# Talk:Riemann hypothesis

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## January 2016: new year, same old story

Re this edit: Pioneer Scientific Publisher is yet another website that accepts pretty much anything, and people have to pay for the privilege of doing so ($400 to$850 according to the source).--♦IanMacM♦ (talk to me) 09:29, 15 January 2016 (UTC)

## Computations

Platt's work (2011 and later) should be added. Also, shouldn't we say something about the degree of rigour of some computations? I've heard that Gourdon-Demichel is a bit ropey on this point, due to non-rigorous sampling. Garald (talk) 22:43, 30 January 2016 (UTC)

As with many other WP articles on physics and math, there is quite a high "baseline level" of knowledge required for the reader. This is counterproductive, as an encyclopedia is supposedly intended for people who do not already know everything about the subject (or else why would they look it up?).

Example from this article: in the section "History", the function "Li" is introduced without any explanation or even link to an explanation. The term "Li" is short enough to have two meanings in math listed in WP: https://en.wikipedia.org/wiki/Polylogarithm and https://en.wikipedia.org/wiki/Logarithmic_integral_function. Thus, being a relative novice and not knowing which one is referred to (although I can guess), I can't even edit in a link here. Please have some perspective and put yourselves in the situation of someone less well educated, but still keen to learn. If you don't, I will suspect that you are more interested in showing off your expertise than in spreading knowledge. Sorry. Wdanbae (talk) 07:31, 2 February 2016 (UTC)

You didn't see the sentence "The function Li occurring in the first term is..." ? It's a few lines down, but all of the lines between the formula and that sentence are also explanations of other parts of the same formula. —David Eppstein (talk) 08:04, 2 February 2016 (UTC)
Sorry, my bad. Although I would have preferred to have the explanation even earlier than that in order not to lose faith, I guess I am oversensitized by all the other occurrences of unexplained or unlinked-to terminology that I have encountered elsewhere. Here, statement withdrawn. Wdanbae (talk) 08:57, 2 February 2016 (UTC)

Sorry for asking something that's not really related to Wikipedia, but here goes. I recently put on line a paper I wrote commenting on the attempt of Louis de Branges to prove the Riemann Hypothesis. How can I bring it to the attention of those who would be interested? Eric Kvaalen (talk) 09:10, 2 February 2016 (UTC)

Any chance you'd be willing to put up a PDF copy? The PNG method is quite inconvenient and slow. If you're not willing to make one generally available, you can email me a copy through Wikipedia. I can't promise I will make any cogent comments, but parts of it do look rather interesting. Sławomir Biały (talk) 13:41, 3 January 2017 (UTC)

## One of the references points at a non-existent page

Mazur, Barry; Stein, William (2014), Primes. What is Riemann's hypothesis - the link http://modular.math.washington.edu/rh/ brings up a 404 when I try to navigate to it. I did a quick look for it, but I wasn't 100% sure exactly which book it was supposed to be. Perhaps someone more knowledgeable than me can point the link towards a working location?142.109.6.1 (talk) 19:09, 11 February 2016 (UTC)

I've updated it to a working link for the same book under a slightly different title and date, http://wstein.org/rh/David Eppstein (talk) 19:51, 11 February 2016 (UTC)

## Popular expositions

Does it really make sense to break out "Popular expositions" as a separate subsection of the references section? Also, I am puzzled why some things were included and not others. The selection seems rather arbitrary in my opinion, and not really connected with any reliable metric of "popularness" of sources. I think WP:NPOV should urge against this arbitrary judgement of some sources to be "popular" (and thus, less good perhaps?) 15:18, 24 April 2016 (UTC)

I completely agree with this separate subsection. Maybe some other works should be included in it also (I haven't gone through all references yet), but these four definitely are - euphemistically - "popular" expositions. And they are (not perhaps but certainly) "less good". In fact I wonder if we should not suppress these references from the article. None of the authors is a specialist of the subject. Sabbagh is not even a mathematician, and his book is his one and only work reviewed by MathSciNet (by D.R. Heath-Brown, who politely reports that it is not a good book). The report on du Sautoy's book states that it is "not sufficiently accurate and complete". The report on Rockmore's book is not good either (also from Heath-Brown). Finally Derbyshire (who is credited with only 3 reviewed works on MathSciNet!) has the worst review ("While some chapters are not too bad, most seem to miss their mark"[…] "I am not sure the author ever answers the question of why the Riemann hypothesis is important.") Sapphorain (talk) 17:12, 24 April 2016 (UTC)
I don't think they should be suppressed, and I think calling them "less good" is an oversimplification, but I agree with keeping them separate. They have a different character than the other references and are aimed at a different audience. Keeping them separate helps that audience to find material on this subject that is readable by them, and helps mathematicians avoid material that is too popularized to be useful to them. —David Eppstein (talk) 18:04, 24 April 2016 (UTC)
I almost agree to conservation. Rather reluctantly concerning Derbyshire's book. But I don't agree at all concerning Sabbagh's books. I just moved in the new subsection his other book on the subject (also published in 2003…), which is not reviewed by MathSciNet and Zbl (and not even indexed by MathSciNet!). Here is journalist, who is writing vulgarization on about everything you can think of, who is not a specialist of the subject, who is not even a mathematician, even in a very large acception of the term, and who publishes two books on the Riemann hypothesis the same year. This is not serious. Sapphorain (talk) 22:39, 24 April 2016 (UTC)

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## Fast Prime?

Sorry if this is well know, but looking at the patterns in 3d (hard to view 4D) of the values of non-prime numbers, it seems like one could simply look at the data around the chosen point to follow it down to 1/2. I guess a proof is (a, all 'fingers' lead down to 1/2 eventually and we know that their are an infinate number of primes.... so proving infinate fingers may be a step. I do apologize if I'm an idiot. I'm no maths whiz but for 20 years this problem has held me in it's grip. My only wish is for SOMEONE to prove, or disprove OR fall into Gödel's incompleteness theorems. — Preceding unsigned comment added by 213.106.56.145 (talkcontribs)

## Failed attempts

1. try to connect mathematically the trivial zeros to the non trivial ones — Preceding unsigned comment added by 2A02:587:4114:9400:486E:F7D4:172C:1629 (talk) 21:11, 17 December 2016 (UTC)
2A02 should speak more clearly. In the theory of analytic functions, all zeros are equally important. He has just volunteered for the task of connecting. — Preceding unsigned comment added by 212.159.119.123 (talk) 13:14, 3 January 2017 (UTC)

## An "In Popular Culture" section?

Anyone think a "In popular culture" section would be appropriate for this very serious article? Wolfram has three and I'm assuming there are more: http://mathworld.wolfram.com/RiemannHypothesis.html— Preceding unsigned comment added by BashBrannigan (talkcontribs) 15:45, 25 February 2017 (UTC)

I tend to agree with WP:TRIVIA that such sections are a waste of time and tend to fill up with uninteresting, unsourced, and insignificant anecdotes. —David Eppstein (talk) 17:02, 25 February 2017 (UTC)
WP:POPCULTURE sections aren't banned, but they can be enormous trivia magnets, and can end up like this cartoon parody showing how not to do it. When something like this is worth mentioning, it can usually be incorporated into the main body of the article.--♦IanMacM♦ (talk to me) 17:29, 25 February 2017 (UTC)

## Quantum system found

A quantum system has been found whose energy levels correspond to the zeros of the zeta function. This system was proposed on 30 of March 2017 in Physical Review Letters by Carl Bender of Washington University in St. Louis, Dorje Brody of Brunel University London and Markus Müller of the University of Western Ontario. See this general audience article:

https://www.wired.com/2017/04/maths-1000000-question-isnt-just-mathematicians-anymore/

2001:44B8:266:D05:85D0:EEF3:C950:5AC (talk) 13:25, 30 May 2017 (UTC)

I would not object to mentioning this in the article. Sławomir Biały (talk) 13:33, 30 May 2017 (UTC)

## Proportion of zeros on the critical line

On 14 June 2017, N. Robles and K. Pratt have submitted a paper that claims to improve the lower bound for the proportion of zeros on the critical line to 41.49%. See https://arxiv.org/pdf/1706.04593.pdf, and the authors page at http://www.math.uiuc.edu/~nirobles/research.html. I hesitate to include the result in the Wiki article before it is peer reviewed, but it's worth to keep an eye on it. If their method turns out to be valid then there is further room for improvement: As they mention in footnote 2 on p.20, they were able to push the bound on the length ${\displaystyle \theta }$ of Feng's mollifier beyond ${\displaystyle {\tfrac {17}{33}}}$, to ${\displaystyle \theta <{\tfrac {6}{11}}}$, and they think that (with some more effort) a bound of ${\displaystyle \theta <{\tfrac {4}{7}}}$ could be reached. This in turn would further improve the lower bound on the number of zeros. Renerpho (talk) 13:46, 16 June 2017 (UTC)

Note that it is often said that Levinson produced a proof for 33.33% and Conrey for 40%. — Preceding unsigned comment added by 31.53.52.243 (talk) 07:21, 14 July 2017 (UTC)