Wikipedia talk:WikiProject Mathematics/Archive/2021/Jun

Proposal: change terminology from "recursive" to "computable"
In many articles concerning the mathematical field of computability theory, I propose changing the terminology from "recursive X" to "computable X". For example:
 * "recursion theory" ⇒ "computability (theory)"
 * "recursive function" ⇒ "computable function"
 * "recursively enumerable", "r.e." ⇒ "computably enumerable", "c.e."

I have two reasons for this proposal:


 * 1) "Recursion theory" was the original name for computability, and the most common name throughout the 20th century. However, in the last 20 years (?), there has been a sea change towards the terminology "computable". Essentially all papers and books written recently about recursion/computability theory use the term "computable" in favour of "recursive". Sadly, ngrams aren't supporting this, but I think this is for the reasons I outline below - the term "recursion" is used in a much broader sense. However, if you look at recently published computability articles on zbMATH, you will notice they all use "computable" instead of "recursive". Further evidence is Soare's 2016 book "Turing Computability", which is essentially a second edition of his 1987 book "Recursively Enumerable Sets and Degrees", with most instances of the word "recursive" replaced by "computable".
 * 2) The word "recursive" is ambiguous, as it can refer to many other things, particularly the more general notion of recursion. In general, the usual (informal) meaning of "recursive" doesn't coincide with the computability-theoretic meaning. Indeed, this was the primary motivation behind the change described in the previous item.

There are plenty of pages which use the outdated terminology, such as recursively enumerable set, recursive ordinal, forcing (recursion theory) and index set (recursion theory). I would rename these to computably enumerable set, computable ordinal, forcing (computability) and index set (computability) respectively.

Note: I am not proposing this change for every instance of the word "recursive". For instance, I would keep primitive recursive and Kleene's recursion theorem as they are, as those are still the popular names for those concepts.

--Jordan Mitchell Barrett (talk) 05:30, 21 April 2021 (UTC)


 * To clarify and reiterate, you're not proposing article moves for those three examples, right? So not replacing the disambiguation Recursive function with Computable function, but rather just a terminology change solely within the prose of articles within computability theory? — MarkH21talk 07:30, 21 April 2021 (UTC)


 * I am proposing a terminology change, which might affect the titles of some articles. However, this change is limited in scope to articles about the mathematical field of computability theory. Regarding the three examples I gave at the start:
 * Recursion theory already redirects to computability theory, so there would be no title changes here.
 * Recursive function is a disambiguation page about the more general, informal notion of "recursive", therefore this is out of the scope of what I'm proposing. Hence no changes here. If there was an article called recursive function (recursion theory), I would be proposing to move it to computable function. However, this is not the case.
 * I am proposing to move recursively enumerable set to computably enumerable set.
 * --Jordan Mitchell Barrett (talk) 08:18, 21 April 2021 (UTC)


 * Oppose The two first proposed changes are almost already done, and completing them does not require any discussion here; the third one is against Wikipedia general policy. In details,  is already a redirect to Computability theory. So, I agree with changing the disambiguating parentheses in article titles from "(recursion theory)" to "(computability theory)". Recursive function is a disambiguation page linking to several meanings; the one that is related to computability theory is General recursive function, which is one of several models of computation for computable functions. "Recursive function" was also presented as an other name for "computable function" before saying that "mu-recursive functions" are a model of computation for computable functions. I have just fixed this. The term recursively enumerable is well established and unambiguous. It is not the role of Wikipedia to change an established term, so I strongly oppose to any change of recursively enumerable. D.Lazard (talk) 09:21, 21 April 2021 (UTC)


 * "Recursively enumerable" or "r.e." is an outdated term, and "computably enumerable" or "c.e." is used instead in modern literature on computability theory (last 20-30 years). You are correct that the term "recursively enumerable" is unambiguous, and established in the sense that older literature uses it. To clarify, I would keep "r.e." as a synonym in the lead, but change all subsequent occurrences and move the article to computably enumerable. --Jordan Mitchell Barrett (talk) 09:45, 21 April 2021 (UTC)
 * You must provide sources attesting that "recursively enumerable" is an outdated term. A source using "computably enumerable" witout discussing the use of these terms is not such a requested source. Without such sources, your assertion that the term is outdated is WP:original research. In any case, Wikipedia is not aimed for specialists of computability theory, and must not be confusing for non-specialists. The systematic change that you propose would be highly confusing for people who use results of computability theory without being specialists of it (for example, the existence of a recursively enumerable set that is not recursive is widely used in algebra and number theory for proving that some properties are not decidable; an important example is Fröhlich–Shepherson theorem of non-computability of polynomial factorization over some explicit computable fields). D.Lazard (talk) 10:42, 21 April 2021 (UTC)


 * naturally, it's hard to find sources attesting to this, but here is what I could find in a quick search:
 * Soare's 1996 essay "Computability and Recursion" was the original proposal to those in the field to change terminology from "recursive" to "computable". He wrote an revised version in 1999, called "The History and Concept of Computability", in which he remarks (sec. 7):
 * "Researchers in the subject have recently changed the the name of the subject from “Recursion Theory” to “Computability Theory” in order to make clear this distinction [in meaning between the terms]. Thus, the term “recursive” no longer carries the additional meaning of “computable” or “decidable,” as it once did. This reinforces the original meaning of “recursive” and induction as understood by Dedekind, Peano, Hilbert, Skolem, Godel ... and by most modern computer scientists, mathematicians, and physical scientists. Presently, if functions are defined, or sets are enumerated, or relative computability is defined using Turing machines, register machines, or variants of these ... then the name “computable” rather than “recursive” will be attached to the result, ... Thus, the terms “recursive” and “computable” have reacquired their traditional and original meanings, and those understood by most outsiders."
 * Soare, in his book "Turing Computability", also discusses the change briefly (sec. 17.7.2):
 * "After the articles [Soare 1996] and [Soare 1999] on the history and scientific reasons for why we should use “computable” and not “recursive” to mean “calculable,” many authors changed terminology to have “recursive” mean only inductive and they introduced new terms such as “computably enumerable (c.e.)” to replace “recursively enumerable.” This helped lead to an increased awareness of the relationship of Turing computability to other areas. There sprang up organizations like Computability in Europe (CiE) which developed these relationships."
 * Cooper and Odifreddi also mention the change in "Incomputability and Nature":
 * "Things started to change in earnest around 1995–96. These changes were rooted in two seemingly unrelated developments, one philosophical and political in content, and the other technical. The first involved a deliberate attempt to reinstate Turing’s terminology in keeping with the subject’s origins in real world questions — ‘computable’ in place of ‘recursive’ etc. — a project outlined in Robert Soare’s 1996 paper on ‘Computability and recursion’."
 * I disagree that this change would be confusing - in fact, I think it would clarify things, as "computable", rather than "recursive", is now the popular and accepted term for the concept, both for specialists in computability, and people who know not the subject. The one exception might be older mathematicians with weak connections to computability theory, who may not be aware of the terminology change (e.g. algebraists). However, your result could equally well be stated "there is a computably enumerable set which is not computable", and I think the meaning of this is clearer. --Jordan Mitchell Barrett (talk) 20:51, 21 April 2021 (UTC)


 * Strong support. It is my understanding that this is the usage in the field these days.  While D.Lazard is completely correct that it is not Wikipedia's role to change usage, that is not what has happened here &mdash; usage has changed in the wild.  Unfortunately User:CBM seems to have stopped editing; he would be the one I would naturally go to to find good sources. As a side note, the content of general recursive function at the moment is largely about one particular model of computation, which could be called μ-recursion.  That content should appear under some such title as μ-recursion, and general recursive function should be a redirect to computable function, which should be slightly rewritten to clarify that it is about the precise concept with many different provably equivalent definitions, and not about informal computability.  See my remarks in talk:general recursive function. --Trovatore (talk) 18:31, 21 April 2021 (UTC)
 * Comment. I just polled some theoretical-CS faculty colleagues on this; they were not aware of a shift in terminology, and tend to use older textbooks (Sipser and/or Lewis and Papadimitriou) where recent trends might not be apparent. But we all agreed that "computable" is an acceptable and familiar alternative to "recursive", and probably preferable because of the potential of confusing "recursive" with the programming-language concept of recursion. —David Eppstein (talk) 19:43, 21 April 2021 (UTC)


 * Yes, (older) people who know some computability, but are not specialists, may not be aware of this change. The TCSists I know like the term "decidable", e.g. for type-checking, and to be clear, I would keep such terms as synonyms in the articles. However, I agree that "computable" is clearer than "recursive" to almost everyone. --Jordan Mitchell Barrett (talk) 20:54, 21 April 2021 (UTC)
 * They were not all older, but "know (and teach) some computability, but are not specialists" is accurate. On the other hand, I think that because the rudiments of this material are commonly taught in undergraduate computer science programs, making the main articles on this material accessible to students at that level is important, per WP:TECHNICAL, and that the nomenclature they learn it by is at least as relevant as current specialist practice in making this decision. Fortunately, this doesn't lead to much conflict: from that point of view, moving away from "recursive" also comes out as a good idea. —David Eppstein (talk) 01:00, 22 April 2021 (UTC)

If I could wave a magic wand and undo the change, would I? Probably not. I've gotten used to it by now. I'm still not a big fan of the "political" subtext of Cooper's paper, linked above, but the terminology does have some practical advantages, in that it decouples the concept from self-reference, whereas on its face "recursive" looks like it's about self-reference. In any case, if we did decide to go with the older terminology, then most of the content currently at computable function should be moved to general recursive function or whatever name we picked, and that article should not be so tightly tied to &mu;-recursion. I don't think that's a very good plan, but it's the only reasonable alternative to the proposed changeover. --Trovatore (talk) 23:02, 21 April 2021 (UTC)
 * Side note I was actually not a fan of Soare's change at the time he initially proposed it, in the mid-nineties, for a couple reasons. One, I'm generally skeptical of self-conscious programs of language reform.  Beyond that, I was concerned that it seemed to be trying to make Church's thesis true by fiat, because I thought of it as "all computable functions are recursive".  It was explained to me that that wasn't the point; that Soare simply wanted to repurpose "computable" as the precise technical term for what had been called "recursive", so that now Church's thesis (or if you prefer the Church–Turing thesis, but I did go to UCLA after all) would be something like "all informally computable functions are computable".

Update: it seems there was consensus around some things, such as changing disambiguating parentheses in article titles from "(recursion theory)" to "(computability)". Hence, I've now moved Forcing (recursion theory) to Forcing (computability), and Index set (recursion theory) to Index set (computability). I tried to move Reduction (recursion theory) to Reduction (computability), but the latter is already a redirect to Reduction (complexity). In any case, it looks like Reduction (recursion theory) should be merged into Reduction (complexity), which I've proposed.

I'd still like to move the following articles: My reasons are as stated above. My interpretation of the above discussion is that I have support from Trovatore and David Eppstein, with some disagreement from D.Lazard (who still hasn't responded after I provided sources witnessing the change in terminology). I would appreciate input from other editors on whether they support or oppose such changes.
 * Recursive ordinal ⇒ Computable ordinal
 * Recursive set ⇒ Computable set
 * Recursively enumerable set ⇒ Computably enumerable
 * Recursively inseparable sets ⇒ Computably inseparable

For now, I don't think we should move Recursive language, as this concept seems more in the realm of theoretical CS, where they may use different terminology. Then again, maybe Decidable language is a more common name? --Jordan Mitchell Barrett (talk) 01:23, 26 April 2021 (UTC)
 * "Recursive language" appears more frequent than "decidable language" in recent publications although both are in similarly-wide use. However, a lot of the Google Scholar hits for "recursive language" appear to be in the context of the development of natural languages, as a way of distinguishing basic utterances from things with a nontrivial syntax, far from the technical meaning used here. "Decidable language" would be more unambiguous. I don't think this has been a very active area of computer science research for the last 50 years; it's more just a basic concept that is occasionally used as a tool in other research topics. So for instance in relativized computational complexity theory (itself not exactly a hot area) one still sees "recursive oracle" rather than "decidable oracle". —David Eppstein (talk) 01:39, 26 April 2021 (UTC)
 * I have not responded before because I had nothing to add to my comment. Presently, I acknowledge that sources have been provided that support the terminology shift. Also, it is better that terminology gives hints to the meaning of the used terms and phrases. This is the positive aspect of this terminilogy shift. So, I do not oppose anymore to the four remaining proposed moves, if a note is added to the moved articles for explaining the terminology shift (a single sentence with a reference to Soares may suffices). D.Lazard (talk) 09:45, 26 April 2021 (UTC)


 * Great! I will absolutely reference the old terminology and explain the shift in those articles. --Jordan Mitchell Barrett (talk) 22:38, 26 April 2021 (UTC)


 * Looking for redirects "r.e." and/or "c.e." (both are important, since they are hard to find by string search), I found the link RE (complexity). Should it be renamed to CE (complexity)? There is also R (complexity); more "R"s might be found in similar classes. - Jochen Burghardt (talk) 07:25, 27 April 2021 (UTC)
 * We shouldn't be making up new names for complexity classes — they're a piece of standardized notation, not merely an abbreviation for an English phrase. You wouldn't propose changing $$\Z$$ to $$\mathbb{I}$$ merely because we're mostly writing in English rather than German these days; this comes across as the same sort of suggestion. I don't know of any sources that call these ones anything other than R and RE. That's how they're listed in the Complexity Zoo, without any mention of synonyms, for instance. —David Eppstein (talk) 07:38, 27 April 2021 (UTC)


 * Support. I agree with Trovatore that, for better or worse, the terminology used by practicing logicians has changed, so it makes sense for Wikipedia to follow. Ebony Jackson (talk) 03:44, 28 April 2021 (UTC)

For your information, user:Cewbot has been removing vital-article templates from the talk pages of these renamed articles. I suspect that that is a mistake. JRSpriggs (talk) 18:48, 30 April 2021 (UTC)


 * Comment. If this change is done then in the disambiguation parentheses (and other contexts where it can reduce potential for confusion) the replacement should be of "recursion theory" by "computability theory", not simply "computability" as was done in some cases.  So Forcing (computability theory) not Forcing (computability). 73.89.25.252 (talk) 19:13, 3 May 2021 (UTC)


 * Not sure I agree - I think Forcing (computability) has exactly the same meaning, is just as unambiguous, plus saves seven characters in the title. --Jordan Mitchell Barrett (talk) 22:46, 1 June 2021 (UTC)


 * Comment. I prefer "computable" and "computably enumerable" because they are more readily understood and far less readily misunderstood by strangers to that area of study. One could also make an argument for saying "More than one editor think that" instead of "More than one editor thinks that", on the grounds that "more than one" is plural, but that is not the way the English language conventionally works. The extent linguistic to which convention should govern this present issue is a question about which I am not prepared to argue. Michael Hardy (talk) 15:56, 11 May 2021 (UTC)


 * Support. I applaud the change. Every time I would stumble over "recursively enumerable" I would have to stop in my tracks and look up the definition and make sure I wasn't cross-eyed while re-reading it for the 13th time. Whereas the meaning of "computably enumerable" is obvious. So Yay! 67.198.37.16 (talk) 21:46, 26 May 2021 (UTC)

Old featured articles – you can help!
I know a number of you have done great work in saving old math-related featured articles from being delisted at FAR. So I figured it might be useful to put together a list of old FAs within this project's scope that could be in danger of potentially losing their star, in the hope of getting them fixed up before somebody starts the formal delisting process. I've done that below; here are a few thoughts: 1) These articles are not all the same. Some may have no issues at all, while others may be practically unsalvageable. 2) You can read the featured article criteria here. While an FA must meet each criterion, in my experience the most important issue for these old FAs is referencing. Our expectations on inline citations have changed a lot over the past twenty years, so making sure that there aren't vast deserts of uncited text is really important. Fixing up any prose issues is also helpful, as is making sure that the article is still a comprehensive overview of the subject. 3) The year provided is the year of the most recent FAC or FAR. Older articles often require more work, but this is of course only a generalization. This list contains only articles that have not been reviewed in more than ten years. 4) If this sort of work interests you, please come help out at WP:URFA/2020. We have an enormous backlog of old featured articles on all subjects that are in need of review.

Notice given: These are the most urgent priorities. Someone has made a note on the article's talk page that the article may not meet the featured article criteria. Such articles are in danger of being imminently taken to FAR. Notice not given: Notice has not yet been given for these articles, so they aren't urgent priorities. Just take a look and see if there are any obvious issues with them that need work. If you feel confident in your understanding of the featured article criteria, feel free to go to WP:URFA/2020 and follow the instructions to either give notice, mark the article as satisfactory, or provide other comments. I hope this list is useful to you all. Getting these FAs taken care of outside the formal process is good for everyone: it reduces the URFA backlog, it gives you all advance notice of potential issues, and it provides an incentive to improve these important articles. Do let me know if I can be of any assistance: while my mathematical expertise is lacking, I'm glad to answer any questions about the FAR process. Cheers! Extraordinary Writ (talk) 18:41, 31 May 2021 (UTC)
 * 1) 1 − 2 + 3 − 4 + ⋯ (2007)
 * 2) Polar coordinate system (2007)
 * 1) Archimedes (2007)
 * 2) General relativity (2008)
 * 3) Georg Cantor (2007)
 * 4) Emmy Noether (2008)
 * 5) Introduction to general relativity (2008)
 * 6) 0.999... (2010)
 * 7) Edward Wright (mathematician) (2008)
 * 8) Emery Molyneux (2008)
 * 9) Johannes Kepler (2007)
 * 10) Numerical weather prediction (2011)
 * 11) Problem of Apollonius (2008)
 * 12) Robert Hues (2009)
 * 13) Émile Lemoine (2008)


 * Why does it matter if an article is a "featured article" or not? 67.198.37.16 (talk) 05:07, 1 June 2021 (UTC)
 * While having the articles be as good as they can be is obviously more important than making them meet arbitrary internal milestones, here are two reasons why we might care about this anyway: (1) we want our best mathematics articles to be highlighted as part of the best content on Wikipedia, to bring readers to them, to show the world that mathematics is an important part of Wikipedia, and to bring interest to mathematics more generally, and groupings like FA, GA, and DYK can provide an opportunity to do that, and (2) the pressure to meet the arbitrary milestone can help us improve the articles, especially when they are deficient in obvious ways. —David Eppstein (talk) 06:41, 1 June 2021 (UTC)


 * Where should one expend effort? One might argue that the energy would be better spent on the most-frequently viewed articles. Another possibility is that all top-priority articles should be made FA. This is balanced by several realities: it is a lot easier to take a low-importance article, and make it FA, than a top-importance article, because the top-importance articles have to say more stuff in exactly the right way, whereas lacunae in low-importance articles are easily overlooked (and, frankly, don't matter). The other reality is that WP is a labor of love: almost all FA articles are created/shepherded by one person who is passionate about that particular topic. If/when that passionate person retires, so does the passion. It's hard (impossible?) for the disinterested bystander to make the kind of edits needed to make an FA article: one is not eating, sleeping and drinking the topic. (Literally. Don't know about you, but when I am creating WP articles I care about, I think about it while I walk the dog, while I fall asleep, when I wake up. All that thinking provides the needed corrections, amplifications and expanded sections. Without this effort, the coverage & content would be just .. meh.) 67.198.37.16 (talk) 17:41, 1 June 2021 (UTC)
 * Perhaps the reason why the percentage of editors is biased is that it was evaluated as FA when there were few editors on wikipedia. Articles marked FA basically do not need to be edited, and it seems unlikely that an inexperienced editor like me would edit an article marked FA. Creating an article from scratch is difficult, so it seems like we start by editing (on wikipedia) the article in the start-class or C-class article. (stub-class editing is difficult.) I'm not confident in editing articles in B-class and above. Perhaps I wouldn't edit FA-class articles without FAR. (My two cents).--SilverMatsu (talk) 06:48, 2 June 2021 (UTC)

Most viewed start article in this Wikiproject
Missing square puzzle	91,834	3,061	Start--Coin945 (talk) 14:59, 30 May 2021 (UTC)
 * I have "resolved" this by reclassifying the article as C-class. (The prose is pretty good; the sourcing is very weak, though.) --JBL (talk) 17:32, 30 May 2021 (UTC)
 * Nice work! However, tonnes of readers are still flocking to this page for information and basing our reputation on it. So, the more comprehensive the better in my books!--Coin945 (talk) 17:58, 30 May 2021 (UTC)
 * I agree, that looks like a C-class article to me. Also, this just goes to show, views ≠ importance. —David Eppstein (talk) 19:15, 30 May 2021 (UTC)
 * Fyi here are the 3 most-viewed stub articles in your Wikiproject:--Coin945 (talk) 19:34, 30 May 2021 (UTC)
 * Convenience sampling	16,992	566	Stub
 * Welch's t-test	16,592	553	Stub
 * 1/2 + 1/4 + 1/8 + 1/16 + ⋯	14,340	478	Stub


 * And some of the most-viewed starts:--Coin945 (talk) 19:34, 30 May 2021 (UTC)
 * Kelly criterion	76,759	2,558	Start	Mid --> for the budding gamblers out there?
 * 666 (number)	62,452	2,081	Start	Low --> for the superstitious lot?
 * Sigmoid function	55,424	1,847	Start	Low --> maths classes?
 * Unit circle	53,839	1,794	Start	Mid --> maths classes?
 * Bernoulli distribution	51,260	1,708	Start	Low --> maths classes?
 * Vertical and horizontal	49,311	1,643 --> always a good reminder!
 * I also re-rated Kelly criterion as C-class, and the three supposed stubs as start-class. —David Eppstein (talk) 16:43, 31 May 2021 (UTC)

By the way, can 1/2 + 1/4 + 1/8 + 1/16 + ⋯, 1/2 − 1/4 + 1/8 − 1/16 + ⋯ and 1/4 + 1/16 + 1/64 + 1/256 + ⋯ be merge? The alternating series are mixed, but I think there is no problem because it converges absolutely. How about the title, such as ′′Infinite sum of multiplicative inverse of Power of two′′?--SilverMatsu (talk) 12:04, 2 June 2021 (UTC)

FAR for Leonhard Euler
I have nominated Leonhard Euler for a featured article review here. Please join the discussion on whether this article meets featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" the article's featured status. The instructions for the review process are here. (t &#183; c)  buidhe  04:06, 8 May 2021 (UTC)
 * This has received some attention since the FAR was announced, but it could benefit from more. XOR&#39;easter (talk) 20:36, 24 May 2021 (UTC)

There's a sentence in the article that's confusing me, and I think here may be a better place than the FAR to get an informed opinion: In the applied mathematics section, it states "He also facilitated the use of differential equations, in particular introducing the Euler–Mascheroni constant". My understanding of the Euler–Mascheroni constant is that its primary use is as the constant error term in the approximation of the harmonic series by the logarithm (or, I suppose, vice versa, but that's the usual direction of approximation for me), and that it belongs more to the analysis or maybe analytic number theory sections than in a section on applied mathematics and a sentence on differential equations. But maybe there's an application of this constant to differential equations with which I'm unfamiliar and which the "Appearances" section of Euler–Mascheroni constant doesn't make clear? —David Eppstein (talk) 07:35, 25 May 2021 (UTC)
 * I agree with you, but I'm also interested in classifying the section names into Riemann zeta functions (Euler zeta function? in Euler's times, complex analysis was not well developed but Euler certainly had the foresight for complex analysis. ) and transcendental number theory (I don't know if it's a transcendental number…), also interested in Euler's infinite series.--SilverMatsu (talk) 14:28, 26 May 2021 (UTC)
 * I agree — I revised the sentence about the constant and moved it to the analysis section. Also, I'd sort of like to eliminate the "Applied mathematics" section altogether, and redistribute its subjects into other sections. Adumbrativus (talk) 04:03, 27 May 2021 (UTC)

The article has been moved to the Featured Article Removal Candidates section. XOR&#39;easter (talk) 17:45, 6 June 2021 (UTC)

Re: John Rognes (mathematician)
Found in new article queue. Please review and expand at your leisure. Many thanks. --Gryllida (talk, e-mail) 06:52, 7 June 2021 (UTC)

Copyvio in Quadratic reciprocity
The proof of quadratic reciprocity given in Quadratic reciprocity is a blatant copyright violation: it is a verbatim copy (letter for letter, down to idiosyncracies in the notation) of almost the complete text (only omitting the initial sentence) of the paper Bogdan Veklych, A Minimalist Proof of the Law of Quadratic Reciprocity, The American Mathematical Monthly 126 (2019), no. 10, p. 928, doi: 10.1080/00029890.2019.1655331. (It’s a short paper.) I tried to remove it, but I am being reverted by user, who hasn’t got the slightest clue about copyright law and scientific publishing (see talk), but is all the more aggressive for it. Can someone else have a look?—Emil J. 07:38, 9 June 2021 (UTC)
 * Yes, can please someone else have a look? I'm pretty sure reproduction of a mathematical proof (of all things!) published somewhere is not copyright violation, otherwise no mathematical proof will be legally reproducible after it's found?! — Preceding unsigned comment added by Strecosaurus (talk • contribs) 11:41, 9 June 2021 (UTC)
 * I've been editing Wikipedia for 7 years (and this section appears to have existed intact for over a year, by the way) and this is the most ridiculous thing I've ever seen. A reproduction of a mathematical proof is forbidden?! What? Then any mathematical proof or definition, once it's found, can never be presented again, because it occurs in the original article, and so reproducing it again would be violating the copyright? Is this the logic?! — Preceding unsigned comment added by Strecosaurus (talk • contribs) 11:50, 9 June 2021 (UTC)
 * Wow. --JBL (talk) 13:56, 9 June 2021 (UTC)
 * Yeah, that's way too close a copy to be permissible. Reproducing the logic of an argument is one thing, but carrying over the prose and the notation practically verbatim is another. And the fact that it hung around for a year is immaterial; a problem is still a problem even if people were late to notice it. XOR&#39;easter (talk) 16:10, 9 June 2021 (UTC)

A pointer
Hi, mathematicians! There's a discussion going on about what constitutes a "routine calculation", and I think it would benefit from your input. Please see Wikipedia talk:No original research.—S Marshall T/C 17:08, 12 June 2021 (UTC)

Retarget Complex variables to Complex analysis
Retarget to Complex analysis, and with hatnote to Function of several complex variables. Also delete "Complex variables (disambiguation)". Also see Redirects for discussion/Log/2021 June 5. thanks!--SilverMatsu (talk) 04:00, 8 June 2021 (UTC)

To be clear, the discussion is invalid in Redirects for discussion (Complex variables (disambiguation)). Apparently, on this page or on the complex variable talk page, the discussion has to be restarted from the beginning. I am sorry to have those who participated in the discussion express their opinions again.--SilverMatsu (talk) 01:14, 9 June 2021 (UTC)


 * I've summarised the issue at Talk:Complex variables. Interested editors can participate there. --Paul_012 (talk) 18:08, 13 June 2021 (UTC)

Draft:Dirichlet character
A draft, Draft:Dirichlet character, was submitted for review. However, it seems to be a modified version of the article that we already have, Dirichlet character, and Articles for Creation is not the way to propose changes to an existing article. I don't know whether it will be obvious to a mathematician what has changed, let alone whether the changes should be made. I just thought I would call this to your-all's attention. Robert McClenon (talk) 20:55, 13 June 2021 (UTC)

every vs. any vs. arbitrary
For example, I would like some advice about Function of several complex variables. I'm wondering whether to make it "any" or "arbitrary". "any" seems to have a similar meaning to "for all" and has been used for one variable (also, "every" was often used), but several complex variable textbooks and papers often use "arbitrary", so only use for $$\Complex^n$$, "arbitrary". Because it feels like arbitrary is randomly selected. There is also an arbitrary complex manifold, but I follow the paper because for several complex variables their nature depends on how the space is taken anyway. Perhaps this is also useful when editing other articles, and I don't understand this well. thanks!--SilverMatsu (talk) 06:01, 30 May 2021 (UTC)
 * I suggest avoiding "any": it can be used in some situations for both existential and universal quantifiers in normal speech, so is confusing about which formal statement it corresponds to. (For example, "if any x satisfies F(x) = 0" as a stand-alone phrase could mean "if every x satisfies F(x) = 0" or "there exists an x such that F(x) = 0", depending on context.)  "An arbitrary" may suffer from the same problem, again depending on context.  "Each", "every", and "for all" do not have this problem.  They have different grammatical behaviors, so which one to use is largely a question of writing style (does the sentence work better with a singular or a plural?). The current lead section of Function of several complex variables has much more serious grammatical/language issues than this choice.  At some point hopefully it will be copy-edited by a fluent English speaker, who will have the opportunity to patch this up.  Personally, I would write "For one complex variable, every domain $$D \subset \Complex$$ is the domain of holomorphy of some function.  For several complex variables, this is not the case, and so ...." Or, if I wanted to really drive home the point: "For one complex variable, every domain $$D \subset \Complex$$ is the domain of holomorphy of some function.  For several complex variables, this is not the case: there exist domains that are not the domain of holomorphy of any function, and so ...." -JBL (talk) 11:36, 30 May 2021 (UTC)
 * It's surprising that Manual of Style/Mathematics does not give advice on this issue. Mgnbar (talk) 12:56, 30 May 2021 (UTC)
 * Thank you for the advice and reply. I edited it a little and replaced it with "every". I agree that the Manual of Style needs advice. Also, apparently there is a page of the arbitrary, but there was no template for WikiProject Mathematics. Replacing "arbitrary" seems difficult about Levi's problem statement seems difficult. For example; each complex manifold chosen for arbitrary? --SilverMatsu (talk) 15:32, 31 May 2021 (UTC)
 * Existential quantifiers can also sometimes be replaced by verbs of possession: "every domain has a function for which it is the domain of holomorphy". —David Eppstein (talk) 19:49, 31 May 2021 (UTC)
 * Thank you for the advice. It's an interesting. By repeating the paraphrase, it becomes clear.--SilverMatsu (talk) 11:32, 1 June 2021 (UTC)

English-speaking mathematicians use "any" too much. They forget that in some contexts, it means "some" rather than "every". "If every A is B then...." is clear. "If any A is B then..." might mean "If there is any A that is B, then..." or it might mean "If it is the case that any A, no matter which one, is B, then..." In the first case, it means "some"; in the second, it means "every". Michael Hardy (talk) 04:38, 6 June 2021 (UTC)
 * Thank you for the advice. Even if the paper uses "any", I will now try to choose clearer words when quoting to wikipedia--SilverMatsu (talk) 03:28, 15 June 2021 (UTC)
 * ✅ I boldly added a note based on 's example at the end of Mathematics#Writing_style_in_mathematics, which seems the most appropriate place to me. Please improve if necessary. - Jochen Burghardt (talk) 15:13, 15 June 2021 (UTC)
 * Thank you!--SilverMatsu (talk) 03:10, 16 June 2021 (UTC)

Feature request on Phabricator
I've submitted a feature request on Phabricator for continuous numbering and cross-referencing of list items. The request itself concerns example numbering in linguistics articles, but I suspect this functionality would be useful for theorem numbering in mathematics articles as well. If you would support this idea or if you would like to add anything to the feature request, you can leave a comment at the Phabricator page. Alternately, if anybody has any handy tricks or secret workarounds using currently existing features, please do share! Botterweg14 (talk) 15:19, 16 June 2021 (UTC)

The 10 most-viewed, worst-quality articles according to this Wikiproject

 * 910	Nim	13,375	431	Unknown	Unknown
 * 31	Charles Hoskinson	99,039	3,194	Start	Unknown
 * 88	666 (number)	61,931	1,997	Start	Low
 * 131	Sigmoid function	52,201	1,683	Start	Low
 * 156	Bernoulli distribution	47,010	1,516	Start	Low
 * 188	Dependent and independent variables	43,152	1,392	Start	Mid
 * 196	Breadth-first search	41,806	1,348	Start	Mid
 * 224	Eric Weinstein	38,784	1,251	Start	Low
 * 226	Googol	38,581	1,244	Start	Low
 * 230	Transpose	38,176	1,231	Start	Mid

WikiProject Mathematics/Popular pages--Coin945 (talk) 07:16, 19 June 2021 (UTC)
 * I don't know why you list Nim as unrated. An anonymous editor just rated it as C-class, two weeks ago. I agree (it's too detailed for start-class and has too much unsourced content to be B-class). —David Eppstein (talk) 07:29, 19 June 2021 (UTC)
 * I'm pulling data from WikiProject Mathematics/Popular pages - it was listed as 'Unknown' there. --Coin945 (talk) 08:19, 19 June 2021 (UTC)

FAR for Polar coordinate system
I have nominated Polar coordinate system for a featured article review here. Please join the discussion on whether this article meets featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" the article's featured status. The instructions for the review process are here. Z1720 (talk) 14:39, 19 June 2021 (UTC)

RM Trapezium and Trapezoid
Members of this project may find Talk:Trapezium and Trapezoid interesting.-- Eostrix  (&#x1F989; hoot hoot&#x1F989;) 16:05, 21 June 2021 (UTC)

Requested move: Indecomposable → Indecomposability (disambiguation)
A RM was started at Talk:Indecomposable; discuss there if interested. (I'm posting a notice here since it's about mathematics but is not in the article alerts.) Adumbrativus (talk) 07:56, 22 June 2021 (UTC)

I would like to create a Hartogs' Inverse Problem as a redirect of Levi's problem
Oka calls Levi problem. problème inverse de Hartogs. Hartogs shows Oka's lemma in the case of two variables, which is Hartogs's problem, and Levi's problem is the opposite. And the problem of Levi problem has various meanings now. (e.g. Stein manifold, Complex projective space, Stein space, etc.) Oka's proof is an unramified Riemann domain ($$\Complex^n$$), so this term may also accurately refer to Oka's achievements. thanks!--SilverMatsu (talk) 16:37, 16 June 2021 (UTC)

I added it to Oka's lemma because there is an aspect that Oka called it. Would you like to redirect to Oka's lemma lemma?--SilverMatsu (talk) 02:30, 19 June 2021 (UTC)

Addendum 1; Perhaps the decision to create a redirect depends on how English-speaking mathematicians often call Levi's problem. From the same point of view, we can decide whether to send the Draft:Gaussian symbol to MfD vs. RfD.--SilverMatsu (talk) 03:16, 19 June 2021 (UTC)

Addendum 2; For drafts, it seems that in some countries the symbol representing the floor function is called the Gaussian symbol, and if English-speaking mathematicians do not use this term often or use it in a different sense, send it to MfD.--SilverMatsu (talk) 07:34, 19 June 2021 (UTC)

I noticed that the draft:Gaussian symbol was translated from Chinese wikipedia, so check Babel and ping .--SilverMatsu (talk) 02:03, 24 June 2021 (UTC)

reference

 * PDF TeX
 * PDF TeX

about Euclid's theorem
I would like to some advice about the edit warring. I tried to avoid the Euler product argument when it was Re(s) = 1. thanks!--SilverMatsu (talk) 10:39, 29 June 2021 (UTC)

I forgot to write a set. perhaps, If P is the set of all prime numbers and the prime number set (set P) is finite set …--SilverMatsu (talk) 11:09, 29 June 2021 (UTC)
 * 1. This is what article talk-pages are for: you made a bad edit, it was reverted, you should now begin discussion on the article talk-page if you want to reach consensus. 2. Have you considered instead editing Wikipedia in whatever your native language is?  I suspect you could be a valuable editor there. --JBL (talk) 11:59, 29 June 2021 (UTC)
 * Thank you for your advice. I apologize for my lack of ability, but I will try my best.--SilverMatsu (talk) 13:33, 29 June 2021 (UTC)

Dirichlet character
I have rewritten the article Dirichlet character.

A number of years ago I edited several number theory articles including Quadratic reciprocity, Arithmetic function, and Floor and ceiling functions under the name Virginia-American. The computer died, I lost my password, etc., and finally now I'm back under a new handle.

Could someone who knows the conventions please add categories, ratings, and so forth?

Thanks

James in dc (talk) 21:33, 30 June 2021 (UTC)