Wikipedia talk:Manual of Style/Mathematics

Abelian et al

There should be guidelines in § Algebra on the use of the terms

1. Abelian
2. anticommutative
3. antisymmetric
4. commutative
5. Non-abelian
6. Noncommutative
7. skew-symmetric
8. symmetric

This should include guidelines on whether to change the style of existing articles. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:55, 1 December 2025 (UTC)

if and only if

this says that if and only if should be avoided and i disagree wholeheartedly. if and only if means something very specific, and other terms might mislead the reader on what is actually happening. i think if and only if should always be used when applicable, and the first use should link to the article Safetypinzz (talk) 18:57, 13 December 2025 (UTC)

The manual does not tell us to avoid "if and only if". There are two relevant passages, that you might be mis-interpreting.

First, the manual tells us to avoid "if and only if" when giving a definition. That can be argued over, but currently one side has won the argument.

Second, the manual tells us to avoid "iff" as an abbreviation for "if and only if". I've never heard anyone seriously argue otherwise, as far as encyclopedia text is concerned.

Does this explanation help you? Do you still have an objection? Mgnbar (talk) 19:57, 13 December 2025 (UTC)

The phrasing "if and only if" should definitely not be avoided. But I think on most articles, it should not be linked. —David Eppstein (talk) 19:57, 13 December 2025 (UTC)

Best practice for exponents (e.g. cubic meters) in non-math articles

What is best way to display cubic units of measurement, e.g.

• m³/sec (using Template:super) vs.
• m³/sec (unicode)

in, say, a geography article? Noleander (talk) 00:57, 9 April 2026 (UTC)

Wikipedia:Manual of Style/Superscripts and subscripts covers this: use ³ or {{sup|3}}. Indefatigable (talk) 02:51, 9 April 2026 (UTC)

OK thanks. Noleander (talk) 03:28, 9 April 2026 (UTC)

Parsing of math alt text

What level of parsing is applied with the <math alt="..."> text? For example, can I write

<math alt="{{math|''&phi;''{{sup|2}}}}">\phi^2</math>

to have the alt text be the HTML that I would have used instead of the LaTeX?

I guess my question really is: regardless of the answer to the above question, would you add something to the project page that explains what is permitted in the alt tag. Thank you —Quantling (talk | contribs) 20:41, 6 May 2026 (UTC)

My understanding is that alt text is intended to be read out loud, not displayed visually. Or maybe it might even be converted to Braille. So trying to do things that clutter the sequence of characters to be read in an attempt to change the (nonexistent) visual formatting is a mistake. In this example, alt="phi squared" might be a better choice. —David Eppstein (talk) 20:59, 6 May 2026 (UTC)

Thank you for the quick response. If I had used only HTML {{math|''φ''{{sup|2}}}} and no LaTeX whatsoever <math>\phi^2</math> how would the read-out-loud / Braille handle it? If that handling is at all reasonable, I'm hoping to get both the LaTeX visual and the read-out-loud / Braille handling with <math alt="{{math|''&phi;''{{sup|2}}}}">\phi^2</math>. —Quantling (talk | contribs) 21:30, 6 May 2026 (UTC)

You would have to ask someone with a screenreader or try it yourself. I would expect the answer to be something like "math ampersand phi sup 2", but I am suspicious that alt text in the math tag actually goes nowhere at all. At least, when I inspect the accessibility properties of the resulting DOM object in the Firefox accessibility inspector, I can't find any alt text.

Why do you want to put any formatting at all into alt text? What do you think that would accomplish? According to Help:Alt text, "The alt attribute can only contain plain text (no HTML or wiki markup such as wikilinks) without line breaks." —David Eppstein (talk) 21:51, 6 May 2026 (UTC)

Yes, that's it — I want a link to Help:Alt text in this project page so that others will know what is possible in the alt tag, and perhaps we'd add the actual sentence you found too. If this were an ordinary article, I'd boldly make that edit. Should I instead wait to see whether there are no objections?

Yes, if it were the case that the read-out-loud / Braile functionality was able to do something reasonable with {{math|''φ''{{sup|2}}}} within article text then I'd want it to do the same reasonable thing when that string is supplied as the alt tag of <math>. But it sounds like my supposition isn't true ... which would make this moot. —Quantling (talk | contribs) 21:26, 7 May 2026 (UTC)

I added a line and a link to Help:Alt text. —David Eppstein (talk) 22:38, 7 May 2026 (UTC)

Citation density

While many mathematics articles are definitely under-cited, I also feel that, especially in the area of WP:GAC/WP:FAC, there is a tendency towards pushing for over-citation. It is quite often the case that we have a paragraph or two of set-up of conditions/explanations prior to introducing a theorem, definition, or other mathematical detail. GA/FA reviewers often insist that every sentence should have a citation (or at a minimum every paragraph), but I do not think this is an actual requirement of any of the PAGs. And in mathematics articles, this tends to produce rather silly results, like citing the same source for every sentence in a paragraph, every paragraph in a section, etc. The section WP:MSM#Including citations and literature references would be a good place to enumerate some best-practices here. I think it is needed to counterbalance the overall trend of overciting, when in mathematics sometimes a paragraph or more of explanatory warmup is the norm before writing down a "citable fact". Sławomir Biały (talk) 07:50, 14 May 2026 (UTC)

Some editors are overly zealous in reverting edits that they believe do not have adequate citations; high citation density and violations of BLUESKY are inevitable consequences. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:10, 14 May 2026 (UTC)

Regarding this last point, a citation is the clearest way to distinguish original research from encyclopedic material. Often with a revert "due to lack of citation", the goal is to remove original research rather than to force a citation for something that is already encyclopedic. —Quantling (talk | contribs) 13:48, 14 May 2026 (UTC)

I don't find appeals to BLUESKY especially convincing in most cases. This is more about things for which there are cited sources, just not in every sentence. For example, when we are stating a theorem, it is usually enough to give one citation, not to cite every sentence or even every paragraph when we give the background needed to state the theorem. The standard in every kind of scholarly practice would be to give one citation rather than overload the background by peppering it with the same citation over and over again. Sławomir Biały (talk) 14:16, 14 May 2026 (UTC)

Repeating the same citation over and over again in a single paragraph is covered already by WP:CONSECUTIVECITE, FWIW. --JBL (talk) 17:24, 14 May 2026 (UTC)

Part of the issue here is that many of the background facts and definitions that one might want to state in setting up a theorem are so obvious to people writing for other people in the field (rather than an encyclopedic general audience) that they don't bother to state them. This leads to shopping around for different references to cite these obvious facts and definitions, and a high density of citations to non-repeating sources. —David Eppstein (talk) 17:47, 14 May 2026 (UTC)

Yes, this is definitely part of the issue. Sławomir Biały (talk) 18:55, 14 May 2026 (UTC)

I don't love the requirement of putting a citation at the end of the text it supports. This often leads to poor visual layout, especially when mathematical content ends in a displaymath equation. I think putting it near the beginning should be allowed as well. The examples around WP:CONSECUTIVECITE don't seem really helpful in the typical use-cases of writing mathematics. Sławomir Biały (talk) 18:55, 14 May 2026 (UTC)

I only know of two explicit requirements. One of them is GA criterion 2(b): 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). Technically, this would allow for a single reference at the beginning of a section that covers the whole section. If the blue linky number is before the start of a paragraph, it's certainly not later than the end of it. Oddly, the FA criteria are less specific. They link out to Wikipedia:When to cite, which is technically only an essay and may actually be looser than the GA criterion, depending on whether the statements in the "Cited elsewhere in the article" part are read as exhaustive or indicative. The other explicit requirement is the special rule for Did You Know hooks: The facts of the hook in the article should be cited no later than the end of the sentence in which they appear. This is for the convenience of the people running DYK and probably isn't relevant here.

My impression is that a low density of citations is way, way down the list of reasons why readers are dissatisfied with Wikipedia's math articles. The complaint that people have again and again is that they're just not comprehensible. Sometimes this complaint is reasonable (we have plenty of pages of disorganized junk that only readers who already know the material could understand), and sometimes they're just wanting a royal road to geometry.

Having many more than one citation per paragraph can be a red flag. It might indicate material that was written first and then justified by adding blue linky numbers later, meaning that ideas are being grouped in a way that no single reference does. Stepwise Continuous Dysfunction (talk) 22:15, 14 May 2026 (UTC)

I believe that the GA pedants interpret this to mean that there must have a footnote after every claim, and that footnote must be somewhere between the text of the claim and the end of the paragraph. I find this often makes is harder for readers to actually figure out where to look for information about a particular section, because instead of just one footnote that says «go read this paper and for background that other paper», when the source covers everything said within a section, we end up with «to learn about this phrase go to page A of X and to learn about that phrase go to page B of Y and to learn about the next sentence go to page C of Z», but a lot of those sources are kind of irrelevant and the specific trivial points being supported are routinely uninteresting or obvious. YMMV. –jacobolus (t) 23:43, 14 May 2026 (UTC)

Some instances of this problem could be avoided if we would allow statements that are directly supported by a wikilink within the statement to be implicitly sourced by the sources at that wikilink, rather than requiring inline footnotes on the statement itself. But the editors who push for more and more stringent footnoting requirements would never allow this. —David Eppstein (talk) 00:41, 15 May 2026 (UTC)

While I'm a fan of WP:CITE EVERYTHING, I think what you're complaining about is analogous to situations where we have a block quote and this block quote can be introduced with "it said:[ref]", except instead of a block quote it's a long paraphrase of a proof. I think this analogy may be instructive for establishing a piece of guidance. Dingolover6969 (talk) 06:19, 5 June 2026 (UTC)

Well, partly yes, but this is only one part of the issue. Often to express anything in mathematics (particularly to make it comply with WP:TECHNICAL), it requires more than one sentence/paragraph of setup before we are even prepared to say the key fact which really does need a citation. This isn't just about a proof though. A better analogy would be something like whether an article on something like the Aharonov–Bohm effect, which might contain a sentence like "The Aharonov–Bohm effect was implies that an electron, which carries a negative charge, experiences an effect due to the electromagnetic potential in a region where the electric and magnetic fields are both zero" needs a citation for "which carries a negative charge". Yes, the material can be cited to any number of texts that are largely irrelevant for the overall claim being made. But the key citation should not be that electrons are negatively charged, which everybody knows, but the actual meat of the sentence. Mathematics is often like this, but it requires many sentences to establish context before a result can even be formulated. For example, the Banach-Mazur theorem states that every real separable Banach space is isometrically isomorphic to a subspace of the Banach space $C([0,1])$. To cover this properly, we need to say what a separable Banach space is, what isometric isomoprhism is, etc. All of these things can be sourced to huge numbers of textbooks, none of which are likely to contain the statement of the Banach-Mazur theorem, which is the thing that actually needs a citation that would be useful to a reader. (To be clear, I am not defending that particular article's treatment of the subject, which seems largely to treat all of these terms as self-evident and not to explain them, nor the lack of sources there even for the statement of the theorem.) The option there would be to cite a pile of irrelevant sources for WP:BLUESKY-like background statements, or to cite one source that states the theorem. Sławomir Biały (talk) 06:43, 5 June 2026 (UTC)

Comments and suggestions. WP:WHENNOTCITE says "Citations are often omitted from the lead section of an article, insofar as the lead summarizes information for which sources are given later in the article". This must apply to everything that is written in WP:summary style. However, there are several levels of summary style, and different actions could be taken.

• In a section introduced with a {{Main article}} template, the summary style must be clear to everybody. So, I propose to add to MOS:MATH#Including citations and literature references: Assertions appearing in the Lead section of an article or in a section introduced with a {{Main article}} template do not require to be cited if they appear explicitely in the body of the article or in the linked article, respectively.
• As this problem is not specific to mathematics, I suggest to open an RfC for adding similar sentences in both WP:summary style and WP:WHENNOTCITE.
• The summary style is often used for background, context, foundational examples, etc., but, in presence of several blue links, it may be difficult to readers where to find an expanded version of the summary. In such a case, I suggest a footnote note such as <ref>For details and references, see [[Mathematics]]</ref>.

I think that these suggestions could solve a large part of this issue. D.Lazard (talk) 15:46, 5 June 2026 (UTC)

There is a long-running discussion at WP:V that, as far as I can tell, proposes to require that sources must attach to every piece of information in an article, background or otherwise. Obviously this does not only affect mathematics, but mathematics seem like the area where such a policy would, if implemented, do the most damage. Sławomir Biały (talk) 15:52, 5 June 2026 (UTC)

References