinion.

Once the editors' reach a consensus, I'd be happy to unprotect the page before the month is up (and any other admin is welcome to do so without consulting me). Cheers. Abecedare (talk) 06:51, 1 July 2018 (UTC)

Given that the discussion below appears to be at a stalemate, I have requested external input from Wikiproject Mathematics' members. Abecedare (talk) 04:16, 2 July 2018 (UTC)

Proposed section on claimed proof by Fokas

Thanks, Abecedare for protecting the page at my request. Here is the section I propose to include. The basic argument is that Fokas is a sufficiently prominent mathematician for his claim to have proved this hypothesis to merit mention on its Wikipedia page. It does not matter that his proof may turn out to be incorrect, or that he may be "embarrassed" to have it mentioned here at this time. What matters is that there are reliable and verifiable sources for it (for the claim of proof, not for its truth). If anyone wishes to suggest amendments, or to propose non-inclusion, please can you say why below.

Claimed proof by Fokas

In November 2017, Athanassios Fokas claimed to have proved the hypothesis,. In June 2018 the University of Southern California reported his claim but then it amended its report a few days later to refer only to his introduction of a new methodology that suggests a solution. His proof has not yet been evaluated through peer review. AlexanderTrampton (talk) 11:05, 1 July 2018 (UTC)

References

I have initiated dispute resolution here, paging in the following users: AlexanderTrampton, BillCherowitzo, Sapphorain, 2a02:586:3909:b400:f00f:8c70:e730:19c8, 94.71.132.212, 131.111.184.3, 131.111.185.9, 31.221.56.70, 109.176.95.172, 132.205.229.213, Jay7yagi, CBM. Sorry if I've missed anybody. Everyone is welcome to participate in the effort to reach a consensus. AlexanderTrampton (talk) 12:12, 1 July 2018 (UTC)

It is almost superfluous now, but let me just repeat one more time why this should not be included. I completely agree that in November 2017, at least reading literally the abstract of v2 of his preprint, Fokas was claiming to "have proved" Lindelof. (Let me add however that at that time this did not attract any attention by experts in the field because the claims were not considered to be particularly credible. Thus, in this sense, the claim was not objectively "prominent", whatever your perception of the "stature" of Fokas.) If we are indeed to understand v2 as a claimed proof, however, we can only understand v4 as a retraction, as the abstract makes clear that the paper no longer is claimed to actually contain a proof. (Again, however, I do not think the retraction per se was wikipedia-notable, as, just like the original claim, it failed to attract any attention by experts.) The only thing that generated some attention, at the level of math online discussion groups that is, is the USC engineering school press release, which appeared after the retraction had already taken place but still referred to Fokas as having "solved Lindelof". This press release has now been amended so as not to refer to a claimed proof. Thus, it is now a non-story. Needless to say, were it necessary to explain these non-events on wikipedia, your proposed section is still inaccurate, not referring to the change in the abstract withdrawing the claim, and containing the sentence "His proof has not yet been evaluated through peer review," suggesting that there is a claimed proof available which could in principle be evaluated through peer review but just hasn't yet. Such a claimed proof simply does not exist. I really wish the best of luck to everyone hoping to prove Lindelof hypothesis in the future, including Fokas. In the meantime, does their really have to be a section on a wikipedia page based on a few days of confusion on some online discussion groups stemming exclusively from a now retracted press release from USC engineering school? 131.111.184.3 (talk) 12:41, 1 July 2018 (UTC)

Thanks for your contribution. Please don't feel it's superfluous. It's welcome. This discussion is where hopefully we will reach a consensus. I would make the following comments.

First, that something is not considered particularly credible cannot be a reason why it does not attract attention. It needs to attract attention to be considered anything. And anyway whether the claim is considered credible and by whom is not of overarching importance here. The claim certainly has been considered of interest by many mathematicians, as the evidence I have cited from Math Overflow, Terence Tao's blog and Reddit shows.

Second, v2 does not contain or constitute a "claimed proof". It contains a claim of proof. And v4 is not a retraction. You may wish to take it as a retraction but that would be your interpretation only, and in my opinion it would be a highly tendentious one. Did you watch Fokas's lecture in which he discusses his recent work on Lindelof? That's the first time he has discussed it at a lecture in Britain. Start at 38 minutes in.

Third, it does the "removal" case no good to use such phrases as "non-events". These are real events, and we are supposed to be discussing whether or not to include a section about them here. You are entitled to your view that it would be better not to include such a section, but why "argue" for that view by calling them "non-events"? I think you are doing yourself a disservice. Either you should argue in a less emotional way or you should consider that perhaps your opinion should be revised and perhaps you should suggest some kind of compromise. I think we should endeavour to cooperate.

Fourth, I accept your point about the possibly misleading effect of the statement in the draft that the proof has not yet been evaluated. You are right to say that that might suggest to some readers that the proof is available or that it has been submitted to a journal or sent out to reviewers. Would you be happy with a formulation that says "His proof has not yet been either published or evaluated by peer review? The section would then look like this (with the four references kept exactly as above, but I have not included them here because I don't know how to get them to sit immediately under the draft text on this talk page):

Claimed proof by Fokas

In November 2017, Athanassios Fokas claimed to have proved the hypothesis. In June 2018 the University of Southern California reported his claim, but then it amended its report a few days later to refer only to his introduction of a new methodology that suggests a solution. His proof has not yet been either published or evaluated by peer review.

AlexanderTrampton (talk) 14:22, 1 July 2018 (UTC)

I really don't know what you mean by "claim of proof". In current mathematical practice one would distinguish between the following statements: 1. I have written a proof which is contained in a publicly available manuscript for consideration by the mathematical community. 2. My proof has been accepted by the community and been published in mathematical journal. What you are suggesting is that the status is "I have a proof in my head but it's not written down yet." The issue thus is that as far as one can tell, his proof "exists" for the time being only in his head. This should not be referred to as "claim of proof" or "claimed proof" which is "unpublished". It is not unpublished, it is unwritten! Let me make my own conjecture: Fokas is not a pure mathematician and might not understand well the serious implications of what he wrote in the abstract of v2, i.e., that it could reasonably be interpreted as an assertion of statement 1 above. Likewise, he might not understand well that by subsequently removing those statements in v4 and changing the name of the paper as he has, it could reasonably be interpreted as a retraction of statement 1. He is an applied mathematician who seems to have limited experience in rigorous proof and in general his use of language throughout is ambiguous. For him, it could be that all these new formulations of the abstract are just novel ways of expressing that "he is confident that he will prove this one day". Now, credibility issues aside, are Fokas's assertions of his "confidence in eventually being able to prove Lindelof", as expressed in any of the forms of v1-v4, objectively noteworthy? No external interest in the mathematical community as far as I can see was generated by the posting and reposting itself of any of v1-v4 of the abstract. This is what I mean by saying that the posting and reposting of these papers were "non-events". I offered above my own possible interpretation of this silence: "Experts viewed the claims as without credibility so didn't discuss them further." I have reasons to believe this is an accurate explanation of the non-reaction but the reasons for this silence are indeed irrelevant here, only the silence itself. So we come to the conclusion that the only thing that generated any sort of reaction (confined mostly to non-experts postings on online discussion groups) was the more recent USC engineering school press release. Moreover, this reaction stemmed from the confusion caused by the fact that the press release certainly seemed to assert that a "claimed proof" existed and appeared in the arxiv preprint, a confusion which was quickly sorted out by experts who pointed out that v4 makes manifest that the paper in question does not contain a proof. The USC engineering school press release has since been amended. Is the above confusion, as represented by a few online discussions, an event in itself? It only lasted for a few days and fortunately never rose to a very loud level so as to be picked up more widely. The whole thing basically has already gone away as far as I can see.131.111.184.3 (talk) 16:57, 1 July 2018 (UTC)

If we stay with the facts, he hasn't stated either 1 or 2. We can safely assume that a currently research-active professor at Cambridge's applied mathematics department is aware of current mathematical practice, although it is possible that you may not be very familiar with current applied mathematical practice which is a case of said practice. I don't agree that what he said in v2 can reasonably be interpreted as a statement of type 1. I do, however, agree with you that what he said in v4 can reasonably be interpreted as a retraction of a claim, but that is only one interpretation and it's not the only one and in my opinion it's not the best one either. I'm sure he knows what a retraction is and would make it clear he was making one if in fact he was making one. If you really insist, we could surely find a neutral way of describing the way events have moved with v4 and the amendment of the press release, a way which does not rely on interpretation, does not refer to a "retraction", and does not necessarily say "this was not a retraction" either.

"He is an applied mathematician who seems to have limited experience in rigorous proof and in general his use of language throughout is ambiguous." C'mon. That's all your interpretation and indeed somewhat biased. You write "I offered above my own possible interpretation of this silence: 'Experts viewed the claims as without credibility so didn't discuss them further.'" That would be interpretative on its face, but more importantly the premise is faulty, and nor does it matter that you say you have private reasons for so believing, because it is not true that there was silence. As for interest from within the mathematical community, did you look at the instances I cited? The fact that some of it was generated by the Arxiv papers only through the medium of the press release is irrelevant, given that we can assume that many of the contributors to the discussions at Math Overflow and on Terence Tao's blog and indeed at Reddit actually read the papers even if they heard about the proof claim from the press release or from somebody's reference to it. There is no need for us to debate the meaning of "generated", becase it is fine on Wikipedia for noteworthiness to be shown on the basis of secondary discussion and commentary. (Incidentally there was a brief reference to the proof claim on Math Stack Exchange prior to the press release.)

I would agree that the principal question is level of noteworthiness, so we are making some ground here. In Wikipedia terms we've got to bear in mind that we don't know what will happen in the future. The issue cannot be decided on the basis of future possibilities or possible future relevance. AlexanderTrampton (talk) 18:56, 1 July 2018 (UTC)

As I said before, the total intensity of online discussion that has been generated, which is the only thing left now, is just too low. There are a few short online threads which all have the same form (1. non-expert sees the USC engineering school press release and asked what is going on 2. confusion as people look at the contradictory abstracts/titles of v1-v4 3. resolution as experts explain that at least v4 of the paper no longer claims to contain a proof). (Before the USC press release there is a single unanswered comment in the whole mathematics blogosphere.) The case of the "discussion" on Tao's blog is indicative: In a thread about something else, a non-expert asked Tao on his blog to comment on the USC engineering school press release, and Tao responded that the press release notwithstanding, (1) the paper does not contain an alleged proof and (2) on looking at the paper, he is skeptical of the whole approach anyway. Is this seriously your case for "notability"? There are much longer, more intense mathematical discussions going on on these blogs constantly, and no one is arguing for these to be mentioned on wikipedia. My interpretative comments above were simply made to help explain to non-mathematicians why it's in the end not so surprising that the number theory community has essentially completely ignored these preprints. I am just trying to be helpful. But indeed, the only important fact (for wikipedia) is that the total amount of notability, positive or negative, even after the USC press release fiasco, is very far below-threshold. 131.111.184.3 (talk) 20:26, 1 July 2018 (UTC)

Intensity of continuing online discussion isn't the criterion. Consider that facts such as the following are mentioned in the article: "Keating & Snaith (2000) used random matrix theory to suggest some conjectures for the values of the coefficients for higher k." How much discussion has there been of their result? Perhaps the entire article requires expansion. Since Lindelof published the hypothesis, I wonder what claims of proof have been made by other mathematicians of Fokas's stature. Probably some have. They should go in too. Like you, I'm trying to be helpful, and I have no problem with us not agreeing about all aspects. It would be great if we could reach a consensus. Your 1-2-3 is certainly accurate regarding a lot of the discussion, although it's not the whole story, because scepticism about the approach is the correct attitude and only to be expected until a proof has been circulated and peer review is complete, and also because for example Alex Gavrilov at Math Overflow doesn't claim to be on top of the field. Fokas is probably ahead of him and may, for all we know, have good reason to believe, or even have already proved, that |ζ(1/2+itτ)|2 is the only solution of that equation. Resolution of the confusion over the press release occurs (good), but there has been and still is some interest in the claim, which is hardly a surprise. As for Tao, he basically says "asymptotics - ooh, you've got to be very careful with that". Sure. It doesn't sound as though he's given the papers a lot of consideration. It'd be nice to hear what asymptotologists are saying about them. Can asymptotology help prove this hypothesis? Personally I haven't got a clue. A world-leading asymptotologist without much of a record in number theory thinks it may be able to. Tao is sceptical and says you gotta be careful. I'll think about what you say. As far as I'm concerned, the amount of notability is borderline, which is part of what makes the argument interesting from a Wikipedia point of view. "Very far below the threshold" is a characterisation I'd save for the many throwaway proofs that have been published over the years, not for this claim of one. Last, I'd like to see the article expanded and given more of a "current" flavour. AlexanderTrampton (talk) 22:46, 1 July 2018 (UTC)

I mentioned "intensity of continuing online discussion" because this is the only criterion left in the case of Fokas's preprints, in view of the lack of any other reference to that work. And I assert again that I find this well below the threshold. Are you now seriously trying to compare the issue of Fokas's arxiv preprints with the work of Keating & Snaith which is referred to in the article? The latter is manifestly a very influential work published in CMP. It has itself given rise to a host of further work, published in the best mathematics journals, see for instance http://annals.math.princeton.edu/2009/170-2/p17. You can find countless references to the conjectures of Keating & Snaith in published papers, online lectures, etc. (and yes, even online discussion groups, though its influence does not need to be primarily evaluated through this). Keating has been subsequently elected a Fellow of the Royal Society on the basis of his work in this area https://royalsociety.org/people/jonathan-keating-11728/. If you are indeed interested in learning more about Lindelof, I would advise you to read the host of correct results (like the above one) which are already published (and would appear to have been carefully selected by expert editors for inclusion in the article), before trying to further expand the article.131.111.184.3 (talk) 06:31, 2 July 2018 (UTC)

I completely agree with User:131.111.184.3. I think this episode should not be mentioned at all in the page. Sapphorain (talk) 12:52, 1 July 2018 (UTC)

You're not getting it, my friend. We are supposed to discuss here, give reasons, apply logic, respond to others' arguments, not act as if we are clicking a Facebook button saying "like" or "dislike". This isn't a vote. AlexanderTrampton (talk) 14:22, 1 July 2018 (UTC)

I have clearly explained, in this much too long discussion above, what my position is, and I don’t see any point in repeating over and over again in different words what I already said. Sapphorain (talk) 00:36, 2 July 2018 (UTC)

Do you mean this: "No matter how 'highly reputable', and 'internationally renowned' the author of a paper can be, Arxiv is definitely not a reliable source just by itself." ? Or this: "It is I think quite sufficient to have a small section near the end of the page, mentioning that several claimed proofs have been published over the years. I wrote such a section, in which a note provides a link to some of these claims (on ArXiv), including Fokas’s." ? Now that I have successfully got the page protected, this discussion is so that we can grasp and then deal with the contentious issues, cooperatively, as 131.111.184.3 and I have made some progress towards doing, listen to each other's arguments, and eventually reach consensus. If you don't want to be part of that process, please don't post on the Fokas proof claim section issue any more. Various new points have been made and facts referenced since you last posted. Can't new points and new facts lead you to revise your opinions? You are welcome to participate and actually get your hands dirty and help improve the article in cooperation with other editors. That's why I paged you in. If you don't wish to, that's fine, but if that's how it is then please don't post to this section of the talk page because otherwise you are just wasting people's time. AlexanderTrampton (talk) 00:54, 2 July 2018 (UTC)

Speaking of wasting people's time. Your position that a false statement (otherwise known as a lie) by a mediocre mathematician about an interesting (but not earth shattering) open question deserves being mentioned in this article is beyond the pale of rational discourse.--Bill Cherowitzo (talk) 04:28, 2 July 2018 (UTC)

Let me help you: "lie" means "deliberate falsehood". Which mathematician are you calling both "mediocre" and a liar? Is it Fokas? Can you speak clearly please, rather than out of the side of your mouth. That's how grownups seek to reach consensus. 131.111.184.3's obvious affiliation with the Cambridge pure mathematics department (DPMMS) and his bias against even extremely highly-cited applied mathematicians at the Cambridge applied mathematics department (DAMTP), such as Fokas, is as plain as anything. His repeated references to the University of Southern California's engineering school should not obscure the fact that DAMTP is higher ranked than DPMMS for research: in other words, Cambridge has a stronger reputation for applied mathematics than for pure mathematics. Nor is there a basis for believing that high-level research in asymptotics is less rigorous than high-level research in combinatorics. You, Wcherowi, are clearly not seeking to discuss properly. If you wish to be taken seriously, either tell us who you are saying lied or withdraw what you typed. AlexanderTrampton (talk) 12:34, 2 July 2018 (UTC)

I agree with IP 131.x.x.x and others that mentioning the preprint is WP:UNDUE. Headbomb {t · c · p · b} 10:53, 2 July 2018 (UTC)

Thanks for your contribution, but this is supposed to be a discussion leading to consensus, not a division leading to a vote. I could say "I disagree with IP 131.x.x.x and believe that mentioning the preprint is not WP:UNDUE." Do you appreciate how stupid that would sound if I wrote that? AlexanderTrampton (talk) 12:34, 2 July 2018 (UTC)

Speaking of Cambridge mathematics, see https://plus.google.com/+AlexanderKruel/posts/ZhQhQmtohkU for Tim Gowers' reaction to the USC engineering school press release.131.111.184.3 (talk) 12:55, 2 July 2018 (UTC)

The "sourcing" here consists of two press-releases and an abstract of an unpublished paper. That is to say, there are 0 reliable sources and 0 coverage in secondary sources. Mentioning this at all is obviously inappropriate and undue. --2601:142:3:F83A:611C:BD4F:C063:4BF2 (talk) 12:36, 3 July 2018 (UTC)

Possibly it is worth noting that the only proponent of inclusion purports to have retired from Wikipedia. They haven't edited in roughly 30 hours, which beats their previous retirement of 30 minutes. --2601:142:3:F83A:84C3:6F5:A4ED:BF8 (talk) 23:35, 3 July 2018 (UTC)

It seems clear to me that the sourcing does not yet meet our standards for inclusion (neither the press releases pushing this as a breakthrough nor the reaction from Gowers). As for calling (Fields medalist) Gowers a "mixed up kid": perhaps this is an attempt at humor, but WP:BLP and WP:NPA apply on talk pages, not just in article space. —David Eppstein (talk) 21:26, 5 July 2018 (UTC)

Yes, you're right -- I should have deleted that comment along with the others by the same user as having no content related to the article and violating guidelines in other ways. (Who creates an account just to go on, at considerable length, about the equivalent of five lines of text in a couple of blog comments? People are weird.) I have done so now. --2601:142:3:F83A:716E:8F86:6A20:1BE3 (talk) 12:59, 7 July 2018 (UTC)

Maybe unsurprisingly all the ranters have now been blocked as sock-puppets. --JBL (talk) 22:57, 13 July 2018 (UTC)

Definition needed

The symbol << is used. It should be defined. It seems to be stronger than <. 2A00:23C7:99A5:9E01:792B:BE8C:EAEA:3477 (talk) 14:48, 28 March 2023 (UTC)

Vagueness should have no place in maths. — Preceding unsigned comment added by 2A00:23C7:99A5:9E01:792B:BE8C:EAEA:3477 (talk) 15:37, 28 March 2023 (UTC)