Wikipedia talk:WikiProject Mathematics/Archive/2021/May

about Function (mathematics)
I was confused about the redirect f(x). (About the ambiguity that appears at the beginning of the function article by redirecting to the function.) The girls group seems like Abelian groups, Lie groups and Galois groups, but they were actually music artists. Personally, I think the function is just f. We might think this is a Dynamics (music) forte. I would like to know what kind of rules an artist has when he uses the theorems and symbols that are often used in mathematics as a respect for mathematics. (This is a rule about article names on wikipedia. Duplicate with the following sentence) If artists add the theorems and symbols commonly used in mathematics to their group (does not Group (mathematics)) names as a respect for mathematics, do they need to be reflected in mathematics articles?--SilverMatsu (talk) 22:56, 21 April 2021 (UTC)
 * I'm confused about what you're trying to ask. But I suspect that in this case the musicians are the ones that meet WP:COMMONNAME (especially because that's their main name, not an alternative name for them) and that the redirect and hat should go the other way. —David Eppstein (talk) 00:53, 22 April 2021 (UTC)
 * Thank you for your reply. The main confusion I had was that the Function (mathematics) would show the music artists, so if we redirect f(x) to the music artists, that's fine. My other question is, if artists, etc. use math-related terms (f(x) this time) in their names, do they need to write in the math article? (function this time) Also about name priority, but this time redirecting f(x) as a music artist was a solution as we didn't have to write about the music artist in the function.--SilverMatsu (talk) 01:26, 22 April 2021 (UTC)
 * If we determine that the primary meaning of "f(x)" is the musicians, then we should move the article to that name, not redirect that name to the article. —David Eppstein (talk) 01:36, 22 April 2021 (UTC)
 * Thank you for your reply and advice. Certainly it seems that we need to consider moving pages as well. I think that the meaning of f (x) is most often used as a function and has a long history, but when we would like to refer to an article function, we probably don't look up f(x). Rather, in a math article, are you trying to refer to another article? When asked, it's strange to move away from articles in the field of mathematics. In fact, I thought it was about math, so I thought of the girls group as a new group by group theory. (This my misunderstanding is a embarrassing.) I was able to confirm whether wikiproject:mathematics needed the article name f(x), apparently, so it seems necessary to leave it to another wikiproject. The math article showed a music artist, so I was very confused about where to consult. After that wikiproject:music?--SilverMatsu (talk) 02:15, 22 April 2021 (UTC)
 * Someone who puts "f(x)" into the search bar is someone who is looking for information about something called "f(x)". If you pick up any calculus textbook, you will see hundreds of equations that contain the expression "f(x)", and the article Function (mathematics) is the obvious starting point for gathering information about what this means.  If you already know that the article Function (mathematics) is the correct starting point for finding information about this topic, you would not use this redirect, but so what?  I think you are not considering broadly who is served by navigational aids like this. --JBL (talk) 12:53, 22 April 2021 (UTC)

Looking at the corresponding talk page, it seems good to move if there is no problem from the viewpoint of mathematics. The f (x) link doesn't seem to be a problem either. Therefore, if there is no objection on this page(discussion), it seems good to move.--SilverMatsu (talk) 07:32, 22 April 2021 (UTC)

I started the discussion. The article itself doesn't seem to be related to mathematics, but you might be interested in discussing the meaning of f (x).--SilverMatsu (talk) 11:16, 22 April 2021 (UTC)
 * Apparently there was a no consensus to move to the musical group. (Thanks to D.Lazard). Thank you for participated in the discussion.--SilverMatsu (talk) 15:05, 1 May 2021 (UTC)

Proposal: move(Change the article name) Several complex variables to Function of several complex variables
This is a complex variable in Talk:Complex analysis and has been discussed. For the one complex variable, it seems like a section redirect to Complex functions(in complex analysis), then, the pair seems like Functions of several complex variables. Also, the article names of Several real variables are Function of several real variables. thanks!--SilverMatsu (talk) 04:49, 11 March 2021 (UTC)
 * To clarify, this is what you are proposing:• Retarget: Complex variable → Complex analysis

• Redirect Complex variables → Function of several complex variables

• Move: Several complex variables → Functions of several complex variables

• Keep: Several real variables → Function of several real variablesIs that correct? — MarkH21talk 05:00, 11 March 2021 (UTC); add "Complex variables" to the list 06:34, 11 March 2021 (UTC)
 * Thank you for clarifying. sorry, I made a misspelling. But also include Retarget changes in the proposal. The correct spelling is Complex variables.(This seems to be a separate page from the complex variable.)--SilverMatsu (talk) 05:17, 11 March 2021 (UTC)
 * So also add "Redirect Complex variables → Function of several complex variables" to the list above? — MarkH21talk 05:44, 11 March 2021 (UTC)
 * Thank you for your help. I was a little confused because I didn't think it was another page without the s(I overlooked complex variable), but I realized it would be better to add the idea you proposal.--SilverMatsu (talk) 05:57, 11 March 2021 (UTC)


 * Support (with two modifications): The proposal looks reasonable to me. The proposed organization clarifies the relationship between the subjects and are also common in the literature. I would probably leave Complex variable as it is, since theory of functions of a complex variable is bolded as an alternative term in the first sentence at Complex analysis. I would also retarget Real variables → Function of several real variables. — MarkH21talk 06:39, 11 March 2021 (UTC)
 * SupportTazerenix (talk) 07:11, 11 March 2021 (UTC)
 * Support (Including modifications to two proposals by MarkH21.)--SilverMatsu (talk) 07:57, 11 March 2021 (UTC)
 * Oppose moving to Function of several complex variables. "Several complex variables" long since became a common name for that whole field of study (it also goes by other names such as "complex analysis in several variables"). Witness how people write books and articles entitled Several Complex Variables, "What is Several Complex Variables?", etc., and how it gets treated as a singular noun. Also note how the Mathematics Subject Classification has, as a top-level heading, "Several complex variables and analytic spaces". The article, whose topic is not just the functions but the field of study, should remain called Several complex variables. Consistency with "Function of several real variables" may seem appealing superficially, but the two cases simply aren't analogous. Adumbrativus (talk) 09:16, 11 March 2021 (UTC)
 * "Several complex variables" is a classical name for the subject (and perhaps the most common), but so are the longer "Functions of several complex variables", "Theory of several complex variables", and "Theory of functions of several complex variables". It's true that "several complex variables" can denote a broader subject than just the function theory (i.e. analytic geometry), although the function theory is the core of the subject and the most classical meaning of the term. For example:• Several Complex Variables: "The present book grew out of introductory lectures on the theory of functions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory"

• Several Complex Variables and Complex Geometry, Part 3: Equates "several complex variables" with the "function theory of several complex variables"

• Several Complex Variables II: Uses "several complex variables" interchangeably with "theory of functions of several complex variables" Perhaps "complex analysis in several variables" (it's unfortunate that this isn't even mentioned at complex analysis) would be a better article title though, for giving a precise and recognizable name for non-expert audiences. — MarkH21talk 16:33, 11 March 2021 (UTC)
 * Oppose: basically per Adumbrativus. The term "several complex variables" seems to be quite well established. While "real analysis" can include the study of functions in several real variables, "complex analysis" is typically limited to functions in one complex variable. So, we need some term to refer to complex analysis in several variables. —- Taku (talk) 18:39, 11 March 2021 (UTC)
 * Thank you for your reply and follow up. What about Function theory of several complex variables? Function theory is the traditional name for complex analysis. But I'm a worried that the meaning of this name is too narrow.--SilverMatsu (talk) 15:30, 12 March 2021 (UTC)
 * Add two textbooks with the title Function theory.--SilverMatsu (talk) 16:38, 12 March 2021 (UTC)
 * Add two textbooks with the title Function theory.--SilverMatsu (talk) 16:38, 12 March 2021 (UTC)
 * Add two textbooks with the title Function theory.--SilverMatsu (talk) 16:38, 12 March 2021 (UTC)


 * Addendum:What I mentioned earlier is about complex analysis in several variables. So for now, I support Functions of several complx variables. Users searching for Several complex variables seem to be looking into what several complex variables mean, and Functions of several complex variables is the concise answer (IMO). It is true that this field is called several complex variables as a branch of complex analysis, but I'm not trying to change Category:Several complex variables.--SilverMatsu (talk) 01:29, 16 March 2021 (UTC)
 * Addendum2:Apparently, Krantz says to limit oneself to the study of one complex variable is to do complex analysis with one eye closed, so it seems too narrow to limit complex analysis to one variable. but, this does not seem to affect the redirect target. One complex variable seems to be a classical complex analysis.--SilverMatsu (talk) 15:32, 20 March 2021 (UTC)

amendment:How about turning Several complex variables into Several complex variables (DAB) pages instead of redirects?--SilverMatsu (talk) 15:25, 13 April 2021 (UTC)
 * Addendum:Article titles keep Several complex variables. Dab is added to clarify the proposal and is not intended to change the article name. (Assuming that the page name has been moved to Function of several complex variables.)--SilverMatsu (talk) 15:35, 15 April 2021 (UTC)

about the lead sentence
Currently, the lead sentence is In complex analysis, the theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions in the space $\Complex^n$ of n-tuples of complex numbers, and especially the the theory of functions of several complex variables is the branch of mathematics part has not changed from the beginning. To be clear, the bold part was initially only the several complex variables. This was one of the reasons I support to functions of several complex variables as the article name, but if the article name doesn't change, it seems like the lead sentence needs to be improved a bit.--SilverMatsu (talk) 15:31, 3 April 2021 (UTC)
 * It seems to have improved now. Thanks to Michael Hardy.--SilverMatsu (talk) 15:08, 13 April 2021 (UTC)

It seems that the page has been moved
See Function of several complex variables. I'll ask if there was a consensus.--SilverMatsu (talk) 20:57, 22 April 2021 (UTC)
 * If there is no opposition, I will close it as moved.--SilverMatsu (talk) 15:24, 1 May 2021 (UTC)

Help requested with some references in the groups article
The article on groups is currently undergoing a featured article review, [here]. In the course of that, it was requested to add references for some statements. I have currently very little time and didn't find immediately one, can anyone help out here, please? thanks a lot (either include the references directly in the article and reply to the requests [here] or tell me and I can add them). Thanks a lot!


 * "The word homomorphism derives from Greek ὁμός—the same and μορφή—structure."
 * "These days, group theory is still a highly active mathematical branch, impacting many other fields." (we have a reference about the activity of this branch, but not about that it impacts many other fields)
 * "A presentation of a group can also be used to construct the Cayley graph".

Jakob.scholbach (talk) 19:19, 2 May 2021 (UTC)
 * Are homomorphic first references useful?--SilverMatsu (talk) 00:50, 3 May 2021 (UTC)
 * Yes, certainly. Jakob.scholbach (talk) 07:12, 3 May 2021 (UTC)
 * , Allen Hatcher's Algebraic Topology has a heading Cayley Complexes in Section 1.3 with a good discussion. It assumes that you also have a list of the elements of the group, which I guess involves solving the word problem for groups.  (So maybe the statement in the article should be tweaked.) Russ Woodroofe (talk) 08:08, 3 May 2021 (UTC)
 * Indeed, the Magnus, Karass, and Solitar source listed in the article says that the problem of computing the Cayley graph from the presentation is obviously equivalent to the word problem. I suggest removing the sentence, and possibly mentioning the Cayley graph elsewhere.  Alternatively, restructure the paragraph to put Cayley graphs in the middle.  I think the right thing to say is that "The elements and a set of generators of a group can be used to construct a Cayley graph, a device used to graphically describe discrete groups." Russ Woodroofe (talk) 09:30, 3 May 2021 (UTC)


 * Wrt. applications of mathematics, the 2016 Nobel Prize in Physics was awarded for the discovery of what are now called topological materials (to my surprise we don't seem to have an article on the whole class of such materials, but we do on the most important subclass, topological insulator). Actually investigating the chemical possibilities of these materials has involved substantial group theory, e.g., Topological Quantum Chemistry, Nature (2017), 547/7663:298-305. &mdash; Charles Stewart (talk) 05:28, 4 May 2021 (UTC)

x naught
Does the team agree that the correct way to read $x_0$ is "x naught" as claimed in ? Certes (talk) 23:54, 4 May 2021 (UTC)
 * I tend to agree with it. But I don't have any good sources.  It's just what I picked up, who knows where. --Trovatore (talk) 00:20, 5 May 2021 (UTC)
 * I have reverted; it is an acceptable way to read the subscript 0, not "the correct" way; I find it deeply implausible that this could be supported by sources. --JBL (talk) 02:08, 5 May 2021 (UTC)
 * For what it's worth, I would probably pronounce it "x sub zero" or "x zero". To my ears "naught" sounds very British. —David Eppstein (talk) 02:23, 5 May 2021 (UTC)
 * x-naught is extremely British. Around here (Canada), it's x-zero. &#32; Headbomb {t · c · p · b} 04:20, 5 May 2021 (UTC)


 * Here in the US, I've heard "x naught", "x sub zero", and maybe "x zero". Bubba73 You talkin' to me? 04:59, 5 May 2021 (UTC)
 * I agree, naught is more British and nought is more American. -- 05:36, 5 May 2021 (UTC)
 * Divided by a common language? I think it's just that British English spells two different concepts differently: naught means 'nothing' and is slightly archaic; nought means zero and in common use. As a British speller, the spelling x-naught jars with me; but either x-nought or x-zero seem quite natural (with their obvious pronunciations). NeilOnWiki (talk) 11:55, 5 May 2021 (UTC)
 * I also use British English and agree with Neil's analysis: nought means zero and naught (archaic) means nothing, but the two are interchangeable in loose chat. I say either "x zero" or something that sounds like "x naught".  Having only written it with a 0 symbol, I never thought much about the spelling, but on reflection I think of it as "x nought". Certes (talk) 12:18, 5 May 2021 (UTC)
 * Thanks for all the useful input. The edit has been reverted, which seems the best course of action.  I just noticed that Aleph number mentions aleph-nought, also aleph-zero or aleph-null so (if we can treat x as a placeholder for $$\aleph$$) I don't think we can say "x naught" is the correct way (my emphasis). Certes (talk) 12:18, 5 May 2021 (UTC)
 * That's the specific one that really bugs me, to be honest. As far as I'm concerned it's "aleph-naught", not "aleph-nought".  --Trovatore (talk) 21:25, 5 May 2021 (UTC)
 * Only now do I realize the missed opportunity: I should have used the edit summary noughty noughty. --JBL (talk) 13:18, 5 May 2021 (UTC)

about Pseudoconvexity
Is it related to Convex analysis? It didn't seem to me to be related, but I wasn't studying enough so I thought I'd ask the community a question.--SilverMatsu (talk) 12:40, 11 May 2021 (UTC)


 * Convex analysis usually considers a situation in real Euclidean space while pseudoconvexity is considered in complex (Euclidean?) space $$\mathbb{C}^n$$. So, no, I think. -- Taku (talk) 07:07, 12 May 2021 (UTC)


 * Thank you for your reply. So, maybe I think no too, so I'll try to get remove of the convex analysis.--SilverMatsu (talk) 08:41, 12 May 2021 (UTC)

By the way, I thought of a short explanation of the same article.
 * 1) Convexity similar to holomorphically convex.
 * 2) Convexity derived from the plurisubharmonic function.

Writing both is probably too long. thanks!--SilverMatsu (talk) 11:48, 12 May 2021 (UTC)

Would you think Numdam will meet Notability (In English wikipedia) like Project Euclid?
It's my first time to add it to Requested articles/Mathematics, so I thought I'd ask before adding it. I've added citations from there several times, but I don't have enough French ability to write the article (Numdam?) myself. (cf. Numérisation de documents anciens mathématiques maybe… ) thanks!--SilverMatsu (talk) 05:50, 12 May 2021 (UTC)
 * The French article has nothing that looks like the kind of reliable in-depth independent sourcing needed to pass WP:GNG. Such sourcing would be needed for it to be notable. And since it is likely that sourcing (if it exists) would be in French, some ability to read French is probably also needed. —David Eppstein (talk) 06:11, 12 May 2021 (UTC)
 * Thank you for your reply. When I search for a paper written in French, I find Numdam, but I haven't found the source of Numdam itself yet.--SilverMatsu (talk) 07:16, 12 May 2021 (UTC)
 * seems a pretty good starting point. &#32; Headbomb {t · c · p · b} 12:20, 12 May 2021 (UTC)
 * Yes, certainly. Thank you! But I don't have any prior knowledge about Numdam so it takes time. --SilverMatsu (talk) 14:43, 12 May 2021 (UTC)

Proposal: Demystify math written in symbols by including programming language style code side-by-side
I'd be surprised if this doesn't come up, but it seems like the math articles are particularly low on value to readers not well versed in mathematical symbols. As a programmer I find these symbols looks impressive and cryptic, but rewritten in computer language style code can appear very trivial and unimpressive and hence easier to grasp, since computer language works with only a few rudimentary symbols instead of abstract levels of arbitrary symbols. All I'm saying is Wikipedia could be a great resource to teach math concepts if it did this I think, and programmers could benefit from being able to easily use math concepts in their work without deciphering them like hieroglyphics first --72.173.4.14 (talk) 10:54, 15 April 2021 (UTC)
 * There are several related problems, and the optimal solution must be a compromise between them.
 * A first problem is that many symbols should better replaced by prose. For example "for $$x \in X$$" is easier understood as "for $x$ in $X$ ". Copy editing articles for making such changes would solve a part of your concern. However many articles have other issues that are worse. So, I make such changes only as a side action of fixing other issues. I suspect that most of the competent math editors do the same. Your help would thus be welcome.
 * A second problem is that any "computer language style code" involves conventions that are programming language dependent. So for a wider understanding, it is better to keep the conventions that are established since centuries. Also many mathematical formulas are hardly expressible in a computer language style.
 * On the other hand, many articles could be improved by replacing a lengthy description of an algorithm by its description in pseudo-code, followed by a explanation of the meaning of the pseudo-code. Examples are Euclidean algorithm, where the very simple pseudocode appears only at the end of the article, and long division, where a pseudo-code description could provide a synthetic view that is difficult to extract from the given verbose description. D.Lazard (talk) 13:17, 15 April 2021 (UTC)
 * For the record I'm seeding the idea, it would be a colossal undertaking to even develop the style guidelines. I don't think the articles should be dumbed down, and this project should (would) be overseen by mathematicians. I'd say the existing notation has problems because it's usually just an image. This kind of concept could help with that by providing a version that can be selected (copy/paste). If I were asked how to format it, I would suggest putting a clickable icon beside appropriate math text that expands a box that cuts across the entire width of the container, so that any text before the math inline notation (including it) is above this box and any after is below it (after expansion) and inside this box just use something like calculator notation for traditional math, and programmer's notation for structured/stateful elements. This could be very useful because abstractions can be written as opaque functions and those can be links that when hovered over with the mouse reveal the body of the function at least up to one level. I just think this would add so much value to the many math articles that can seem impenetrable to non-mathematicians. Programming is something more and more people are familiar with and is generally easier to understand with less memorization and familiarization with symbols. For math that is not inline inside text it would be good to put the code in an already expanded box beside the math notation to put it on the same level, especially because often it's likely to be more readable to a layman --72.173.4.14 (talk) 15:01, 15 April 2021 (UTC)
 * Further note, a lot of this would probably be done by bots after some test pages are developed. It just seems like a commonsensical thing to do. Especially since the images that are currently generated are so unlike the rest of the text in Wikipedia --72.173.4.14 (talk) 15:05, 15 April 2021 (UTC)
 * RE "for x in X" I think this would be perfect to put in the "title" element in the HTML so it shows in a balloon when the mouse hovers over it. This will teach people the math symbols too if they do it enough times, which would be enriching. Edited: As for putting an icon to the side, it could be clicking anywhere on these static images also expands an info box just as such an icon would, just so it's less trouble to get your mouse over a small icon --72.173.4.14 (talk) 15:08, 15 April 2021 (UTC)
 * It's a nice idea, but there are many devils in the details. Much of math is not algorithmic, so you may be overestimating the fraction of math articles that could benefit. As a test case, you might think about how to implement your idea for the article Limit (mathematics). It's an extremely common topic that exists somewhere in the middle of the abstraction spectrum (not as concrete as arithmetic, but less abstract than much of the mathematics of the past couple centuries). Mgnbar (talk) 13:59, 17 April 2021 (UTC)
 * A good rule of thumb is to ask if a programmer without a degree in mathematics (who doesn't or can't memorize formulas, etc.) needs to implement the math in a program, then if that situation could arise, how would they do it. If it's a concept so trivial or abstract that it doesn't make sense in that context then it probably isn't a good candidate for a practical (non symbolic) translation to a less specialized language than that of a mathematician. The thing about programming languages is their syntax is usually minimal compared to mathematical syntax, preferring nested function names to introduction of hieroglyphics not found on keyboards --72.173.4.14 (talk) 00:46, 3 May 2021 (UTC)
 * With respect to a style guide, that doesn't matter for your proposal yet. Style guides attempt to encourage consistency with what we have: the rules can only be made when the practice exists. &mdash; Charles Stewart (talk) 08:33, 22 April 2021 (UTC)
 * There has been some work done on making mathematical formulae self-explaining using information stored in Wikidata. For example, if you click on the formula E=mc^2 you will be connected to a query of Special:MathWikibase which gives an explanation in English. How this is done is partially explained in this paper. In October several of the equations in the article Matter wave were expanded to do this. StarryGrandma (talk) 06:08, 20 April 2021 (UTC)
 * Hmm. I have to say I'm skeptical that that's really a good idea.  Clicking on equations is not an intuitive interface.  It would be better to give a brief explanation in text, with links for further exploration. --Trovatore (talk) 02:17, 22 April 2021 (UTC)
 * +1 At least in the current the links don't yield any useful information, but at best repeating informations that usuallsy is already contained in the article using the formula. In addition there is visual marker clearly indicating that the formula represents a link.--Kmhkmh (talk) 16:05, 12 May 2021 (UTC)
 * Whatever anyone can take from this I think the current status quo of representing math with static (non-interactive) images is abysmal and should be an embarrassment to the math pages of Wikipedia. If that problem can't be solved automatically then at least this proposal could begin to supplement it. Honestly static images feels like the WWW of 20 years ago --72.173.4.14 (talk) 00:49, 3 May 2021 (UTC)
 * , I'm not seeing it, maybe I'm looking in the wrong place. Can you specify an example equation? S Philbrick  (Talk)  13:59, 12 May 2021 (UTC)
 * Browse through the article's source and seek for &lt;math qid=....&gt; --CiaPan (talk) 14:26, 12 May 2021 (UTC)
 * The equation in StarryGrandma's post is an example. --JBL (talk) 14:37, 12 May 2021 (UTC)
 * Indeed. I didn't notice that until tested in Edge. --CiaPan (talk) 15:19, 12 May 2021 (UTC)
 * (ec) Also, the equation placed above is linked, too. Alas, the link seems to not work in Samsung Internet browser in my phone nor in Google Chrome browser in my laptop. It does, however, in MS Edge. No idea how it behaves in other browsers. --CiaPan (talk) 14:38, 12 May 2021 (UTC)
 * It works fine for me on Edge (running on Windows) and on Firefox (running on a Mac). --JBL (talk) 17:42, 12 May 2021 (UTC)

Ugly duckling theorem
Could somebody please have a look at the dispute Talk:Ugly_duckling_theorem and help to settle it? The controversy is whether the Ugly duckling theorem applies to a finite number n of objects or to a countably infinite number n. Many thanks in advance. - Jochen Burghardt (talk) 12:28, 27 April 2021 (UTC)
 * More precisely, the dispute is whether the Ugly duckling theorem applies to countable sets of $$n$$ objects or to some other sets of objects, such as sets of objects represented by ordinal numbers that do not commute under addition.Guswen (talk) 13:13, 27 April 2021 (UTC)
 * Thanks for helping with the capitalization, but this wasn't our problem. The dispute Talk:Ugly_duckling_theorem is the one we need external help for. In my view, it boils down (per WP:RS) to the question whether the source Woodward.2009 does allow n in Ugly_duckling_theorem to be countably infinite (as sees it) or not (as I see it; I summarized my view on Woodward.2009 in the last paragraph of Ugly_duckling_theorem). - Jochen Burghardt (talk) 12:35, 12 May 2021 (UTC)
 * I was not able to make any sense of Guswen's arguments at all. --JBL (talk) 13:39, 12 May 2021 (UTC)
 * And what are your counterarguments? Guswen (talk) 13:55, 12 May 2021 (UTC)
 * More precisely, the dispute is whether the Ugly duckling theorem applies to countable sets of $$n$$ objects, i.e. whether the objects considered in the Ugly duckling theorem can be counted or not.
 * The meaning of the phrase "n things in the universe" is simply imprecise. Are these things countable? Or perhaps they are uncountable?
 * The grounds of our dispute are therefore broader that just WP:RS. Guswen (talk) 13:54, 12 May 2021 (UTC)
 * What do you think the definition of "countable" is? --JBL (talk) 13:55, 12 May 2021 (UTC)
 * You shall find my definition of a countable set in this Wikipedia article: countable set. Guswen (talk) 14:01, 12 May 2021 (UTC)
 * Please learn how to indent your posts properly. In the sentence "Suppose there are n things in the universe", what do you think the symbol n represents? (It may help you to read the introduction of the article when answering this question.) --JBL (talk) 14:03, 12 May 2021 (UTC)
 * I have no idea what does it represent. The meaning of the phrase "n things in the universe" is simply imprecise in my opinion. Would you please enlighten me? Guswen (talk) 14:07, 12 May 2021 (UTC)
 * I see your point. But the UDT does not apply to finitely many objects (Cf. Woodward.2009) Guswen (talk) 14:09, 12 May 2021 (UTC)
 * At present, the article is about a 50-year-old theorem concerning finite collections of objects. Woodward appears to introduce a new extension of that theorem, to countably infinite collections of objects.  Maybe it is appropriate to have a section of the article Ugly duckling theorem that discusses this extension (I do not have an opinion on this).  But what you have been doing is not that.  The article talk-page would be a good place to discuss whether and how best to discuss the extension (again, something I do not have an opinion on). --JBL (talk) 14:19, 12 May 2021 (UTC)

The ugly duckling theorem was derived by Satosi Watanabe in 1969 in the publication "Knowing and Guessing: A Quantitative Study of Inference and Information". It is a part of a chapter "Logic and Probability" (begins at p. 299). In Section 7.3. of this chapter ("Formal Concept of Probability") on p. 336 he writes: ""We consider a set $X$ of objects $x$ (…). The number of $x$’s in $X$ may be finite, countably (enumerably) infinite, or continuously many.”"

Then in Section 7.6 "Theorem of the Ugly Duckling" on p. 376 he proceeds to derive his theorem writing, among others: ""The purposes of this section is to show that from the formal point of view there exist no such thing as a class of similar objects in the world""

He provides an instructive comment also in p. 5 (my emphasis added): ""In the following we usually discuss the case in which $n$, the number of elements in a logical spectrum, is finite. Many of the results obtained will remain valid for the case in which $n$ is countably many (enumerably infinite), although they sometimes break down when $n$ becomes continuously many.”"

This theorem is 52 years old, indeed. But his author derived it for enumerably (countably) infinite set of objects. This is not an extension of this theorem. This is the theorem itself.

If you want to derive your own similar theorem(s), within the ordinal numbers domain, for example, by all means please do.

But this article is about the original Satosi Watanabe ugly duckling theorem derived in 1969. Guswen (talk) 16:37, 12 May 2021 (UTC)
 * There is an existing article written at Ugly duckling theorem. If you read it, you will discover that its subject is, unquestionably, a theorem about finite collections.  Maybe it would be appropriate for the article to, in addition or instead, discuss a theorem (of Watanabe or of Woodward or of someone else) about infinite collections. (I do not have an opinion about whether that would be good or not.)  But, again, nothing you have done so far is related in any conceivable way to making that happen.  The article talk-page is the correct place to discuss whether and how best to extend the article. --JBL (talk) 17:39, 12 May 2021 (UTC)

Precisely. There is the Ugly duckling theorem Wikipedia article, that is supposedly about the original Satosi Watanabe ugly duckling theorem derived in 1969. But the subject of this article, as you correctly mentions, erroneously states that it is a theorem about finite collections. It is not. Satosi Watanabe derived his own theorem in 1969 for enumerably (countably) infinite set of objects.

Therefore, this article requires appropriate correction to reflect the intentions, but more importantly derivations, of the author of this theorem. This Wikipedia article itself states that "It [the ugly duckling theorem] was derived by Satosi Watanabe in 1969."

Perhaps you would like to write your own Wikipedia article entitled "A version of the ugly duckling theorem for ordinal numbers", or similarly. But then (1) derive this extensional theorem, (2) peer-review it, (3) wait until the concept matures, and eventually (4) write this new Wikipedia article. I will keep my thumbs up for such an endeavor of yours.

For now, we're discussing the original Satosi Watanabe ugly duckling theorem that his own author derived for enumerably (countably) infinite set of objects. Your saying "of Watanabe or of Woodward or of someone else" is not only disrespectful to Satosi Watanabe. It also means that you do not understand this theorem.

Guswen (talk) 18:48, 12 May 2021 (UTC)
 * There is definitely a failure to understand happening in this conversation, but it's not at my end. --JBL (talk) 21:54, 12 May 2021 (UTC)

Let us then wait for a few days for some external feedback and then we will have to correct this article to reflect the author of this theorem (Satosi Watanabe) derivations. Guswen (talk) 21:59, 12 May 2021 (UTC)

Help with illustration needed
Is there anyone good with illustrations? I am currently brushing over determinant, and I'd like to include a few illustrations explaining the basic properties of the determinant of 2 x 2 matrices. We do have a few files along the lines I am thinking about in commons, such as the one here, but these also have a few shortcomings, and not everything I'd like to illustrate is there.

If anyone is good at illustrations and is willing to help out, please ping me and I will elaborate further. Thanks a lot. Jakob.scholbach (talk) 18:20, 12 May 2021 (UTC)
 * You could add a request at Graphics Lab/Illustration workshop. Certes (talk) 13:30, 13 May 2021 (UTC)

Behnke–Stein theorem (1939 or 1938) vs Behnke–Stein theorem (1948)
There seem to be two versions; the theorem on increasing sequences of domain of holomorphy and pseudoconvex domain (1939 or 1938), also the theorem claiming that the concatenated non-compact Riemann surface is a Stein manifold (1948).--SilverMatsu (talk) 14:17, 28 April 2021 (UTC)
 * So would you also add the 1948 theorem to Behnke–Stein theorem?--SilverMatsu (talk) 15:34, 1 May 2021 (UTC)
 * If there are RSes that call the second theorem by the same name (as you say the Narasimhan paper does), then it's suitable to either create a section about the different theorem or a new standalone article entirely (assuming it's notable in the Wikipedia sense, e.g. WP:GNG). If there's not much to say, you can also just mention the other usage very briefly in the lead with a citation. — MarkH21talk 18:33, 13 May 2021 (UTC)
 * Thank you for your reply. I create Draft:Behnke–Stein theorem (1948). I would also like to start the discussion of merging. I'm wondering whether to make the category complex analysis vs several complex variables.--SilverMatsu (talk) 05:12, 14 May 2021 (UTC)
 * Category:Several complex variables is a subcategory of Category:Complex analysis anyways, so the former should be fine. — MarkH21talk 05:49, 14 May 2021 (UTC)
 * Thank you for the advice. Yes, certainly.--SilverMatsu (talk) 11:13, 14 May 2021 (UTC)

Articles for deletion/Titanic prime and the large prime number article proposal
A recently concluded AfD, Articles for deletion/Gigantic prime, was closed as 'redirect to megaprime', and following the general sentiment there I began a related AfD, Articles for deletion/Titanic prime. In it, has proposed that we merge all treatments of ranges of large prime numbers with the current treatment of largest prime number into a comprehensive article, the not-yet-extant large prime number.

I've created a topic on an article talk page for more specific discussion about what to do with these pages at Talk:Largest known prime number. Since this affects a fair few maths articles, pointed out that it would be good to advertise this discussion here. The search for large primes is one of the more media-friendly parts of maths, so this could be an effort with more than usually observable impact for us. &mdash; Charles Stewart (talk) 01:38, 15 May 2021 (UTC)

Median of a gamma distribution
I've been involved in a rather one-sided discussion (that is, with almost nobody but me) at Talk:Gamma distribution for about 2 years now. I could use a second and third opinion. My contribution to the problem was to do some original research and get it peer reviewed and published. Maybe someone will say yes or no to us using it in the article now. (Please excuse the cross-posting with WikiProject Statistics.) Dicklyon (talk) 22:47, 15 May 2021 (UTC)
 * Actually, an editor already added a paragraph to the article about it, before I posted there. More eyes are still welcome. Dicklyon (talk) 22:53, 15 May 2021 (UTC)
 * It wouldn't be the only journal paper written and published for the main purpose of providing a source to add a claim to Wikipedia. Thanks for taking such efforts to improve the article. —David Eppstein (talk) 22:59, 15 May 2021 (UTC)
 * Agreed! --JBL (talk) 02:29, 16 May 2021 (UTC)

about Blackboard bold
Before we talked about blackboard bold in the style manual, but the blackboard bold article still seems to explain not to use blackboard bold except on the blackboard. Do we improve the article?--SilverMatsu (talk) 15:49, 15 May 2021 (UTC)
 * the blackboard bold article still seems to explain not to use blackboard bold except on the blackboard The article Blackboard bold is not an instruction manual, and it also does not say what you've said. You should of course feel free to improve any article on Wikipedia; for the particular article Blackboard bold, the best way to improve it would be to find reliable sources that discuss it (rather than, as is currently the case, a bunch of primary sourced claims that various individual books or authors happened to use or not use it in various contexts).  --JBL (talk) 15:57, 15 May 2021 (UTC)
 * Thank you for the advice and article improvements. Certainly the article doesn't seem to say what I pointed out. But the article will be improved because you tagged it properly.--SilverMatsu (talk) 08:41, 16 May 2021 (UTC)

Help needed for an edit war
There is an edit war in which I am implied at Flat module. Help would be welcome. D.Lazard (talk) 07:21, 9 May 2021 (UTC)
 * This isn't an edit war. You are blindly removing new material off this page and refusing to let any improvements in. Taking a few minor complaints about a few (small) points does not warrant a blank removal of material. If you want a citation, try asking if the author knows of one, or try to dig one up yourself. Furthermore, if something could be restated in a more conformant way of wikipedia standards, make that edit. Those are some more constructive avenues for handling disagreements over material. Kaptain-k-theory (talk) 16:42, 10 May 2021 (UTC)
 * It is definitely an edit war, and both of you should stop. Meanwhile, it is extremely unhelpful to personalize disputes, as you have done at Talk:Flat module; please try to focus on content, not on other contributors. --JBL (talk) 18:22, 10 May 2021 (UTC)
 * I hope that a resolution has been found by now :) — MarkH21talk 17:32, 18 May 2021 (UTC)

Links to disambiguation pages
Hi. There are a few mathematics-related disambiguation pages that have attracted some links that need fixing: total relation (18 links), boundedness (10 links), and minimal prime (3 links). Is there a mathematician who feels like tackling some of these? Thanks in advance! Lennart97 (talk) 10:45, 12 May 2021 (UTC) As regards tail sequence &mdash; as far as I can work out, it's saying something pretty trivial (basically the complement of an initial segment of a limit ordinal) in a complicated and indirect way, bringing in "normal functions" only to not really use them. Doesn't seem to be used anywhere, and I don't recall running across it as a term of art (it's plausible as a nonce term, but I would expect the author to give at least a brief gloss). If the page creator has an attestation, it might rate a line in glossary of set theory if there is such a page; otherwise I'd say delete. --Trovatore (talk) 17:39, 13 May 2021 (UTC)
 * I've fixed the last one (all Minimal prime (recreational mathematics)) but will leave the others to an expert. Certes (talk) 10:58, 12 May 2021 (UTC)
 * I've mostly done bounded. If someone else could take a look at Hilbert–Pólya conjecture (should that be unbounded function, bounded operator, unbounded operator?) and Tail sequence (should this unsourced definition-only orphan be merged somewhere?) that would be great. --JBL (talk) 23:24, 12 May 2021 (UTC)
 * For Hilbert–Pólya conjecture, the hypothetical operator would be a linear operator that is not a bounded operator. However, note that the cited reference does not mention boundedness anyways, and there aren't many good references for this since it's hypothetical and seems to be mostly of more tangential interest to physicists and receives little more than speculative interest in number theory. I'm not sure why unbounded operator specifically restricts to operators of subspaces of a given space since that is not always the convention in all areas of mathematics. — MarkH21talk 23:42, 12 May 2021 (UTC)
 * Would it be appropriate to merge somewhere? BD2412  T 02:56, 13 May 2021 (UTC)
 * If you mean Hilbert–Pólya conjecture, it's still notable (GNG-wise) and separate enough from Riemann Hypothesis to have a standalone article. If you were referring to JBL's question about Tail sequence then I don't know! — MarkH21talk 13:46, 13 May 2021 (UTC)
 * Maybe BD2412's comment was about Unbounded operator? But also  do you have any thoughts about what should be done with Tail sequence? --JBL (talk) 14:09, 13 May 2021 (UTC)
 * I was responding to [User:MarkH21|MarkH21]]'s comment that "there aren't many good references for this since it's hypothetical and seems to be mostly of more tangential interest to physicists and receives little more than speculative interest in number theory". I believe that was in reference to Hilbert–Pólya conjecture. However, I'm always for a good merge for any of these topics that may be better suited for explanation in the context of a broader topic. BD2412  T 16:02, 13 May 2021 (UTC)
 * Prodded and notified. --Trovatore (talk) 18:21, 13 May 2021 (UTC)
 * I think you might not have parsed the definition correctly: if we call your class of sequences coinitial sequences, my interpretation is that tail sequences are subsets of coinitial sequences that are cofinal in those sequences. That the definition is unclear enough that I'm not altogether sure which interpretation is right only provides further support for your PROD. &mdash; Charles Stewart (talk) 09:00, 14 May 2021 (UTC)
 * Hmm, let's go ahead and reproduce the short definition here in case it gets deleted:
 * In mathematics, specifically set theory, a tail sequence is an unbounded sequence of contiguous ordinals. Formally, let β be a limit ordinal.  Then a γ-sequence $$s \equiv \langle s_{\alpha}| \alpha < \gamma\rangle$$ is a tail sequence in β if there exists an ε < β such that s is a normal sequence assuming all values in $$\beta \setminus \epsilon.$$
 * Following the pipe from "normal sequence" to normal function, we read that it's a continuous, strictly increasing map. Putting all these things together (and we don't even need "continuous"), the only possible way to satisfy these requirements is if $$\gamma=\beta-\epsilon$$ and $$s\,\!$$ is the obvious  $$s_\alpha=\epsilon+\alpha$$.  That's why I said it was "bringing in normal functions only to not really use them".
 * Not, as you say, that it really matters for the purposes of this discussion. --Trovatore (talk) 16:34, 14 May 2021 (UTC)
 * Hmm, for completeness, I should agree that there is a small ambiguity. I was implicitly reading "assuming all values in &beta;\&epsilon; to mean all and only values in &beta;\&epsilon;.  You could read it instead to mean that it also assumes some values below &epsilon;.  But in that case there is a smallest (only) &alpha; such that s&alpha; = &epsilon;, and from that point on, it's just the complement of an initial segment. --Trovatore (talk) 17:54, 18 May 2021 (UTC)

Proposal: Template:infobox theorem
I would like to propose a standardized template for mathematical propositions and results (theorems, conjectures, axioms, lemmas, etc.). It should contain, in the very least, the following:
 * Author
 * Year authored
 * Lay statement
 * Precise statement
 * Illustration
 * Fields affected / concerned
 * Reference number (in some suitable index)

We can take cues from existing templates before submitting to WP:RT. What do you think? — Preceding unsigned comment added by François Robere (talk • contribs) 17:26, 16 May 2021 (UTC)
 * I think infoboxes work well for things that can be adequately described by database entries (stars, for example) and very badly for things that require nuance and reasoned description rather than filling in boxes. I think theorems fall more on the "requires detailed textual description rather than filling in boxes" side of that dichotomy. I think adding infoboxes would put great emphasis on the wrong aspects of the topic (such as who proved it and when) rather than emphasizing the important aspects (the mathematics that the theorem is about), and even for the aspects they emphasize are likely to oversimplify (most important theorems have a long history of refinement and rediscovery rather than a single prover and date). See WP:DISINFOBOX and particularly the description there of bad infoboxes as "an oversimplified mass of disconnected facts devoid of context and nuance". —David Eppstein (talk) 19:26, 16 May 2021 (UTC)
 * Do you have any views on ? Certainly nuance is involved there. Michael Hardy (talk) 17:47, 17 May 2021 (UTC)
 * Judging from the first of the "links here" pages, Marbury v. Madison: The first two lines of text of the actual article tell me the important stuff about what kind of thing the topic is (a US Supreme Court case) and what point of law it established. The infobox, on the other hand, is purely decorative for the equivalent of six lines of text, followed by purely technical information that is essentially completely uninformative to me. It is not the sort of thing that should be taking up so much screen real estate in the article and distracting attention away from the important information. It is at best a waste of space, when it is not actively taking away value from the article by distracting readers from the actual information. So although I have no expertise or interest in editing law case articles, I think that WP:DISINFOBOX is very relevant there as well. —David Eppstein (talk) 18:25, 17 May 2021 (UTC)
 * This already exists, at Infobox mathematical statement. — MarkH21talk 19:10, 17 May 2021 (UTC)
 * Thanks! How did I miss that? :-P François Robere (talk) 19:53, 17 May 2021 (UTC)
 * The existing template has a single "statement" field; would it be better to add an optional field for precise notation? François Robere (talk) 10:40, 18 May 2021 (UTC)
 * What do you mean? What would the optional field be called and what is it for? — MarkH21talk 17:20, 18 May 2021 (UTC)
 * The way I understand it at the moment, there are three ways for describing eg. a conjecture: rough verbal description (in "lay terms"), precise verbal statement, and precise symbolic statement. For example, for the first of the Weil conjectures we could state imprecisely that "$ζ(X, s)$ is a rational function of $T = q^{−s}$"; and more precisely that "$ζ(X, s)$=$$\prod_{i=0}^{2n} P_i(q^{-s})^{(-1)^{i+1}} = \frac{P_1(T)\dotsb P_{2n-1}(T)}{P_0(T)\dotsb P_{2n}(T)}$$ " (or something of the sort). François Robere (talk) 17:40, 18 May 2021 (UTC)
 * I've seen the changes. Thanks! François Robere (talk) 18:14, 18 May 2021 (UTC)
 * I personally like an idea of infobox in general and not just for non-math articles. A common complaint on math articles is that they look like they are written and are aimed at math people not the general public. At least an infobox can be helpful in addressing this issue. Mathematically, when a theorem is proved or who proved it might be *irrelevant* but non-mathematically some readers might find such info interesting. I suggest the infobox have a column "related theorems"; that would be good for navigation. E.g., the Hahn--Banach theorem infobox can have the hyperplane separation theorem as a related theorem. -- Taku (talk) 01:41, 20 May 2021 (UTC)

about Template:PlanetMath
Apparently, id seems to be obsolete and should be replaced with title name, the Canonical name should remove the space from the title name. Would anyone edit it directly or create a bot? thanks!--SilverMatsu (talk) 06:40, 28 May 2021 (UTC)
 * It's not obvious that this can be done automatically or by a simple textual substitution as you suggest without creating even more errors. The most recent discussion in 2019 suggested that there were few enough of these that it would be better to handle them one at a time by hand: https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mathematics/Archive/2019/Feb#RIP_PlanetMath%3F —David Eppstein (talk) 07:35, 28 May 2021 (UTC)
 * Thank you for teaching me.--SilverMatsu (talk) 08:22, 28 May 2021 (UTC)

Assessment of Transfinite number
The priority of the article Transfinite number was last assessed in 2008, when it was lowered from High to Low. Its class was changed from Stub to Start in 2018. I think that the low priority assessment was at least partly based on the poor quality. The quality still leaves room for improvement, but shouldn't its priority be higher? Based on my feeling that the subject is "a must-have for a print encyclopedia", combined with the criteria of, I wonder if its importance should in fact not be rated as. (I have more problems applying this WikiProject's own priority rating scheme, as I think the criteria as presented there cannot be applied to a subject in isolation, but only to an article as a node contextualized in an everchanging web, and seem to be more coupled to an article's quality than is desirable for a supposedly independent parameter.) --Lambiam 08:29, 23 May 2021 (UTC)
 * Definitely not top. That is for things that every educated person (not just every mathematician) should know about. Might be medium rather than low, I'm not sure. Importance ratings are not very important, though. —David Eppstein (talk) 16:46, 23 May 2021 (UTC)
 * I would rate it as High priority, not Top. Low seems very wrong; I agree that there's often a bias against articles with currently low quality. - CRGreathouse (t | c) 02:34, 24 May 2021 (UTC)

I might add that there's a third possibility. As I understand it (and I have no good sources for this) Cantor used the term "transfinite" as a sort of middle ground between the finite and what he saw as the truly infinite. His transfinita ordinata were beyond a bound (that is, greater than a limit ordinal), but none of them was without bound. This is a very interesting and subtle idea, closely connected for Cantor with his ideas about God, who is truly infinite, unlike the mere transfinite numbers. If we (found sources and) rewrote the article to be specifically about that idea, I would love to see that listed as mid-priority. --Trovatore (talk) 04:48, 26 May 2021 (UTC)
 * I agree with high; not top. Bubba73 You talkin' to me? 02:49, 24 May 2021 (UTC)
 * ✅, I've restored it to . Not letting an article's low quality bias its priority assessment seems important to me; large discrepancies between high priority and low quality can be used to flag articles that need attention. --Lambiam 09:56, 24 May 2021 (UTC)
 * You are aware the Transfinite number is merely a disambiguation page that links to Ordinal number and Cardinal number, aren't you? The latter articles are the "must-have(s) for a print encyclopedia". - Jochen Burghardt (talk) 10:48, 24 May 2021 (UTC)
 * Hmm, maybe it should be such a disambiguation page, but it isn't, currently, at least not literally. There's a wrinkle here; some writers seem to use "transfinite" to mean any non-Dedekind finite set, in a non-axiom-of-choice context.  In my opinion this is ahistorical, but it is a usage that exists, and in covering it the page seems to have become to some extent about the term "transfinite" (generally undesirable but possibly hard to work around in this case).
 * If the page is destined to continue to be about the term, then I sort of agree it's low-ish priority, medium at best. If we were to turn it into a legit disambig page, I think those are not even eligible for priority rankings. --Trovatore (talk) 02:30, 26 May 2021 (UTC)

I've added ratings to hundreds if not thousands of math articles. That one strikes me as "low", or "mid" at most. (It's currently marked "high") Why? It is providing a a definition for a historical term that has kind of fallen by the wayside. The definition is not particularly complex or important. "High" is usually something reserved for something important that school students would study or need to know. This is not that. I agree with Trovatore that if it had more history-of-math to it, it would be mid.

BTW, removed a section called "wolfram spam", but the removed material predates wolfram by at least 5 decades. It is covered in J.H. Conways book On Numbers and Games but I'm fairly certain it predates Conway, as he seems to be recaptulating known results. However, I'm not restoring that content, because I don't think it belongs in this article anyway. (I don't know where it belongs). 67.198.37.16 (talk) 23:14, 26 May 2021 (UTC)
 * That removal was part of a massive cleanup of material added to many articles by Wolfram employees in order to boost the visibility of A New Kind of Science and Wolfram more generally. A not-insignificant fraction of the material they added was badly written and/or poorly sourced content on textbook topics. XOR&#39;easter (talk) 23:34, 26 May 2021 (UTC)
 * Conway certainly gave lectures on the topic in the early 1980s (in which he wrote out $$\omega^{\omega^{\omega^{...}}}$$ then rotated the blackboard to display $$\varepsilon_{\varepsilon_{\varepsilon_{...}}}$$). Certes (talk) 23:42, 26 May 2021 (UTC)
 * OK Thanks. I restored the section and credited Conway. I'm starting to suspect that its actually due to Cantor, but can't quickly research that. I expanded On Numbers and Games slightly; all the details are in surreal numbers. 67.198.37.16 (talk) 01:55, 27 May 2021 (UTC)
 * Incidentally, I've just discovered that there's more Wolfspam around, related to his book "Idea Makers".  I just nuked one at Richard Feynman (added by OrdinaryArtery), but there's also this at Richard Crandall; presumably it's been spammed onto articles of people not named Richard, as well.  --JBL (talk) 02:06, 27 May 2021 (UTC)
 * Just the four I think. Certes (talk) 10:38, 27 May 2021 (UTC)
 * Thanks, Certes. I cleaned up Crandall.  The paragraph in Ada Lovelace sounds like it was written by one of the socks but was in fact added by, and the reference in List of Jewish mathematicians, which is not accompanied by any promotional text, was added by .  The mention at Stephen Wolfram is appropriate. --JBL (talk) 12:18, 28 May 2021 (UTC)
 * OMG. Selecting a random link from User contributions for Spikeylegs shows spam on Combinatory logic. I find this highly objectionable. Cleaning up this particular instance now. I now imagine there's a lot of them.
 * Huh. I looked at the other SpikeyLegs contributions and it looks like more or less all of them have been reverted. I must have gotten lucky finding the one that was not.67.198.37.16 (talk) 02:17, 29 May 2021 (UTC)
 * Check out User:Blablubbs/Wolfram (this is the same link XOR&#39;easter gave above) -- we got most of it, but there are probably bits and pieces that got missed. --JBL (talk) 02:41, 29 May 2021 (UTC)

FAR notice
I have nominated Laplace–Runge–Lenz vector 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. Extraordinary Writ (talk) 21:06, 29 May 2021 (UTC)


 * Please do help in improving the Laplace–Runge–Lenz vector, particularly by adding citations to reliable modern sources, clarifying confusing passages, or simply by adding your comments to its featured article review. Thank you very much! :)  Willow (talk) 09:42, 31 May 2021 (UTC)