# Wikipedia talk:WikiProject Mathematics

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## Proposal: move(Change the article name) Several complex variables to Function of several complex variables

HAVE BEEN MOVED
Close the discussion as; several complex variables have been moved to the Function of several complex variables. Because I considered that the bold part of the lead sentence is Function of several complex variables, and that no one undone the page movement. I think the discussion has stopped, so I'll leave the other agendas as they are. Anyone is free to improve the several complex variables because they just moved. (So it seems that this discussion hasn't come to a conclusion as to what to do with the contents of several complex variables.) However, I feel that I cannot keep the discussion open forever, so I will close the discussion once. Thanks to the participants in the discussion and all the editors who improved the page.-- SilverMatsu ( talk) 03:35, 2 May 2021 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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:
Is that correct? — 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 Function of several complex variables" to the list above? — 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 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 → Function of several real variables. — 06:39, 11 March 2021 (UTC)
• Support Tazerenix ( 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. — 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)
@ Adumbrativus, MarkH21, TakuyaMurata, and Tazerenix: 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)
Krantz, Steven G. (1992), Function Theory of Several Complex Variables (Second ed.), AMS Chelsea Publishing, p. 340, doi: 10.1090/chel/340, ISBN  978-0-8218-2724-6
Noguchi, Junjiro (2016), Analytic Function Theory of Several Variables Elements of Oka’s Coherence, p. XVIII, 397, doi: 10.1007/978-981-10-0291-5, ISBN  978-981-10-0289-2
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)

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 ${\displaystyle \mathbb {C} ^{n}}$ 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)
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

## 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 ${\displaystyle x\in X}$" 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. — 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 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)
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)

## 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? — 07:30, 21 April 2021 (UTC)
@ MarkH21: 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:
-- 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)
@ D.Lazard: 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 — 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)
• 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".
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 μ-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)

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.

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 ${\displaystyle \mathbb {Z} }$ to ${\displaystyle \mathbb {I} }$ 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 [1], 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)
• 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)

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)

## Ugly duckling theorem

Could somebody please have a look at the dispute Talk:Ugly_duckling_theorem#Countable_set_of_objects_to_which_the_Ugly_duckling_theorem_applies 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 ${\displaystyle n}$ 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)

## 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)

### References

• Behnke, H.; Stein, K. (1939). "Konvergente Folgen von Regularitätsbereichen und die Meromorphiekonvexität". Mathematische Annalen. 116: 204–216. doi: 10.1007/BF01597355.
• Heinrich Behnke & Karl Stein (1948), "Entwicklung analytischer Funktionen auf Riemannschen Flächen", Mathematische Annalen, 120: 430–461, doi: 10.1007/BF01447838, S2CID  122535410, Zbl  0038.23502
• Raghavan, Narasimhan (1960). "Imbedding of Holomorphically Complete Complex Spaces". American Journal of Mathematics. 82 No.4: 917–934. doi: 10.2307/2372949. This reference also reads the 1948 theorem as Behnke–Stein theorem.

## 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)

Jakob.scholbach Are homomorphic first references useful?-- SilverMatsu ( talk) 00:50, 3 May 2021 (UTC)
Yes, certainly. Jakob.scholbach ( talk) 07:12, 3 May 2021 (UTC)
Jakob.scholbach, 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 [2] (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. — Charles Stewart (talk) 05:28, 4 May 2021 (UTC)

## x naught

Does the team agree that the correct way to read ${\displaystyle x_{0}}$ 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. 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. --{{u| Mark viking}} { Talk} 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#Aleph-nought mentions aleph-nought, also aleph-zero or aleph-null so (if we can treat x as a placeholder for ${\displaystyle \aleph }$) 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)

## 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 · c) buidhe 04:06, 8 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)

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