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Suggestions for further improvement

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@Farkle Griffen, I saw you asked for review of this article elsewhere and for suggestions for further improvement.

First, good work so far on the article: I think it's definitely much improved.

As one next improvement I'd suggest adding a "background" to the "In logic" section, mirroring the "background" for the "In set theory" subsection, that discusses how equalities were the defining predicates for the category of "quantity" in Aristotle's Categories and then (very briefly) the development of mathematical logical equality to Leibniz from the Scholastic study of the Categories as part of the Organon. I don't immediately have a source for that in mind, but one or two shouldn't be hard to find. RowanElder (talk) 20:35, 22 January 2025 (UTC)[reply]

@RowanElder, The bit about Aristotle is intresting, and seems relevant enough to the section; apart from that, I'm not sure how much more there is to say. From what I can find, Scholastics generally didn't really care much about quantitative equality, at least not in a way that seems relevant enough to mathematics to justify mentioning in the article. Does what I've added so far work? – Farkle Griffen (talk) 21:21, 23 January 2025 (UTC)[reply]
Yes, what you've added should roughly work, though it may need a minor rewording to avoid creating the impression that Aristotle conflated identity and equality.
The stuff about the Scholastics is harder to find and it's not as high a priority as Aristotle's Categories. Mathematician-philosophers like Richard Swineshead were crucial for the development of the ideas of equalities of intensities, i.e., the development of intensive quantities (forces, pressures, temperatures) in contrast to the extensive quantities (lengths, areas, volumes) ubiquitous in Euclid and Aristotle. This was studied by historians of math and science like Marshall Clagett. The Scholastic developments involved some subtle reasoning about quality and quantity that proved crucial to the development of, e.g., quantifiable temperature (one of Clagett's thesis topics), and thereby also to the way in which Leibniz conceived of the properties relevant to the substitution principle.
That material can be a bear to wade through, though, so no rush: your existing addition will hold the eventual place for it well. If you're on the verge of nominating this as a good article and it's still a pain to find this even with the Clagett and Swineshead pointers, I'll be happy to go find some up-to-date summary sources for this article myself, just say when (and give me about a week to get around to it). RowanElder (talk) 22:06, 23 January 2025 (UTC)[reply]
@RowanElder, sorry for the delay, it's been busy.
Your pointers were very helpful, and I've done my best to try to summarize the sources I could find, but I may over/underemphasize details. Is what I've added satisfying?
I wouldn't say I'm on the verge. There's still a few details I need to iron out, better sources for some parts, and I'm not sure what I'm going to do about Homotopy type theory yet, so if there's any issues, there's time to get it worked out. – Farkle Griffen (talk) 20:25, 10 February 2025 (UTC)[reply]
No rush at all on my end. I appreciate what you've added and I'll try an edit to sharpen it up in a little while. I've been wanting to make time to finish work I started at I. Bernard Cohen first, though, so it might be a week or two unless you'd like this done sooner rather than later. I hope you enjoy figuring out what to do with HoTT! RowanElder (talk) 20:40, 10 February 2025 (UTC)[reply]
@RowanElder, I've done more or less what I wanted to do. I think I'm going to hold off on an HoTT section for now unless theres a real push for it during GA review (I don't think its necessary for GA, but I'll add it if I go for FA).
I'd like to talk about the paragraph on the Scholastics. Looking at it again, I'm a bit lost on how exactly it relates to equality. "Equalities of intensities", sure, but that can just mean a number with units. Was there something fundamentally about equality in its definition that I'm missing here? – Farkle Griffen (talk) 05:02, 1 March 2025 (UTC)[reply]
Sounds good re HoTT. Re the Scholastics, the fundamental thing there is that they worked out what it meant for intensities of qualities to be equal to each other and thereby what it meant for those intensities to be quantifiable (since equality was the predicate proper to quantities in the Categories). We now take it for granted that each is "just a number with units," but historically it was a difficult advance. RowanElder (talk) 17:46, 1 March 2025 (UTC)[reply]

Section on Type theory

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I'd like some opinions on this. I've been back and forth with myself for a month or so about what to do. Should this article include a section on Type Theory? On the one hand, Homotopy type theory has quite a bit (and quite interesting things) to say about equality, enough to fill a small section. On the other hand, it's somewhat obscure in that a mathematician could go their whole career never hearing about it. It makes it hard to determine how much is WP:DUE. I'd appreciate any opinions on this. – Farkle Griffen (talk) 20:36, 10 February 2025 (UTC)[reply]

I think a small section is warranted, personally. It has a decent footprint in computing, especially in functional programming circles, in addition to its pure mathematical audience. It has come up in conversations at every recent AI conference I've attended. RowanElder (talk) 20:46, 10 February 2025 (UTC)[reply]

Peer review

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Equality (mathematics)

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Article (edit | visual edit | history) · Article talk (edit | history) · Watch • Watch peer review

I've listed this article for peer review because I'm looking to prepare this article for a GA review. I've never done a GA review, so I don't really know what I'm doing. I'd mostly like to make sure this article isn't missing any major details, and doesn't have any issues that might cause it to quick-fail. Thank you! – Farkle Griffen (talk) 05:24, 1 March 2025 (UTC)[reply]

In a different place regarding this, see here. I'm just passing the redirection. Dedhert.Jr (talk) 14:45, 4 March 2025 (UTC)[reply]


Article update

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Hi @Farkle Griffen: How goes it. I would start by finding references for each note entry. Its an auto-fail of GA before it even starts if they are missing. scope_creepTalk 09:23, 3 March 2025 (UTC)[reply]

Gotcha. I can work on that – Farkle Griffen (talk) 02:27, 4 March 2025 (UTC)[reply]
I took a slightly different route. How's it looking? – Farkle Griffen (talk) 07:36, 4 March 2025 (UTC)[reply]
@Farkle Griffen: The two remaining still need references. Next thing which is low hanging-fruit is to go around each image and add an alt tag. scope_creepTalk 10:06, 6 March 2025 (UTC)[reply]
@Farkle Griffen: On the references on many of them, you are missing location, publisher (e.g. ref 72) edition fields, isbn, page numbers (e.g. ref 19), most egregiously, authors, . There is no oclc links. You get that field from worldcat which links the the ref to the worldcat entry. These are quick fail at GA. scope_creepTalk 12:06, 6 March 2025 (UTC)[reply]
I see you have listed it at WP:PR. It will take 3 to 6 weeks before somebody comes acround. It might be longer due to the specialism of the subject. scope_creepTalk 12:10, 6 March 2025 (UTC)[reply]
@Scope creep What are oclc links? – Farkle Griffen (talk) 00:20, 25 March 2025 (UTC)[reply]

GA review

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Passed. Remsense 🌈 论 02:55, 2 June 2025 (UTC)[reply]

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.

GA toolbox
Reviewing
This review is transcluded from Talk:Equality (mathematics)/GA1. The edit link for this section can be used to add comments to the review.

Nominator: Farkle Griffen (talk · contribs) 21:46, 26 March 2025 (UTC)[reply]

Reviewer: Remsense (talk · contribs) 17:46, 28 March 2025 (UTC)[reply]

I've really enjoyed seeing your work on this article develop! Claiming, after ensuring my little touch ups before don't constitute my being a major contributor.

Criteria

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Good Article Status - Review Criteria
Further information: WP:WIAGA

A good article is—

  1. Well-written:
    2. (a) the prose is clear, concise, and understandable to an appropriately broad audience; spelling and grammar are correct; and
    (b) it complies with the Manual of Style guidelines for lead sections, layout, words to watch, fiction, and list incorporation.[1]
  2. Verifiable with no original research:
    3. (a) it contains a list of all references (sources of information), presented in accordance with the layout style guideline;
    (b) reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose);[2]
    (c) it contains no original research; and
    (d) it contains no copyright violations or plagiarism.
  3. Broad in its coverage:
    4. (a) it addresses the main aspects of the topic;[3] and
    (b) it stays focused on the topic without going into unnecessary detail (see summary style).
  4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each.
  5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute.
    6. [4]
  6. Illustrated, if possible, by media such as images, video, or audio:
    7. [5]
    (a) media are tagged with their copyright statuses, and valid non-free use rationales are provided for non-free content; and
    (b) media are relevant to the topic, and have suitable captions.[6]

Notes

  1. ^ Compliance with other aspects of the Manual of Style, or the Manual of Style mainpage or subpages of the guides listed, is not required for good articles.
  2. ^ Footnotes must be used for in-line citations.
  3. ^ This requirement is significantly weaker than the "comprehensiveness" required of featured articles; it allows shorter articles, articles that do not cover every major fact or detail, and overviews of large topics.
  4. ^ Vandalism reversions, proposals to split or merge content, good faith improvements to the page (such as copy editing), and changes based on reviewers' suggestions do not apply. Nominations for articles that are unstable because of unconstructive editing should be placed on hold.
  5. ^ Other media, such as video and sound clips, are also covered by this criterion.
  6. ^ The presence of images is not, in itself, a requirement. However, if images (or other media) with acceptable copyright status are appropriate and readily available, then some such images should be provided.

Review

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  1. Well-written:
    2. Criteria Notes Result
    (a) (prose) The reviewer has left no comments here Pass Pass
    (b) (MoS) The reviewer has left no comments here Pass Pass
  2. Verifiable with no original research, as shown by a source spot-check:
    3. Criteria Notes Result
    (a) (references) The reviewer has left no comments here Pass Pass
    (b) (citations to reliable sources) The reviewer has left no comments here Pass Pass
    (c) (original research) The reviewer has left no comments here Neutral Undetermined
    (d) (copyvio and plagiarism) The reviewer has left no comments here Pass Pass
  3. Broad in its coverage:
    4. Criteria Notes Result
    (a) (major aspects) The reviewer has left no comments here Pass Pass
    (b) (focused) The reviewer has left no comments here Pass Pass
  4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each.
    5. Notes Result
    The reviewer has left no comments here Pass Pass
  5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute.
    6. Comment Result
    Relatively new and no sign of edit warring or ongoing Pass Pass
  6. Illustrated, if possible, by media such as images, video, or audio:
    7. Criteria Notes Result
    (a) (images are tagged and non-free images have fair use rationales) The reviewer has left no comments here Pass Pass
    (b) (appropriate use with suitable captions) The reviewer has left no comments here Pass Pass

Result

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Result Notes
Neutral Undetermined The reviewer has left no comments here

Discussion

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  • Firstly, I am a comparatively hands-on reviewer, and will go ahead and change stuff as well as asking questions and pointing out issues. I know nominators can potentially be stressed out by that if they don't feel entirely on the same page, so please don't hesitate to revert or question anything I do! I tend to view GAN as a good time for two invested editors to really deliberate on higher-level improvements, even if not strictly necessitated by the GA criteria. Remsense ‥ 论 18:03, 28 March 2025 (UTC)[reply]
    Thanks for taking this up! I'm not picky about small details, so I probably won't care too much about any changes. I would ask for you to be clear about why you make the changes you do because I'd like to be capable of doing reviews in the future, but your edit summaries are usually pretty thorough.
    I'm going to be slightly busy until Wednesday, so if there's any large issues, I may not be able to fix them them until after that, but I should still be able to do everything within the seven days (per WP:GAN/I#HOLD.) – Farkle Griffen (talk) 18:35, 28 March 2025 (UTC)[reply]
    @Farkle Griffen, @Remsense. It's already over a month. Is there any continuation of this nomination? Dedhert.Jr (talk) 08:27, 29 April 2025 (UTC)[reply]
    Yes. The delays are all entirely my fault, and we're wrapping it up in May as I pre-empt their next availability. Remsense ‥ 论 08:28, 29 April 2025 (UTC)[reply]
    @Remsense I see you're starting the review again! What are your thoughts so far? Anything I can do to spruce it up in the meantime? – Farkle Griffen (talk) 01:24, 4 May 2025 (UTC)[reply]
    In this edit, you get rid of a lot of url's... I agree they are technically redundnant if theres a doi, but kinda prefer "url", since it links the title, which feels cleaner. Any chance those can stay? – Farkle Griffen (talk) 01:36, 4 May 2025 (UTC)[reply]
    Oh! You can make the doi link to the title by setting |doi-access=free—if indeed the resource is freely accessible (cf. H:CS1), if it's not the title probably shouldn't tease the idea of it in a link, is the idea I think. Remsense ‥ 论 01:38, 4 May 2025 (UTC)[reply]
    Most of them are links to Springer, so not free unfortunately. Seems strange though... even if a resource isn't free I find it nice to have a link to exactly where the source was found, and a title link feels the cleanest. – Farkle Griffen (talk) 02:02, 4 May 2025 (UTC)[reply]
    It's worth noting that CS1 treats title-link as free access by default (linking to Britannica or whatever), and one further specifies registration etc. restrictions. If you chose to do that, you'd most properly have both a redundant parameter (your choice!) but also a big honking red Paid subscription required, showing |url-access=subscription. So the idealized choices are
    • Hodges, Wilfrid (1983). Gabbay, D.; Guenthner, F. (eds.). Handbook of Philosophical Logic. Dordrecht: Springer. pp. 68–72. doi:10.1007/978-94-009-7066-3. ISBN 978-94-009-7068-7.
    • Hodges, Wilfrid (1983). Gabbay, D.; Guenthner, F. (eds.). Handbook of Philosophical Logic. Dordrecht: Springer. pp. 68–72. doi:10.1007/978-94-009-7066-3. ISBN 978-94-009-7068-7.
    Remsense ‥ 论 02:14, 4 May 2025 (UTC)[reply]
    Okay, I see your point, and you're right. I'll leave those your way. – Farkle Griffen (talk) 20:21, 4 May 2025 (UTC)[reply]
    BTW, in a couple of instances where the url was removed, the archive link (which is free) was also removed. Did you use a bot to do this? If not, why were those removed? – Farkle Griffen (talk) 02:07, 4 May 2025 (UTC)[reply]
    You're free also to (tell me to) put those back—I just find archives of generally robust repositories (e.g. GBooks) to be more clutter and hassle than they are worth, all else being equal. Remsense ‥ 论 02:16, 4 May 2025 (UTC)[reply]
    I'm confused... what's "clutter" or "hassle" about a link to the source in a repository? – Farkle Griffen (talk) 20:26, 4 May 2025 (UTC)[reply]
    @Remsense: @Farkle Griffen: I haven't seen any updates to the review in the last two weeks, so I would like to politely ask if there were any new developments since then? Gramix13 (talk) 00:59, 21 May 2025 (UTC)[reply]
    @Gramix13: Looks like Remsense hasn't been active for about a week now. Last time this happened they said they had a family emergency. I'm willing to wait for them to come back unless someone else is willing to take over. – Farkle Griffen (talk) 14:26, 21 May 2025 (UTC)[reply]

Tying up my dysfunctional review

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To readers: if I ever do anything like this again to a submitter, shoot me into space with a cannon. No, really, I gave myself goals irrelevant to the criteria, was beyond poor in communicating absences and issues, and took literal months. If I ever do this again, that should be my last GAN review. Mea culpa. Spot check I'm pushing through.

I was very disorganized and much of my work is on the article itself and my talk page as well, but I did engage deeply with most of the longform cited material and my work was detail-oriented, not needing to address basic compositional or structural issues. Here's my spot-check: PERMALINK TO PASSING VERSION Generally, there are no sources I wouldn't find acceptable at the FA level on a math article. Reference works, mathematics textbooks, journal articles.

  • Cajori 1927, cited at [8] in § Etymology. A book published nearly a century ago requires at least some special validation in my mind, and this one is covering basic claims of historical fact without any reason to worry age matters too much. Modern discussions of 16th century mathematical development in Europe read like this also.
  • Beckenbach 1982, cited at [10] in § Basic properties. Fine.
  • Landin 1989, cited at [11] in § Basic properties. Fine.
  • Suppes 1957, cited at [12] in § Basic properties. Fine.
  • Tao 2022, cited at [13] in § Basic properties. Fine. These all do well synthesized to undergird the most crucial of several definition lists throughout this article. Style-wise, I wonder if those should all be formatted identically? I didn't make them so because I wasn't sure.
  • Zalabardo 2000, cited at [48] in § History. Perfunctory.
  • Aristotle tr. Edghill, cited at [49] in § History. Totally fine.
  • Ferreirós 2007, cited throughout the discussion of 20th-century set theory and Zemelo (§ Background). This was actually my "big book rec" from not properly doing this GAN in time, so I'm even more sure it's cited correctly, especially as it's my kind of book discussing history as much as technical details. .
  • Stoll 1963, cited early throughout § In set theory. Every cite had no problems.
  • Pinter 2010, cited throughout § Isomorphism. Group theory is my least comfortable subfield easily among the disciplines used here, but I checked with a friend who made sure I was reading the only sentences I had trouble with correctly. That's a me problem.

My suggestions for further improvement include fleshing out aspects I'm more keen to, e.g. history and philosophy overlaps. Reading about Mesopotamian math now, so I wonder if pre-Aristotle has its place. Remsense 🌈 论 02:54, 2 June 2025 (UTC)[reply]

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.

Did you know nomination

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The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by DimensionalFusion talk 20:36, 19 June 2025 (UTC)[reply]

(
)
  • ... that the symbol for equality in mathematics wasn't used for 61 years after its introduction, and was popularized by Isaac Newton?
  • Reviewed:
Improved to Good Article status by Farkle Griffen (talk). Number of QPQs required: 0. Nominator has fewer than 5 past nominations.

– Farkle Griffen (talk) 22:50, 6 June 2025 (UTC).[reply]

General: Article is new enough and long enough
Policy: Article is sourced, neutral, and free of copyright problems
Hook: Hook has been verified by provided inline citation
QPQ: None required.
Overall: Based on user Farkle Griffen's nomination the article Equality (mathematics) was promoted to a Good Article status on June 2, 2025 (see: Talk:Equality (mathematics)/GA1). The nominated DYK hook is interesting, sourced and presented in the article. So I think this nomination satisfy all DYK criteria and has no other issues. -- Pofka (talk) 09:41, 7 June 2025 (UTC)[reply]
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