Talk:Glossary of mathematical symbols

Page was much more legible before the merge

I have been using "List of mathematical symbols by subject" as a reference for several years. I have some feedback on the recent merge:

• "Glossary of mathematical symbols" contains much less information relevant (e.g. LaTeX code). The summary of the symbols isn't all that helpful because I could always click on the hyperlink to see a summary of the symbol at the top of the relevant page.

• The inconsistent spacing between symbols when scrolling by eye makes it much harder to visually identify a symbol about which one potentially has no information other than the visual appearance.

• The typesetting of operators and symbols alongside text is very messy and the article in general does not look professional. I would recommend at least setting individual symbols in-line with their text.

• Entries such as:

□(□)
□(□, □)
□(□, ..., □)

are ambiguous. Is this all one object or three examples?

• The section/sub-section structure is less useful. Why does 'calculus' have no subsections while 'brackets' does? The structure was more useable when it was more granular but with effective high-level section headings.

• There is less information on the new page.

I appreciate what this merge was attempting to do, but as it is this page seems to serve a difference purpose than that from before. Personally, I will replace my bookmark to direct me to the historical page, as that was much more useful. HyadesHoliday (talk) 17:20, 25 March 2024 (UTC)

I strongly agree with this opinion. I also have been using Symbols by Subject for the Latex codes, and after the merge, it has become much more difficult to find the code for the symbol. Additionally, I agree it is inconvenient to read which symbols were better when they were displayed on the tables. And I agree that this merged article seems to serve a different purpose than the Symbols by Subject. This became very less useful for me. 59.7.50.242 (talk) 01:44, 1 April 2024 (UTC)

This article is for general use, not for Wikipedia editors or typographers. As said in the introduction, it suffices to read the source of the article to know latex codes, and this should be easy for a Wikipedia editor. Otherwise said, the article is about the mathematical meaning of the symbols, not about their typography. Possibly, the latex code and the Unicode name could be added in the {{term}} fields, but I am not sure that this would be an improvement. In any case this would require a consensus here. D.Lazard (talk) 09:14, 1 April 2024 (UTC)

@D.Lazard I am not sure what side you are coming down on here; I am a general-use user as I was using the merged page to write a thesis in computer science, not Wikipedia articles. I should not need to inspect the source of an article in order to find out relevant information. For this purpose the merged page was much more useful. We are all agreed that this article is about the mathematical meaning, not the typography - however this is why the merged page served a distinct function and should have been kept separate. In any case, legibility is the greatest part of understanding and in that regard the merged page was more useful as it was much easier to read and the links to the relevant (and complete!) descriptions, as contained within the dedicated Wikipedia pages for each symbol, were easy to identify. Not to mention that there remains many more symbols on the merged page than on the current one, so however one looks at it, information has been lost. HyadesHoliday (talk) 14:29, 2 April 2024 (UTC)

See Wikipedia is not a manual. The purpose of the article is to explain mathematical notation. It is not its function to tell you how to write LaTeX. There are many (better) resources for that. It is as undue to include it as it would be to derive one of the functions it describes. 𝕁𝕄𝔽 (talk) 17:09, 2 April 2024 (UTC)

"Wikipedia is not a manual" does not apply here because simply using some functionality for a practical purpose does not mean that functionality is "manual-like". There are many useful mathematical and physical articles on Wikipedia that I have used for references for equations and so on in the past, but no-one would argue that the inclusion of, for example, F=ma in an article about Newtonian force is inappropriate because "wikipedia is not a manual", because F=ma is a relevant piece of information for the subject. Likewise, in an article about a symbol it is relevant to include common encodings of that symbol. If you disagree, consider that any decent article for a mathematical symbol includes the unicode and LaTeX for that symbol, e.g. https://en.wikipedia.org/wiki/Equals_sign#Not_equal, https://en.wikipedia.org/wiki/Turned_A, https://en.wikipedia.org/wiki/Radical_symbol. Should we remove the TeX from those as well?

Anyway I think we agree that he article is to explain mathematical notation, which, again, is why having a separate page with LaTeX and so on was so helpful. Besides, if the merge could be undone, and the LaTeX removed, that would at least address five of my six complaints with this merged page (although, again, I don't see why such functionality should be removed). HyadesHoliday (talk) 11:47, 3 April 2024 (UTC)

For the latex syntax of those Latex symbols that are available in Wikipedia, see Help:FORMULA#Formatting using LaTeX. For HTML symbols, see Help:FORMULA#HTML entities. D.Lazard (talk) 15:17, 3 April 2024 (UTC)

As a holding position, the last version of the list article is here, so you can at least get on with writing your thesis. I realise that this doesn't help anyone else, so a more sustainable solution is needed. Could the LaTeX article be improved instead? --𝕁𝕄𝔽 (talk) 15:49, 3 April 2024 (UTC)

@HyadesHoliday: Among the external links of another article, I see The Comprehensive LaTeX Symbol List. I don't know how "official" it is but would it help to add that to the end of this article? --𝕁𝕄𝔽 (talk) 20:37, 4 April 2024 (UTC)

@D.Lazard: The issue isn't that I don't have a reference to LaTeX code, as I know I can find the code elsewhere and I can use the old page. The issue is that where once this page was a useful collection of information on the name, meaning, and typographical information of many mathematical symbols, the typical user will now only see a the name and meaning of fewer symbols with worse formatting, and I was trying to give a user (rather than an editor) perspective on this. For example, it's ridiculous to expect the average user to access Help:FORMULA#Formatting using LaTeX for LaTeX symbols. I will survive, since I have the old page bookmarked, and I think I've said my piece on the utility of this one. HyadesHoliday (talk) 11:18, 5 April 2024 (UTC)

It helps me, as I also relied on the list for my academic writing, and came to this talk page looking to find out what happened. The glossary seems to be less comprehensive than the old list (e.g., there is no section on category theory), in addition to lacking the LaTeX codes, and doesn't observe the clean subject hierarchy of the other page. If I had suggestions to add on top of putting in the LaTeX codes, they would be expanding the article to at least the comprehensiveness of the list, and to introduce a similar hierarchy that breaks up symbols by field and topic within the field, for ease of navigation. As has been mentioned earlier, it was useful that there was a page that collected the name, meaning, and typographical information of just mathematical symbols, in one place.

I am also not fond of the glossary's formatting and didn't have much trouble with the tables on mobile, but consent that a large page of just tables doesn't conform to Wikipedia's readability norms. I'm not sure what would help with readability, something to more clearly break up the subsections for individual symbols, maybe. I do like that this page contains more description than the list. 173.206.19.146 (talk) 16:21, 30 June 2024 (UTC)

In a time where more and more people are switching to digital writing tools, I'd argue that the people who need to understand mathematical notation and the people who need to be able to type it are mostly the same. It doesn't make sense to differentiate between "general users" and editors/typographers here. 2.243.191.37 (talk) 14:34, 12 May 2024 (UTC)

Support: I think the ways of typing out a symbol are quite basic information on that symbol, and are also very useful for the people looking up lists of symbols. In the same way it's sensible to include a reference table in the ASCII article, I believe it sensible to include the typographic information on an article about symbols. DIYLobotmy (talk) 09:04, 23 May 2024 (UTC)

LaTeX commands

One of the merged articles used to contain the Latex commands that produce each symbol. I found this very useful. Can I still find the table anywhere else? Or some table like that one...

The LaTeX commands are in the source, but it's not the same. Madhing (talk) 21:25, 21 April 2024 (UTC)

Nevermind, this has been discussed before. Madhing (talk) 21:35, 21 April 2024 (UTC)

For the convenience of future readers with the same question, see The Comprehensive LaTeX Symbol List. --𝕁𝕄𝔽 (talk) 22:35, 21 April 2024 (UTC)

Bullet operator

The article Bullet (typography) says A variant, the bullet operator (U+2219 ∙ BULLET OPERATOR) is used as a math symbol, akin to the dot operator. Specifically, in logic, x • y means logical conjunction. It is the same as saying "x and y" (see also List of logic symbols). Is it significant enough to be included here? --𝕁𝕄𝔽 (talk) 13:16, 20 July 2024 (UTC)

IMO, for being included, a symbol must be commonly used. This means that there must be textbooks that use it (the mention taht there is an author that used once the symbol is not sufficient). Clearly, Bullet (typography) is not a reliable source, not only per WP:USERGENERATED, but also because this is not a mathematical article. The anonymous table given as a reference is not a reliable source either. IMO, the use of a bullet instead of $\land$ is much too marginal for deserving a mention. D.Lazard (talk) 14:06, 20 July 2024 (UTC)

TYVM, until I saw that sentence, I had only ever heard of $\land$ as a logical AND, but assumed that the fault was mine. I guess somewhere in the Unicode Consortium correspondence there is an explanation. I don't propose to pursue it further. --𝕁𝕄𝔽 (talk) 23:37, 20 July 2024 (UTC)

References

𝕁𝕄𝔽 (talk) 13:16, 20 July 2024 (UTC)

Angle brackets

I have seen angle brackets used with the following definition

$\langle \cdot \rangle =\mathrm {max} (\cdot ,0)$ ,

as in

$\langle \mathrm {f} (x)\rangle =\mathrm {max} (\mathrm {f} (x),0)$ .

But not sure how common that usage is. —DIV
Support good-faith IP editors: insist that Wikipedia's administrators adhere to Wikipedia's own policies on keeping range-blocks as a last resort, with minimal breadth and duration, in order to reduce adverse collateral effects; support more precisely targeted restrictions such as protecting only articles themselves, not associated Talk pages, or presenting pages as semi-protected, or blocking only mobile edits when accessed from designated IP ranges.
(1.145.47.43 (talk) 10:59, 16 August 2024 (UTC))

says who?

The lead includes the claim the standard typeface is ... upright type for upper case Greek letters. Really? According to what standard? Dondervogel 2 (talk) 09:37, 11 January 2025 (UTC)

See Donald Knuth's TeXbook. Also, if you type <math>(\Gamma,\gamma)</math> you get $(\Gamma ,\gamma ).$ This show that LaTeX, the standard fo mathematical typesetting, implements this standard by default. D.Lazard (talk) 15:43, 11 January 2025 (UTC)

I was under the impression that international (ISO) standards required upper case Greek symbols to be in italics. Hence the tag. However, a brief search did not reveal evidence to support my impression. I'll come back here if I find something. Dondervogel 2 (talk) 15:55, 11 January 2025 (UTC)

In any case, ISO is a standard developped for engineering and is generally not accepted by mathematicians. D.Lazard (talk) 22:10, 11 January 2025 (UTC)

That might be your opinion. I don't share it. In any event, I've found the standard I was looking for (ISO 80000-1:2002), which confirms my impression is correct (indeed, it is likely the source of that impression. I'll come back with the details. Dondervogel 2 (talk) 22:28, 11 January 2025 (UTC)

In any case, ISO is a private company, and its standards apply only to corporations and communities that decide to apply them. For the typography of formulas, it is not the case of the mathematics community, and more generally the academic world. It is also not the case of English Wikipedia, see MOS:MATH#Greek letters. D.Lazard (talk) 10:46, 12 January 2025 (UTC)

Your 'not invented here' attitude has no bearing on the relevance of ISO. I can clarify here if you wish, or just edit the article to correct the imbalance. Which do you prefer? Dondervogel 2 (talk) 13:36, 12 January 2025 (UTC)

On the contrary, you appear to be applying "not invented by ISO". Although I am a strong supporter of international standards in general and ISO in particular, context matters. Mathematics has long established customs and practices and the form that a symbol takes matters. The "same" letter presented in different typefaces has different meanings. ISO has no interest in this level of detail and you should not try to enforce it outside its domain. See Scope creep.

Put simply, you will not get consensus for such an insertion. 𝕁𝕄𝔽 (talk) 17:12, 12 January 2025 (UTC)

Three questions:

1. If ISO has no interest in this level of detail, why does it publish ISO 80000-2:2019 Quantities and Units - Mathematics?
2. What insertion are you suggesting there would be no consensus for?
3. Are you saying that the scope of this article is limited to mathematical symbols not defined by ISO?

Dondervogel 2 (talk) 17:32, 12 January 2025 (UTC)

Saying otherwise: for that matter, ISO 80000-2:2019 is a WP:Primary source; so, for being acceptable, one needs a reliable WP:secondary source that discusses the matter and concludes that it applies in mathematics. Without such a secondary source this is WP:original research produced by ISO consortium, and so, ISO 80000-2:2019 cannot be accepted as a source for mathematical articles. D.Lazard (talk) 21:51, 12 January 2025 (UTC)

Pointing out the existence of ISO 80000-2, while observing that compliance with its requirements would conflict with Donald Knuth's TeXbook, does not seem like WP:OR to me. They are simple and indisputable facts. Dondervogel 2 (talk) 06:14, 13 January 2025 (UTC)

Huh, what? You can indeed deduce facts via original research—surely this would be the goal much of the time.

This is functionally identical to the fourth example given at WP:SYNTH. Likewise, it would be original research, and Wikipedia does not publish original research. I am interested a bit in whether you have heard the phrase "verifiability, not truth" here before. Remsense ‥ 论 06:17, 13 January 2025 (UTC)

If something is obvious to anyone who reads and understands the sources that are supposed to support it, then it's not SYNTH. Dondervogel 2 (talk) 06:56, 13 January 2025 (UTC)

Well, no. Any claim not directly supported by a particular RS is original research, and that's pretty incontrovertible. Sometimes we feel like doing it anyway because we feel it to be obvious or otherwise harmless, but the fact remains no matter how many smarmy sections we pen in an essay about it. (Cards on the table, if I could ask God to send a little solar flare that results in exactly one page getting erased from project space forever, I might just pick this one. I disagree at least in part with most of the sections, and I think at best it encourages a proudly sloppy approach to research, and at worst it is directly contradicted in spirit by the plain meaning of our core content policies. Using IAR as a thumbs-up for SYNTH if you feel like it is just...gah, I have to stop now.)Remsense ‥ 论 06:59, 13 January 2025 (UTC)

A more appropriate reply would have been "Well, yes". The words you were responding to were not my interpretation but were copy-pasted from not SYNTH, so perhaps I should have put them in quotation marks. Try it like this: "If something is obvious to anyone who reads and understands the sources that are supposed to support it, then it's not SYNTH." Dondervogel 2 (talk) 07:25, 13 January 2025 (UTC)

Firstly, yes it is! Original research can be as obvious as you like.

Secondly, this argument isn't meaningful because I don't know what extrapolations and deductions would be obvious to everyone, and neither do you. The best I can do is sticking to tertiary analysis that presents only those claims that sources themselves say directly. That's the point of the policy as far as I can tell, but everyone's got a few edge cases they think are obvious or harmless. Remsense ‥ 论 07:32, 13 January 2025 (UTC)

Not being made of money, I have no idea what is in ISO 80000-2, perhaps you will enlighten us? But the abstract seems to suggest it is nothing more than a glossary of symbols used in Mathematics that may be relevant to science and technology, not a standard for mathematical typeface choice irrespective of context. The abstract reads:

This document specifies mathematical symbols, explains their meanings, and gives verbal equivalents and applications.
This document is intended mainly for use in the natural sciences and technology, but also applies to other areas where mathematics is used.

That second statement, I suggest, tells us all we need to know.

No, the scope of this article is the set of symbols used in mathematics. The set of mathematical symbols listed in the ISO standard is almost certainly a subset of it: if you find any that are not, then it is probably an oversight that should be rectified.

You will need to quote verbatim the relevant text from the standard if this is to be taken any further because right now it is impossible to take it seriously. I think it most unlikely that ISO would presume to contradict the thousands of mathematics publications and their authors. 𝕁𝕄𝔽 (talk) 00:41, 13 January 2025 (UTC)

You seem to be saying that mathematics, once applied to the physical sciences, is no longer mathematics. That makes no sense to me, and I doubt it is your intended meaning. Please clarify.

Happy to provide examples. There are likely others, but one is the ISO requirement to use italics for upper case Greek characters when they represent variables. I'll return with a verbatim quote. Dondervogel 2 (talk) 06:23, 13 January 2025 (UTC)

Even with a verbating quote, ISO's original research would remain original research. D.Lazard (talk) 09:51, 13 January 2025 (UTC)

No, WP:NOR only applies to Wikipedia itself. OSI standards are WP:RSs and are generally written by subject experts. (Though, if Dondervogel has read it correctly, clearly not mathematical subject experts.) 𝕁𝕄𝔽 (talk) 12:00, 13 January 2025 (UTC)

No, what I am saying is that ISO appears [rather astonishingly] to be specifying the form that mathematical symbols should take when used in science and technology. It is not (I hope!) purporting to tell mathematicians what symbols they should use, for what purpose, with what meaning, in which typefaces and fonts. 𝕁𝕄𝔽 (talk) 11:57, 13 January 2025 (UTC)

Ah, OK. I knew I must have misunderstood. Your first sentence makes complete sense to me. The second one is less clear though. ISO 80000-1 (and ISO 80000-2) do not tell anyone what do do. Instead they provide requirements and recommendations for those who wish to follow the standard on a voluntary basis, including any mathematicians applying they skills to science and technology. As far as I can tell, the present article is not limited to pure mathematics, which means the scope also includes applied mathematics, and ISO 80000 is most relevant to the latter scope. Dondervogel 2 (talk) 12:08, 13 January 2025 (UTC)

Well let's see the quote. But I really can't see it meriting more than a footnote. See WP:UNDUE.

But cheer up, it could be worse: in the days when typesetters had to deal with handwritten manuscripts, this is what they were up against: The printing of mathematics (Oxford University Press, 1994) The only reference to upright v slanting Greek is to π on page 2: upright when used as a constant, slanted when a variable. 𝕁𝕄𝔽 (talk) 13:09, 13 January 2025 (UTC)

LoL. ISO's position is that all constants (1, 2, 3, ..., pi, e, i, etc) are upright, which is consistent with the OUP 1994 advice. It's probably to avoid use of the symbol pi for anything other than it's usual 3.14159265...

A footnote might work. I still need to find the text for you, although you can find a preview at ISO/IEC 80000 Dondervogel 2 (talk) 15:06, 13 January 2025 (UTC)

I pointed out the existence of this discussion at ISO/IEC 80000 Dondervogel 2 (talk) 18:03, 13 January 2025 (UTC)

• Here's the verbatim extract (clause 7.1.1) from ISO 80000-1:2022

Symbols for quantities are generally single letters from the Latin or Greek alphabet, sometimes with subscripts or other modifying signs. Symbols for characteristic numbers, such as the Mach number, symbol Ma, are, however, written with two letters from the Latin alphabet, the initial of which is always capital. It is recommended that such two-letter symbols be separated from other symbols if they occur as factors in a product.

The quantity symbols shall be written in italic (sloping) type, irrespective of the type used in the rest of the text.

The quantity symbol is not followed by a full stop except for normal punctuation, e.g., at the end of a sentence.

Notations for vector and tensor quantities are given in ISO 80000-2.

Symbols for quantities are given in ISO 80000-3 to ISO 80000-5 and ISO 80000-7 to ISO 80000-12 and IEC 80000-6 and IEC 80000-13.

No recommendation is made or implied about the font of italic type in which symbols for quantities are to be printed.

• Clause 7.4 contains the Greek symbols in four different forms (upper case v. lower case, italic v. upright).
• Annex A.5.3 includes some examples (see ISO 80000-1).

Dondervogel 2 (talk) 15:19, 13 January 2025 (UTC)

So coming back to your statement that kicked off this discussion (I was under the impression that international (ISO) standards required upper case Greek symbols to be in italics.), can we now say that your recollection was mistaken, that the rubric only applies to quantities? (How does it define quantities? When or where are uppercase Greek letters used? (not micro- or nano-, obviously). But in any case it certainly can't be declared to apply of generic use of Greek letters in mathematics (pure or applied – or physics, for that matter), but there may be specific cases (such as?). --𝕁𝕄𝔽 (talk) 18:31, 13 January 2025 (UTC)

Argh! Perhaps everyone should take a step back. Firstly, Donald Knuth is evidently talking about (his?) TeX specifically (the statement needs rewording to make this restriction clearer, and IMO does not belong in the lead). Secondly, ISO is, as has been noted, a recommendation that can be followed by those who choose to (it acts to help produce more uniform presentation). Thirdly, and most importantly, this article is clearly just an informal glossary with no claims made about general applicability, and should in no sense claim to describe a uniform standard – at best, it could serve as a guide for the MoS to reference, i.e. usable in the domain of WP, and not claiming to apply anywhere else other than possibly describing specific uses that occur. All this talk of OR, verifiability, etc. seems to be misplaced. —Quondum 18:43, 13 January 2025 (UTC)

My recollection was correct, though I might have phrased it better. I was referring to any upper case Greek symbol representing a quantity (the example given by ISO 80000-1 is Φ, but it can be any one of 24 upper case Greek characters). The point is that ISO 80000 requires the character to be italic (Φ), not upright (Φ).

I believe the full set is ΑΒΓΔΕ ΖΗΘΙΚ ΛΜΝΞΟ ΠΡΣΤΥ ΦΧΨΩ. If any of those 24 characters are used to represent a quantity (as opposed to an object or concept or operator), compliance with ISO 80000 means the symbol for that quantity would be italic. As an example, imagine the quantity Χ is defined as the sum of Ψ and Ω. The equation relating these three quantities is Χ = Ψ + Ω and not Χ = Ψ + Ω.

I hope this clarifies. Dondervogel 2 (talk) 19:25, 13 January 2025 (UTC)

I have edited the lead. The statement being commented on in this thread might or might not belong: I'm not sure myself, so I've left it as an invisible comment, in a less contentious form that simply describes the different conventions, in case someone wishes to change it into visible text. —Quondum 00:05, 14 January 2025 (UTC)

Thank you. Your edit completely addresses my concern. Dondervogel 2 (talk) 08:52, 14 January 2025 (UTC)