# Wikipedia talk:WikiProject Mathematics Information

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## 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:
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 Complex variablesFunction 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)

Regarding section Oka's theorem, the content of the theorem seems correct (since the article name is a plurisubharmonic function, there is no need to use the term pseudoconvex domain.), but I have doubts about calling the content of this section Oka's theorem. (also, I think the prove to ${\displaystyle \mathbb {C} ^{n}}$ space was the IX'th Oka's paper in 1953.) There is no doubt that it was Kiyoshi Oka who solved Levi's problem for ${\displaystyle \mathbb {C} ^{n}}$ space (Riemannian domain), but it was Cartan who extended Levi's problem for Stein manifolds, which is written on this article and it seems like Grauert prove that. I'm wondering if Levi's problem with Stein manifolds should be included in Oka's theorem. I'm not sure about this because I just called it Levi's problem. thanks!-- SilverMatsu ( talk) 15:00, 5 April 2021 (UTC)

## Typesetting \mathbb{1} within Wikipedia articles

How can I use 𝟙 in a math equation? It seems from various sources that I need to use the bbm package. Is it possible to use LaTeX in Wikipedia articles that use packages? -- Yoderj ( talk) 13:37, 9 April 2021 (UTC)

I have used some funny business in the Heaviside step function article:

<big>𝟙</big>$\,\!_{x > 0}$

but there must be a better way -- Yoderj ( talk) 13:45, 9 April 2021 (UTC)

I asked this question over at the help desk and Mike Turnbull guided me here:

Hi Yoderj. You should be able to get some guidance at WP:LATEX. Alternatively, seek out the Talk Pages for the maths projects and an expert in this stuff will likely help. Mike Turnbull ( talk) 15:16, 9 April 2021 (UTC)

Thanks! -- Yoderj ( talk) 18:38, 9 April 2021 (UTC)

I've created a phabricator task. T279805. -- Salix alba ( talk): 19:31, 9 April 2021 (UTC)
Looks like its upstream, and the syntax does not work in standard mathjax. It might be possible to add one of the packages mentioned in the stack exchange thread. -- Salix alba ( talk): 19:44, 9 April 2021 (UTC)
For an indicator function, I'm sure this isn't the answer you wanted, but I would suggest using a plain ${\displaystyle 1}$ or bold ${\displaystyle \mathbf {1} }$ which are more common notations than blackboard bold in this context. (I don't mean to detract from your technical typesetting question which is interesting in its own right and I hope will be resolved.) Adumbrativus ( talk) 19:48, 9 April 2021 (UTC)
I agree with Adumbrativus. -- JBL ( talk) 19:55, 9 April 2021 (UTC)
A bold one it will be. Thank you. -- Yoderj ( talk) 22:05, 9 April 2021 (UTC)
So are there any cases where we would want this notation? Getting something through code review is a lot of work for something which might not be used. -- Salix alba ( talk): 15:36, 10 April 2021 (UTC)

## Good edit?

Did this edit fix an error, or introduce one? Maths articles can be quiet, and problems might linger unnoticed; this seemed like the best place to ask. Cheers, BlackcurrantTea ( talk) 10:21, 10 April 2021 (UTC)

Looks good to me: a function of s is integrated over the range s=0 to s=t. However, you're right in principle that lots of superficially similar edits are mistakes or subtle vandalism, both of which need to be reverted. Certes ( talk) 11:06, 10 April 2021 (UTC)
It's those mistakes or subtle vandalism I fear I'd miss in this area. Thanks for taking a look at it. BlackcurrantTea ( talk) 14:34, 10 April 2021 (UTC)

## Minimal polynomial of 2 cos(2π/n)

The formatting of the title of Minimal polynomial of 2cos(2pi/n) is abominable, and the DISPLAYTITLE template didn't help. How to proceed? Michael Hardy ( talk) 00:11, 11 April 2021 (UTC)

The present title is not only not convenient for a good display, it is also not convenient from an encyclopedic point of view: Viewing this title, a reader should naturally ask the question "Why considering specifically these numbers". So, I suggest to rename the article Real parts of roots of unity. One may object that this article is not about the the real parts, but about twice the real parts, but the difference is small enough for not being confusing.
Another question is whether this article should be merged into Cyclotomic polynomial. D.Lazard ( talk) 09:48, 11 April 2021 (UTC)
Merging it into Cyclotomic polynomial, perhaps into a section entitled "Related polynomials", sounds like a good idea to me. Ebony Jackson ( talk) 02:45, 13 April 2021 (UTC)
That seems plausible to me also, although I also like D.Lazard's suggestion for a better title. Something I wonder in thinking about this possible merge: the article states that these polynomials can be expressed either in terms of the cyclotomic polynomials or the Chebyshev polynomials, so I would think this also means that the cyclotomic and Chebyshev polynomials can be related by transitivity. But currently neither the cyclotomic polynomial nor the Chebyshev polynomials article mentions the other. Should they? — David Eppstein ( talk) 06:46, 13 April 2021 (UTC)

## Script to show short descriptions in Wikipedia categories

I'd like to call attention to a user script that has been developed to show WP:Short descriptions in category listings: User:SD0001/shortdescs-in-category

This might be of particular interest to mathematics users as categories of mathematical theorems typically show titles of the form "So-and-so and Other-person theorem," i.e. just the names of discoverers, which conveys little or no information about the result proved (or conjectured). When this script is installed and the Show SD button that appears is clicked, any short description associated with an article title is displayed beneath it. To the extent that these SDs are available and informative, it becomes much easier to understand the content of a theorem category.-- agr ( talk) 17:54, 14 April 2021 (UTC)

Neat! — 18:00, 14 April 2021 (UTC)

## New promotional math articles

Editors may want to monitor the flurry of new math articles by Remitbuber, including Math crisis, Adrián Macías, Blas Méndez, Virus Matemático, General Assembly of the International Mathematical Union, ICM 1966, ICM 2014, ICM 2026. Many do not seem notable and may involve a fair amount of COI. — 20:35, 14 April 2021 (UTC)

Nicolás Atanes was also very promotional when first created; it's now been stubbed down (and is still not a good article but at least is not overwhelmed with promotionalism). [Of course you MarkH21 know this, since you did much of the cleanup.] Most of these topics are closely related to Atanes, suggesting paid editing or at a minimum a serious COI. Probably worth a trip to WP:COIN. -- JBL ( talk) 22:01, 14 April 2021 (UTC)
In fact, someone has since taken this to ANI: Wikipedia:Administrators' noticeboard/Incidents#User:Remitbuber! — 22:05, 14 April 2021 (UTC)
Math crisis has been BOLDly redirect to Math anxiety. One of the remaining articles is now at AfD: Wikipedia:Articles for deletion/Adrián Macías. — 13:29, 15 April 2021 (UTC)
@ MarkH21: If Math crisis isn't noticeable, I'd suggest AfD instead of redirects. See the Foundations of mathematics lead statement.-- SilverMatsu ( talk) 15:01, 15 April 2021 (UTC)
by the way, the story changes but, I happened to see Math anxiety with redirects. I thought Hereditary Genius and American math education were over-summarized. Hereditary Genius was later added and summarized. Therefore, although it has references, it does not seem to have much to do with the referenced books and treatises. -- SilverMatsu ( talk) 23:35, 18 April 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 ${\displaystyle x\in X}$" 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)
• 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)

## Is it better to avoid just writing domain in articles?

Complex analysis articles sometimes say open connected set, is this better than writing domain alone?-- SilverMatsu ( talk) 08:57, 17 April 2021 (UTC)

Using domain seems correct, and may lead to a simpler (and thus clearer) formulation. However, we have several articles on related sorts domains (some of them being not listed in Domain (disambiguation)): Domain of a function, Domain of definition, Domain of holomorphy, Natural domain, and maybe others that I have not identified, and some that are lacking ( Domain of continuity, Domain of differentiability, Domain of smoothness, ...). My suggestion is to merge all these articles into Domain of a function or Domain (mathematical analysis). I have not a clear opinion whether these two articles should be merged. A possibility would be to redirect Domain of a function to function (mathematics), with a clear link in the lead of the new Domain (mathematical analysis). D.Lazard ( talk) 09:56, 17 April 2021 (UTC)
There is value in cleaning up the terminology, to make it less confusing. There is also value in using the same terminology as other sources (even before we bring Wikipedia policy into it). How about explicitly stating which meaning of "domain" is meant, at the first use in the article? And the correct wikilink might suffice for that. Mgnbar ( talk) 14:03, 17 April 2021 (UTC)
Thank you for your reply. D.Lazard's advice will take some time, but I think we can clearly formulate the domain. but, I don't think we have to merge. Even if the content is duplicated, I think it is okay to write what is written on the branch again on the trunk. In other words, improve Domain (mathematical analysis) based on your ideas and and think about merge as another discussion. As another topic, I think that complex analysis can be improved based on such an idea. Of course, I will try to be as concise as possible ... On the other hand, Mgnbar's idea is that it can be implemented immediately. Already, domain has been used for various articles, and the articles need to be improved immediately. On wikipedia, we can't expect to read all the articles from top to bottom, so we probably need to include that in article lead. Conversely, if we can't include it in we lead statement, you probably need to improve that lead statement. thanks!-- SilverMatsu ( talk) 00:02, 19 April 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)