Wikipedia talk:WikiProject Mathematics/Archive/2024/Oct

Should Algebra be reverted to the version of 21 Decembre 2023?

The present state of Algebra results of numerous edits done by a single editor, Phlsph7 since 21 Decembre 2023. It results that that the article presents a biased and misleading view of algebra that reduces algebra to universal algebra and the part of algebra that is taught in secondary educalion ("abstract algebra" and elementary linear algebra). This make that the article is very incomplete. I started a tentative to completing the article, without changing its structure, but it appeared soon that this is an enormous task this would require an amount of time that I am not willing to do.

Nevertheless, the article goes against the policy WP:NPOV by excluding a very large part of algebra.

For previous related discussions, see Talk:Algebra#Incompleteness of the article and Wikipedia:Featured article candidates/Algebra/archive1‎‎#D.Lazard

So, I suggest to restore the version of 21 Decenber 2023], which has many issues but respect the policy WP:NPOV. As this is a major change, I needs the advice of the community. D.Lazard (talk) 15:35, 30 September 2024 (UTC)

A few links to reviews of the current version:

• Good article review: Talk:Algebra/GA1
• Peer reviews: Wikipedia:Peer review/Algebra/archive1
• Featured article reviews: Wikipedia:Featured article candidates/Algebra/archive1

Except for D.Lazard's recent comments, none of them mention an NPOV-problem. Phlsph7 (talk) 15:50, 30 September 2024 (UTC)

@Phlsph7 This is a common problem with reviews: it is easy to examine the content that is there and judge its style, but takes deeper thought to figure out a neutral and relevant high-level scope, organization, and narrative flow for articles about broad topics. –jacobolus (t) 16:27, 30 September 2024 (UTC)

Forgive me if I lack adequate understanding of all the connections here, but it seems like this sense of iniquity is at least partially based on confusions regarding use versus mention of terminology, of labels versus concepts. I hope I'm not explaining perfectly obvious and accounted-for points here, but we generally write articles about concepts, not the terms we apply to them—cf. God versus God (word)...versus God in Islam versus Allah. When you say the previous version adheres to NPOV, it seems like you view an article that covers "every distinct sense that the label algebra is applied to" as the goal, rather than an article that covers "the core, contiguous concept most commonly labeled algebra". In fact, the pseudo-disambiguation section in the old version almost forces me to hold this view. Have you accounted for this potential discrepancy in the present misunderstanding? Remsense ‥ 论 15:57, 30 September 2024 (UTC)

It's not as scattered a semantic field as I implied, after a refresher reading through the previous discussions linked. I would strike my reply altogether as I don't feel like I have as much as others here to offer in terms of domain-specific analysis; but I'll risk the possibility of making further less-than-helpful remarks by trusting my generalized analysis here: the present article seems to lend itself better to expansion outward than any other course of action with the previous revision, and I can't help but see its reversion or total denaturing as counterproductive to solving what everyone seems to agree are the present issues to one degree or another. Remsense ‥ 论 16:56, 30 September 2024 (UTC)

I do not see how reverting would be the right course of action here. By all means, add material about topics that are missing, and adjust the section headings for better organization if necessary. But the current version is a better point to build from than the one from last December. XOR'easter (talk) 15:58, 30 September 2024 (UTC)

I think Universal algebra is overemphasized. It is not one of the main branches of algebra. It does not even have an MSC code. The main divisions are 08 (general algebraic structures), 12 (field theory and polynomials), 13 (commutative algebra), 15 (linear algebra), 16 (associative algebras), 17 (non-associative algebras), 18 (category theory), 20 (group theory). Tito Omburo (talk) 16:15, 30 September 2024 (UTC)

A revert to a version from a full year ago when the article has already passed a GA review and is currently going through FAC makes absolutely zero sense. More information on other branches could maybe be added, but I'm not knowledgeable enough to speak to that. QuicoleJR (talk) 16:18, 30 September 2024 (UTC)

An article with such a problem of non-neutral point of view should should not have passed a GA review. D.Lazard (talk) 16:26, 30 September 2024 (UTC)

This is more of a comprehensiveness issue than an NPOV issue, so it wouldn't be nearly as important at GAN than it would be at FAC. QuicoleJR (talk) 16:30, 30 September 2024 (UTC)

Yes, I think this is a comprehensiveness (and organization) issue. XOR'easter (talk) 16:35, 30 September 2024 (UTC)

Comprehensiveness is very important at GAN, one of the six top-level criteria of WP:GACR (#3). If the reviewer failed to properly address it, then that is a problem with the GA review and maybe should be brought to GAR. —David Eppstein (talk) 18:04, 30 September 2024 (UTC)

I know you are aware, but it's worth repeating here that "comprehensive" is a word used only in the FA criteria, while GA criterion 3a only requires that an article addresses the main aspects of the topic. Remsense ‥ 论 18:08, 30 September 2024 (UTC)

Yes, there's a difference between the GA "adequately broad" and the FA "comprehensive". I have a lot of bad memories about the GA processes and don't want to get into that world again, but I think it's fair to say that the former is arguably met and the latter not. XOR'easter (talk) 22:44, 30 September 2024 (UTC)

I don't think reverting is particularly helpful, but it would be good to get more experts involved in substantially expanding this article and somewhat reorganizing it (hopefully people with significant professional mathematical experience directly in algebraic topics – this does not include me). –jacobolus (t) 16:21, 30 September 2024 (UTC)

I agree to oppose reversion with Remsense, XOREaster and others. I don't have the mathematical knowledge to judge the validity of the complaints raised, though many other editors do, and I note that so far we have yet to see others appearing to diagnose the same problem with the same level of seriousness, despite several stages of review. However, assuming that the problems are real and need fixing, they are very much a WP:SOFIXIT issue rather than cause to undo a great deal of hard (and excellent) work by a conscientious and skilled editor. Big articles like this will never please everybody, but equally we should be very cautious when talking about applying drastic measures to articles which, by their nature, take time, negotiation and skill to build up. UndercoverClassicist ^T·C 17:32, 30 September 2024 (UTC)

Taking a glance at the suggested version to restore, I see little missing from the current version, except that most terms in the enlightening "Areas of mathematics with the word algebra in their name" list have been dispersed into the prose. The discussion on universal algebra should be pared down and sections reformatted, but a complete reversion is unreasonable. Pagliaccious (talk) 04:16, 1 October 2024 (UTC)

I don't see a case for reverting, but I do see a major problem and a minor problem.

Each of group theory, ring theory and field theory is of greater centrality than universal algebra: Algebra § Group theory, ring theory, and field theory should be split and greatly expanded.

The minor issue is that Algebra § Linear algebra really belongs under Algebra § Abstract algebra. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:07, 1 October 2024 (UTC)

Request for comment on Indeterminate (variable) article

I am attempting to clarify the definition and description of "indeterminate" in the article as I do in this version, however, another user seems to disagree with how my sources define the term and is enforcing the this version, and we can't seem to come to a consensus.

To be clear, this was the original version before this dispute started.

Can anyone offer their opinion or suggestions for moving forward? Farkle Griffen (talk) 14:31, 28 September 2024 (UTC)

To be clear, I elaborated this version for resolving concerns that I have with the old stable version and, partly, for including some relevant remarks providen by Farkle Griffen, in particular the fact that some authors give a definition of an indeterminate that implies that every polynomial and the constants π and e are indeterminates. D.Lazard (talk) 15:36, 28 September 2024 (UTC)

Well, technically they would only be considered indeterminates over the integers and rationals, but I digress. Farkle Griffen (talk) 15:48, 28 September 2024 (UTC)

I think Griffen's version of the lede is clarifying. I don't think the definition of an indeterminate as a transcendental over a ring is appropriate, precisely for the reason noted that this implies π is an indeterminate over the rationals, when it is clearly a *specific* element of the completion of Q at the infinite place, not an "indeterminate" one. This seems to be missing the point in a bad and confusing way that we should avoid if possible. Tito Omburo (talk) 20:05, 28 September 2024 (UTC)

@Tito Omburo, I think I see your point. But one comment I have is that I think the word "indeterminate" is a bit of a misnomer. Many authors don't see indeterminates as literally indeterminate, but rather as a kind of (unchanging) object; specifically, the indeterminate X is an element of the ring R[X], and it doesn't change within it. But one still wants to allow "substitution" of X for elements of R. Since X isn't a variable, authors get around this by defining "substitution" as a Ring homomorphism from R[X] to R. The transcendental definition just formalizes this.

Dummit and Foote explain it like this:

"We generally reserve the expression “‘t is an ‘indeterminate’ over F’’, when we are thinking of evaluating t. Field theoretically, however, the terms transcendental and indeterminate are synonymous (so that the subfield $\mathbb {Q} (\pi )$ of $\mathbb {R}$ and the field $\mathbb {Q} (t)$ are isomorphic)."

But, again, I digress.

I do, however, see your point. Having this definition in the lead is confusing and too technical for the average reader. But I do still believe it deserves to be mentioned in the article. How about these formalizations simply be moved to a new section further down? Farkle Griffen (talk) 20:08, 29 September 2024 (UTC)

@Tito Omburo, How do you feel about this current version, compared to the previous version? Farkle Griffen (talk) 17:27, 1 October 2024 (UTC)

@Farkle Griffen Some comments: (1) In general, please do not ever use more than ~3 footnotes in a row (even 3 in a row is pushing it) – it is unnecessary to bludgeon readers with footnotes, and in the lead section it's often better to have no footnotes at all if the same material is sourced from the article body. (2) It is not really that useful in my opinion to link to a bunch of course notes, whenever other sources are available; these are not usually considered "reliable sources" by Wikipedia standards, though they can sometimes be leaned on in a pinch. (3) Your lead section is in my opinion much too long and not that legible. I'd focus on getting the main point across, and elaborating about details later in the article. I think the existing lead does a decent job of giving an idea what an indeterminate is and why such a concept exists, but it would certainly be helpful if we could find some kind of historical survey better explaining the history of the word (not sure any such source exists, unfortunately). –jacobolus (t) 22:57, 28 September 2024 (UTC)

@Jacobolus,

(1) Is this a Wikipedia policy, or your opinion? I'm not asking to be snarky, I just don't know. Either way, yes, I will hereon take this into consideration.

(2) I'm a bit confused what you mean by this? Of the sources given, only two are course notes, Howlett and Grinberg, and the rest are textbooks; though these two can be removed if you believe they are problematic.

Although, as a bit of explanation: the only reason I've opted to include them is because of the high standard of sourcing being imposed on claims (due to the several accusations of WP:Original research). Howlett for the informal description of indeterminates in the sequence definition, noting: "X, X^2 , X^3 , . . . are nothing more than symbols written alongside the coefficients to enable us to see which is the 0th, which the 1st , which the 2nd, and so on.", and Grinberg for added support that authors do consider this definition "more formal."

(3) That's a fair point. I agree these formalizations aren't helpful in the lead. However, I do believe they are helpful to more experienced readers to know such formalizations exist. How about we move these definitions to a seperate section? Then the lead becomes much shorter, and very similar to the current one

And I don't agree about their lead. The biggest issue is "An indeterminate is a variabe" creates unnecessary confusion between indeterminates and variables. As far as I can tell, no source defines indeterminates as variables. And this is for good reason; one usually wants to use indeterminates so that, for instance, the polynomials over $\mathbb {Z} _{5}$, x and x^5 are not equal if x is an indeterminate, even though they are equal if x is a variable within the ring. And moreover, their description "just a symbol used in a formal way" doesn't add any clarity, and is more likely to confuse readers. Farkle Griffen (talk) 18:43, 29 September 2024 (UTC)

(1) is more of a matter of taste than a formally adopted policy, but see Wikipedia:Citation overkill. –jacobolus (t) 18:52, 29 September 2024 (UTC)

@Jacobolus, in terms of (3), how do you feel about the lead in this current version? The goal was to clarify where and how the term is mostly used, while keeping in mind your notes in (3). Farkle Griffen (talk) 17:37, 1 October 2024 (UTC)

About citations in the lead, here's the relevant part of the manual of style (which, as a guideline, is lower in the hierarchy of Wikipedia rules than a policy but much higher than one person's opinion): WP:LEADCITE --JBL (talk) 19:43, 29 September 2024 (UTC)