Wikipedia talk:WikiProject Mathematics/Archive/2024/Sep

Updates to "Math theorem" Templates: Improved style and new proof parameters

Currently, there are two templates for inserting formatted theorems and proofs into articles: {{Math theorem}} and {{Math proof}} In many cases, however, the proof of a theorem directly follows the theorem. The formatting when juxtaposing these templates is not great, however:

Theorem — My theorem statement.

Proof

My proof statement.

I have written a modified version of {{Math theorem}} (see {{Math theorem/sandbox}}, at [this revision]) to improve the formatting by incorporating the proof as a new parameter for {{Math theorem}}, and also bringing the default formatting of theorems in line with typical math texts:

Theorem. My theorem statement.

Proof. My proof statement.∎

Please join the conversation at Template talk:Math theorem there if you have opinions about the proposed change. The-erinaceous-one (talk) 04:50, 2 September 2024 (UTC)

Can you give examples of articles where you think this template should be used? Personally I find that most of the time ordinary paragraphs are sufficient for theorem statements and proofs (in some articles where authors put theorems in flashy boxes, sometimes with color, etc., I have found the decorations more distracting than helpful). Proofs are helpful in particular in articles that are directly about a theorem or a few theorems, or occasionally in articles where a particular theorem is fundamentally important to the topic, but in cases I'm thinking of collapsing the proofs would defeat the point of including them. Most of the rest of the time I'd skip the proofs altogether (proofs in external resources can be linked from footnotes, or if a proof seems distracting but necessary, it could be put in a footnote in full). –jacobolus (t) 06:35, 2 September 2024 (UTC)

I envision the new version of the template replacing the current {{Math theorem}} template and also being used anywhere else that a formal theorem statement could be useful. As you noted, many pages currently display theorems and proofs in boxes, which I agree are undesirable. Editors might sometimes intentionally add boxes around theorems and proofs, but I think in many cases they simply use {{Math theorem}} because they assume it is the "standard" Wikipedia formatting of theorems. By updating the template, we would improve the formatting across all of those pages that use it and discourage editors from doing ad-hoc formatting of theorems (e.g., boxes and colors).

Regarding the formatting of proofs, I'm not married to the idea of making the proofs collapsed by default, or, in fact collapsible by default. We could choose the default to not make proofs collapsible and then allow editors to enable it using a parameter flag. I am also looking into adding another parameter that allows displaying the proof in a footnote, although I personally find this a worse option than a collapsible box since it requires readers to scroll up and down if they want to see the theorem while reading the proof.

One example of a page that would benefit from a nicely formatted Theorem template is Liouville's theorem (Hamiltonian). Despite the name of the page including "theorem", there is not a formal statement of the theorem. The closest thing it has is

The distribution function is constant along any trajectory in phase space.

but this doesn't state the formal assumptions of the theorem. The-erinaceous-one (talk) 22:58, 2 September 2024 (UTC)

I was looking around for an example of a proof in the footnote, but didn't find one quickly. Here's what I have tried for the {{Math theorem}} template.

Theorem. Mathy mathy math.

The-erinaceous-one (talk) 23:27, 2 September 2024 (UTC)

I would recommend against replacing the previous template, since authors who used it were intending the behavior as provided at the time, not an entirely different appearance chosen by someone else later. I also disagree that Liouville's theorem (Hamiltonian) would benefit from having parts of it wrapped in boxes or reformatted. Ordinary paragraphs are working fine there. In my opinion you should make a new template under a new name if you want it, and then adopt it on pages you write yourself or do significant work on, but should leave other pages alone. Aside: your sandbox version probably has some kind of malformed HTML which causes it to render outside of a colon-indented talk page response (which uses a definition list element). –jacobolus (t) 23:44, 2 September 2024 (UTC)

It looks like the existing template does not work well in lists either. [Edit: I placed an example here, but it broke our ability to use the "reply" editor]. The-erinaceous-one (talk) 00:07, 3 September 2024 (UTC)

Regarding Liouville's theorem (Hamiltonian), I think a weakness of that page is that it is difficult to figure out what "the theorem" actually says. First you have to search through the page to find the quoted text I copied above (which is not clearly labeled as the theorem). Then, you have to reconstruct and/or guess what the assumptions of the theorem are from the rest of the article. The-erinaceous-one (talk) 00:13, 3 September 2024 (UTC)

In other words, it's a typical explanation of something that physicists call a theorem. XOR'easter (talk) 02:31, 3 September 2024 (UTC)

Skimming through links at Special:WhatLinksHere/Template:Math theorem and Special:WhatLinksHere/Template:Math proof, these templates aren't really all that widely used, and in my opinion most of the articles where they are used would be improved by avoiding the templates (and sometimes taking out the proofs). YMMV. –jacobolus (t) 06:51, 2 September 2024 (UTC)

Their usage might not be ubiquitous, but 400+ pages is not insignificant and improving the available template(s) would improve those pages and making nicely formatted theorems and proofs easier. Regardless, the {{Math theorem}} template already exists and is used, so the question is whether the proposed changes would be improvements---not whether we should completely stop using it. The-erinaceous-one (talk) 23:01, 2 September 2024 (UTC)

Also, many of the pages I've opened up use the templates multiple times, so the total number of uses is well over 400. The-erinaceous-one (talk) 00:34, 3 September 2024 (UTC)

Yeah, if it were up to me at least half of those would not have any such template. But it's disruptive to make changes like this at large scale. People should feel free to use this list as inspiration for finding articles which could be improved, including by removing the templates. –jacobolus (t) 01:45, 3 September 2024 (UTC)

I agree with @jacobolus that we don't want to put too much emphasis on proofs. Many articles would actually benefit from removing some of their proofs. This has been discussed multiple times on WPM. From the Proofs section of MOS:MATH: A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result. In many cases it would be more beneficial to work on replacing the proofs with some suitable references to reputable sources instead of incorporating them into some new template. PatrickR2 (talk) 03:19, 3 September 2024 (UTC)

Even without the issue of incorporating proofs or not, I often find the current template (and the new template) which wraps the result in a "template box" to be distracting and annoying. In articles that discuss multiple results, it gives undue weight to those that happen to have an official name of "Theorem of Such-and-such" compared with those results that don't. That unnecessarily breaks the flow of exposition. Better use something less intrusive like "Theorem of such-and-such: statement ..." in the text itself. One case where the template could be justified is an article or section dedicated to a single theorem. But most of the time, the use of the template seems misguided to me. PatrickR2 (talk) 03:28, 3 September 2024 (UTC)

References

There are two different matters: how to update the current theorem template and whether its use is appropriate. I commented on the first in the talk page of the template and so here I comment on the second. As someone who actually likes using the template (and the one who actually imported the template from French Wikipedia), I think it depends on how it is used within an article. I agree in some instances, boxes can be jarring especially if there are too many of them. On the other hand, emphasizing a statement in some way is a good idea in some other instances. The axiom of choice articles gives a good example in my opinion: since the article is about a single statement. (As the proof template, I have never used it personally but apparently some people like it) —- Taku (talk) 08:26, 3 September 2024 (UTC)

Square bipyramid proposal to split

Discussion on splitting article the square bipyramid is ongoing. See Talk:Octahedron#Create a square bipyramid or regular octahedron article. More opinions are welcome. Dedhert.Jr (talk) 11:08, 4 September 2024 (UTC)