# Talk:Equality (mathematics)

@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)

@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)
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)
@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)
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)
@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)
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)

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)

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)


### Equality (mathematics)
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)

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

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)

Gotcha. I can work on that – Farkle Griffen (talk) 02:27, 4 March 2025 (UTC)
I took a slightly different route. How's it looking? – Farkle Griffen (talk) 07:36, 4 March 2025 (UTC)
@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)
@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)
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)
@Scope creep What are oclc links?  – Farkle Griffen (talk) 00:20, 25 March 2025 (UTC)