Wikipedia talk:Manual of Style/Mathematics

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WikiProject Manual of Style
WikiProject icon This page falls within the scope of WikiProject Manual of Style, a drive to identify and address contradictions and redundancies, improve language, and coordinate the pages that form the MoS guidelines.

Wikilinking formulae[edit]

I just came across the following [[Green's relations#The H and D relations|''H''<sub>1</sub>]], rendering as H1 which somehow struck me as unsatisfactory. Would it be a good idea to suggest that as a matter of style one should not wikilink to formulae unless they happen to be the actual article title, such as E8 (mathematics) or Ζ(3)? Deltahedron (talk) 21:35, 31 August 2014 (UTC)

I agree. To me this sort of thing is similar to what WP:SUBMARINE warns against. If the H and D relations need to be glossed for readers who might not know what they are, better to do it in text rather than in easily-missed links within the notation. —David Eppstein (talk) 22:39, 31 August 2014 (UTC)

"d" in integration and differentiation[edit]

There seems to some dispute whether the "d" should be upright in integrals and derivatives:

  1. \int_1^\infty x^{-2}\, dx
  2. \int_1^\infty x^{-2}\,\mathrm{d}x

Any comments. I have no personal preference, except it should be consistent within articles. — Arthur Rubin (talk) 19:12, 19 September 2014 (UTC)

There is a standard ISO 31 described in this Tugboat article that claimed it should be a roman d. But this standard is widely ignored. The TeXBook has an italic d. It might be a math vs engineering culture issue. Integral#Terminology and notation seems to recommend an italic d, but mentions the roman d is used, too. I generally follow the TeX conventions established by Knuth. --Mark viking (talk) 19:50, 19 September 2014 (UTC)
This has been discussed many times at this project (see the archives back to perhaps 2011, maybe earlier...). (Admittedly I used to be one of those that would "straighten" out the "d"s, part of the problem and not the solution). We should just keep them consistent within articles and close to what most sources use, as WP:MOSMATH#Choice of type style says. M∧Ŝc2ħεИτlk 22:49, 19 September 2014 (UTC)
I knew I should have read MOSMATH more closely. As far as I'm concerned, this is resolved. — Arthur Rubin (talk) 01:26, 20 September 2014 (UTC)
When this topic comes up I frequently point people to WP:RETAIN, which, despite being stated in a different context, captures the right spirit. Also, usually this topic comes up because someone changes an article, and then I (gently, with a talk page note) revert them. Ozob (talk) 04:06, 20 September 2014 (UTC)
This issue came up today at Fourier transform. Italics should be reserved for variable symbols. Using them for operators is confusing IMO because dx looks like the product of d and x. In the International System of Quantities, it should be dx. Dondervogel 2 (talk) 16:46, 24 July 2015 (UTC)
This recommendation is almost universally ignored in the literature. There is no policy mandating that we must follow proprietary ISO standards in our mathematics articles, especially not when those recommendations contradict prevailing use (as well as other style recommendations such as Knuth). Besides, in one of the perennial discussions on this very issue, someone has already pointed out that dx is not an operator "d" applied to a variable x, but the unit dx is a separate variable denoting an infinitesimal increment. Sławomir Biały (talk) 16:57, 24 July 2015 (UTC)
I think that this is something that does not need to be covered by policy. I have no preference, except I think dx is easier to write than \mathrm{d}x. --Sammy1339 (talk) 17:09, 24 July 2015 (UTC)

Revising the page[edit]

I am not a member of this group, and came here looking for specific advice that could be given at a Edit-a-thon so I am loathe to make any changes without starting a discussion first and listening to the opinions of the subject experts- but I do get the feeling that this page is very dated, inaccurate and wishy-washy. The formating is not consistent etc- it is heavily dated. If I can't stimulate anyone else to do the work- I give notice that I want to bring this advice upto date to reflect current good practice.-- Clem Rutter (talk) 11:41, 24 February 2015 (UTC)

As far as I'm aware, it's not dated, inaccurate, or wishy-washy; it represents the current consensus of WP:WPMATH. Can you provide examples? Ozob (talk) 01:49, 25 February 2015 (UTC)
Thanks for responding. Examples coming shortly.-- Clem Rutter (talk) 08:57, 25 February 2015 (UTC)

Specific Points[edit]

My first warning bell was the line

Lastly, a well-written and complete article should have a references section. This topic will be discussed in detail below. Which refered to

Including literature and references

It is quite important for an article to have a well-chosen list of references and pointers to the literature. Some reasons for this are the following:

Compare that with WP:REF. WP:CITEHOW- Where is the strong statement that

WP uses secondary sources and is not OR, so all statements should be supported by an inline reference.

This is a MOS not an essay on the history of maths publications- so where is the statement that various methods of citation are supported but WP:WPMATH advises to use Harvard or Vancouver- or sfns. See the comment in the FARs eg Wikipedia:Featured article review/Infinite monkey theorem/archive2.

Should we just add a sandbox page here and knock together a tougher version. I have gone from looking at MOS pages for advice- to using them to teach post-graduate newbies the ropes. I see from the history that this is basically a 2002 page that that has been cp'd in 2005- and then tweaked. It still feels like the musings of 2002 (Magna Carta- rather than Criminal Justice Act!).

Even changing this line to:

All Wikipedia articles must have references supporting each edit. This topic is discussed below.

Would be make the page factually accurate. Looking to include material from Wikipedia:Scientific citation guidelines might be be more beneficial.

The Wikipedia:cite sources article has more information on this and also several examples for how the cited literature should look.

It has examples- but choices and no firm advice about current practice. This is a major confusing area for academics- and the editors I am training want firm advice here- newbies are not encouraged by doing wild wikilink chases. They have a message, which they want to put on wiki- correctly reference it and format it (and they have two hours).

Sections and lead

What section headings are required, in what order and what sections always occur? So I look at Wikipedia:Manual_of_Style/Mathematics#Suggested_structure while bearing in mind Wikipedia:Manual_of_Style/Chemistry#Article_types and Wikipedia:WikiProject_Computer_science/Manual_of_style#Structuring_different_kinds_of_articles.

Briefly looking at Wikipedia:WikiProject_Mathematics#Good_articles we have four types of article.

  1. Mathematicians
  2. Mathematics
  3. Mathematical problems
  4. Mathematical physics

What are the sections that we would hope to see in a GA/FA for each of these, and how does the MOS help us to write one?

So what do we have at the moment

Suggested structure
Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds.

That is not about structure but a POV on writing pitfalls- though of course very true. (This sentence was copied across to the CompSci MOS and tweaked suggesting how they wrote theirs).

A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds.

This is advice on the writing process- not on the contents or structure or style of a WP:WPMATH approved article. A possible easy alternative is to take the table from Wikipedia:WikiProject_Mathematics/A-class_rating#Criteria To achieve a well structured article that fulfills the objects of Wikipedia and WP:WPMATH articles should attempt to follow a common structure. There are four principal types of article that have achieved FA status, and their advised structure is considered separately.

We then follow the method used at CompSci giving proformas for each of these article types. In my POV- study links to FAs and GAs for each type of article work.

Laying out the page.

Not Typesetting- please- there is no hot lead or Linotypes involved. For a maths article this is critical. My first question was- Do I centre a formula, right justify, left justify or put in inline in a sentence? That is what a newbie will ask me- that is what a MOS says. We don't. The essay on LATEX is complete and fun to read- but is addressing the wrong audience. To put it bluntly it reads as if a group of editors have finally understood the intricacies of the markup and demonstrating their mastery. It does not say:

The body text of a mathematics article will be written using standard wikitext markup,<sup> and <sub> will be used push the text up and down. Wikitext can use latin and greek letters. More complex text can be included inline and in separate paragraph using maths markup as explained in a separate section. All standalone maths markup and formulae should align usually using one indent ( :) from the left margin.

To summarise- there is nothing wrong with the mathematical consensus on this page- but it is not an adequate MOS page as it is not written for the potential user- particularly the brilliant time-poor mathematician who wants to get an article up and running.

I propose we open a sandbox page here and knock together a tougher version. And we focus that version from the point of view of a wiki-newbie who comes with a strong Mathematical background and the tutor who is mentoring her/him -- Clem Rutter (talk) 11:49, 25 February 2015 (UTC)

In part, you seem to be asking for us to establish consensus about topics that have no consensus. There is no consensus on citation style. There is no consensus on how to format inline mathematics. There is no consensus on what article headings are required and in what order. Moreover, there are people with strong opinions on each of these. I'm not averse to improving the current MOS page, but my past experience has led me to believe that consensus is unachievable and issuing diktats accomplishes nothing.
That said, I would welcome an attempt to improve this page. I don't think it makes all its points in a compact fashion. Drafting a new version may be helpful. Ozob (talk) 13:12, 25 February 2015 (UTC)
This is a time consuming process- and I am plugging away in one of my sandboxes. I hope to have a report and a suggested alternative ready by Friday. The lack of consensus hasn't really caused any difficulties- it is handled by being open about it. It is really about focusing on what the page is about, and must include and what are interesting footnotes. I have just penned this note to let you know I am alive- and working on it, all be it slowly. -- Clem Rutter (talk) 21:51, 10 March 2015 (UTC)
I have just posted the page Wikipedia:Manual of Style/Mathematics/sandbox where I have presented my ideas- discovered a sheaf of inconsistencies. I send respect and greetings to past contributors having experienced some of the difficulties they must have encountered. Please do feel free to start a debate on the talk page. — Preceding unsigned comment added by ClemRutter (talkcontribs) 17:09, 14 March 2015 (UTC)

The use of \text in <math> in certain circumstances[edit]

Recently I've seen a use of \text in <math> tags update< incorrectly >, like Planck units#Base units:

 \frac{F}{F_\text{P}} = \frac{\left(\dfrac{m_1}{m_\text{P}}\right) \left(\dfrac{m_2}{m_\text{P}}\right)}{\left(\dfrac{r}{l_\text{P}}\right)^2}.

If you are using MathJax renderer, it doesn't look harmonious at all, as MathJax renders \text as sans-serif like the surrounding text. I've been in the process of changing some articles to use \mathrm, so it looks like this (please switch to MathJax in order to see the difference):

 \frac{F}{F_\mathrm{P}} = \frac{\left(\dfrac{m_1}{m_\mathrm{P}}\right) \left(\dfrac{m_2}{m_\mathrm{P}}\right)}{\left(\dfrac{r}{l_\mathrm{P}}\right)^2}.

For me at least it looks a lot better, so I went ahead and changed some of them. However I just want to ask here the community's opinion before proceeding further. What do you think about the tag used?

Some other options that don't work in MathJax:


 \frac{F}{F_\textrm{P}} = \frac{\left(\dfrac{m_1}{m_\textrm{P}}\right) \left(\dfrac{m_2}{m_\textrm{P}}\right)}{\left(\dfrac{r}{l_\textrm{P}}\right)^2}.

\mathsf (shows sans serif in PNG too)

 \frac{F}{F_\mathsf{P}} = \frac{\left(\dfrac{m_1}{m_\mathsf{P}}\right) \left(\dfrac{m_2}{m_\mathsf{P}}\right)}{\left(\dfrac{r}{l_\mathsf{P}}\right)^2}.

Timothy G. from CA (talk) 02:17, 3 March 2015 (UTC)

Also not working in MathJax but working in PNG:


 \frac{F}{F_\mbox{P}} = \frac{\left(\dfrac{m_1}{m_\mbox{P}}\right) \left(\dfrac{m_2}{m_\mbox{P}}\right)}{\left(\dfrac{r}{l_\mbox{P}}\right)^2}.

So it seems that only \mathrm works in all setups, others just look plain weird.

Timothy G. from CA (talk) 02:21, 3 March 2015 (UTC)

Also works for all layout engines: \rm

 \frac{F}{F_{\rm P}} = \frac{\left(\dfrac{m_1}{m_{\rm P}}\right) \left(\dfrac{m_2}{m_{\rm P}}\right)}{\left(\dfrac{r}{l_{\rm P}}\right)^2}.

Timothy G. from CA (talk) 23:32, 4 March 2015 (UTC)

Note that I do not want to change every single \text to \mathrm, only ones appropriate should be changed. Some of the circumstances I can think of where \text is appropriate is prose labels or anything that does not strictly need mathematical notations, like some equations on Navier–Stokes equations#Incompressible flow. Timothy G. from CA (talk) 01:10, 5 March 2015 (UTC)

Descriptive subscripts ought to be \mathrm in LaTeX. If it looks better, and it's more correct in principle, then that sounds like a double win to me. Quietbritishjim (talk) 16:58, 4 March 2015 (UTC)
@Quietbritishjim: that's what I thought. Do you think this should be added to the MoS? Timothy G. from CA (talk) 17:48, 4 March 2015 (UTC)
@Quietbritishjim: "ought to be"? I'm not saying anything either way at this point, but your rationale would be appreciated.
@Timothy Gu: \mbox is deprecated/discouraged, as I understand it. I get a "[Math processing error]" with MathJax on the machine I'm on at the moment, so difficult to comment. If \text is producing a problematic (non-harmonious) display on some browsers, it may make more sense to get to the bottom of the problem with the rendering, rather than to fix it via avoidance in the MoS. \text has been a standard part of TeX on WP for a long time. —Quondum 19:34, 4 March 2015 (UTC)
@Timothy Gu: Well, that is just my opinion and understanding of convention. But I believe such labels should be should be in the math font if it differs from the text font (as it does on Wikipedia, and a Times text / CM math document) because although the label is descriptive it's still part of some math. I also believe they should be upright regardless of whether the surrounding text is italic, either because the whole document is ( D-: ) or because this math is in emphasised text (e.g. in a theorem). \text gets both of them wrong, while \mathrm gets them right and agrees with \operatorname. Looking into it more, I notice that there is a problem though: if the math font is sans-serif then \mathrm still produces serif characters, which is not what you want. Unfortunately it seems there is no built-in math equivalent of \textup. Quietbritishjim (talk) 22:02, 4 March 2015 (UTC)
My opinion: \text and \mathrm are for two different things, both useful. \text is for when you want to include English-language prose within an equation, for instance the word "otherwise" in a \cases. \mathrm is for when you want to have short sequences of Roman alphabet letters that are themselves mathematical notation (not free-form prose); the example of a roman letter subscript is one where \mathrm is the better choice. Another alternative coding to consider is \operatorname, for mathematics notation written out as short sequences of Roman letters used as a function or operator (e.g. sin or cos) but not already built into LaTeX. The letters themselves should be formatted the same as \mathrm but the spacing around the operator should be better with \operatorname. So we should not be telling editors to prefer \text over \mathrm or vice versa, we should be using both where appropriate. —David Eppstein (talk) 22:43, 4 March 2015 (UTC)
@Quietbritishjim: I'd agree with David Eppstein here. But as LaTeX uses serif and it is unlikely to change in the future I'd stick with \mathrm. Timothy G. from CA (talk) 23:32, 4 March 2015 (UTC)
@Quondum: seems like I didn't make myself clear enough. I do not intend to do a wholesale removal of \text in all articles. I most certainly have seen cases where it is appropriate (can't find the article right now). Timothy G. from CA (talk) 23:09, 4 March 2015 (UTC)

Also I found out about a similar discussion on TeX StackExchange. It suggests to use \textnormal which is not available in MathJax at least; \mathup, but it is with a custom definition; and then \mathrm. So, I guess mathrm it is. Timothy G. from CA (talk) 23:32, 4 March 2015 (UTC)

If we do put something into the MoS, something like what David Eppstein proposes seems to make sense. The distinction between a subscripted text label and a Roman symbol is potentially semantically significant, so it would seem to me to be that \text is still semantically appropriate for labels. For example, the electron magnetic moment might be denoted \text \mu_\text{e}, where the subscript is literally a text label ("e" for "of the electron"), not a mathematical symbol such as a specific element of a set, for which I would prefer \mathrm.
@Timothy Gu: You are proposing a workaround for a rendering bug, not an issue of style. Subscripted text can be text and not symbols, so this does not contradict what David Eppstein is saying. Perhaps you should raise this at the Village pump (for fixing it), and at a place like WikiProject Mathematics (with respect to a settling on an interim workaround)? —Quondum 00:10, 5 March 2015 (UTC)
@Quondum: I agree with David's point as well. However, as I already said in my last reply, I was only referring to some specific use, not general-purpose labels. Plus, I do not consider \text being rendered as the way it is a bug, therefore I don't want to go to village pump for this. It is by definition rendered to the styles of surrounding text, which it is. It is just that many usage of \text is inappropriate on a semantic level as well. An appropriate use of \text IMO can be found on Navier-Stokes equations#Incompressible flow, reproduced below:
\overbrace {\underbrace {{\frac {\partial {\mathbf {u}}}{\partial t}}}_{{{\begin{smallmatrix}{\text{Variation}}\end{smallmatrix}}}}+\underbrace {{\mathbf {u}}\cdot \nabla {\mathbf {u}}}_{{{\begin{smallmatrix}{\text{Convection}}\end{smallmatrix}}}}}^{{{\text{Inertia (per volume)}}}}\overbrace {-\underbrace {\nu \nabla ^{2}{\mathbf {u}}}_{{{\text{Diffusion}}}}=\underbrace {-\nabla w}_{{{\begin{smallmatrix}{\text{Internal}}\\{\text{source}}\end{smallmatrix}}}}}^{{{\text{Divergence of stress}}}}+\underbrace {{\mathbf {g}}.}_{{{\begin{smallmatrix}{\text{External}}\\{\text{source}}\end{smallmatrix}}}}
The sans-serif font of the labels fits perfectly with the surrounding text.
To reiterate my point, certain if not most usage of \text is not appropriate and should be changed to \mathrm, but \text is still useful in many cases where non-mathematical/prose text is required, and I am happy with the way it is rendered as-is. Timothy G. from CA (talk) 01:10, 5 March 2015 (UTC)
In the MathML+SVG rendering mode that the developers are (IMO foolishly) standardizing on, when viewed in Chrome (which uses the SVG fallback), the labels are not sans-serif. They are a serif font that is unrelated to the body text. —David Eppstein (talk) 17:58, 24 July 2015 (UTC)
@Timothy Gu: I hear you that you do not intend to change everything. But if it renders differently in a respect that is significant in different rendering environments (and it is obviously significant, because you're making a thing of it to the point of suggesting a MoS change), it is a bug, period. \text renders as a serif font in every context that I can test at the moment (MathML and PNG), and I'll check tonight (when I have a different computer) whether it is the same on MathJax for me; this is already makes your "I am happy with the way it is rendered as-is" inapplicable. It is sounding as though your entire argument is based around rendering on a single browser+configuration+installation+MathJax. —Quondum 01:50, 5 March 2015 (UTC)
@Quondum: TBH I am surprised that you did not check the output from MathJax until this moment, which makes your argument sounds moot. This "bug" applies to all browsers using MathJax, so you can easily reproduce this. It is not depended upon your "browser+configuration+installation". Timothy G. from CA (talk) 02:28, 5 March 2015 (UTC)
Surprised? I indicated earlier that 'I get a "[Math processing error]"' on the machine I was working on when selecting MathJax (in place of every expression that MathJax was supposed to be rendering), and thus could not check. I see now that I have had the opportunity that I get the same rendering error on my other machine, though this had worked in the past. I'll accept that it might be uniform for all MathJax (when it works at all), but it still depends on whether MathJax is being used. But I have no interest in this argument; I do not support a change to the MoS along these lines, but I'll leave it to others to contribute to any consensus on this. —Quondum 03:06, 5 March 2015 (UTC)

I have just posted the page Wikipedia:Manual of Style/Mathematics/sandbox[edit]

I have just posted the page Wikipedia:Manual of Style/Mathematics/sandbox. I made several pointed remarks above- so I felt it was appropriate to rejig the whole page, trying to address some of my criticisms. Yes it was a major job. I feel that this was important as we wont get articles to FAC- unless they are MOS/Mathematics compliant- so having a tightly constructed page is a service and a duty to all FA hopefuls.

I tried not to add a single word- and certainly not change any existing decisions- through out the document I have left notes on the task and problems. Discovering an advised structure for the articles is an incomplete task. I have added a few suggestions. Unfortunately, no FAs or GA seem to follow the previous pattern. Exceptions- yes- but 25 out of 25!

Which brings me to the question of the structure of this MOS. Following other subjects- I detected a vague order, and have re-ordered the sections here to come into line. If this new order is accepted I feel it opens up the article to further improvement. At the moment we have hit a brick wall.

The second brickwall is there were three ways of presenting good/bad text. Obviously a C&P of three peoples work. When combined it was irritating to see first an example of bad text, a criticism then good text. Then the next paragraph- the convention was reversed! There are templates to help so I used them cf {{xt|----}} and ((markup|---|xxx}}.

What make this page unique is that we try and talk about good/bad text at the same time as trying to demonstrate <text> and html markup. I see no need to demonstrate bad text or bad markup here. (But it is essential to do it elsewhere in a tutorial page- or as a {{efn| ---}}

Let the discussion commence--- Clem Rutter (talk) 17:36, 14 March 2015 (UTC)

Three weeks- no comment. Okay I will be bold. I will build up the new page in Wikipedia:Manual of Style/Mathematics/temp-I will strip out my comments, and alternatives for discussion from this page I will then do a single copy and paste over Wikipedia:Manual of Style/Mathematics I then intend to format up the HTML sections to match the LaTeX sections. Wish me luck.-- Clem Rutter (talk) 17:20, 5 April 2015 (UTC)

Inappropriate italicisation of mathematical constants[edit]

In the International System of Quantities, mathematical constants, like e, i and pi are always upright. The MOS advice is to italicise, which means they can be mistaken for variables. What is the benefit of departing from the international standard? Dondervogel 2 (talk) 17:08, 24 July 2015 (UTC)

Apparently, ISO tried to standardize mathematics without any coordination with the International Mathematical Union. Therefore, there is no hope that mathematicians will change their typographical conventions for adopting ISO choices. For mathematical articles I do not see any benefit to adopt a "standard" which is not the standard in mathematics. In mathematical texts, the mathematical constants are usually italicized, as is every symbol consisting of a single letter (such as a function name). On the other hand the names consisting of several letters are upright. D.Lazard (talk) 18:35, 24 July 2015 (UTC)
I see. Remember that mathematical equations are used in physics and engineering too. What does the IMU have to say on the matter? Dondervogel 2 (talk) 18:37, 24 July 2015 (UTC)
As far as I can tell, the most definitive mathematical-society-produced style guide is still the AMS's Mathematics into Type. It uses italic for e (section 2.4.2c, p.20). I didn't see any examples with π or the imaginary unit meaning of i, but since they generally follow TeX conventions I would expect them to support italic for those as well. —David Eppstein (talk) 20:12, 24 July 2015 (UTC)
The ISO standard is almost universally ignored by mathematical sources. In no way should we mandate a proprietary convention like the ISO, which purports to be "standard", when it is in fact very much non-standard. Sławomir Biały (talk) 20:44, 24 July 2015 (UTC)
Yes. For another example of this, see binary logarithm, where the ISO's recommended notation "lb" is used far less than even the fourth-most-used alternative notation (lg, log2, log, and ld). —David Eppstein (talk) 20:59, 24 July 2015 (UTC)

Unlike what happens in chemistry, astronomy, and biology, mathematicians have no authorities who decree standards. Rather, standards evolve from conventions. And they are sophisticated and precise. Crowdsourcing vindicated yet again. Michael Hardy (talk) 20:14, 24 July 2015 (UTC)

The problem with ISO's attempt to impose a standard for this is that successful standards usually reflect existing practice (except in subjects that are completely new and have no existing practices). There are hundreds of years of mathematical typography in which d, e, and so on were italicized. Decreeing that all of it was wrong changes no one's mind, which is why people have continued writing italics just as they always did. Ozob (talk) 01:11, 25 July 2015 (UTC)
I don't see that ISO is trying to impose anything, nor decreeing anything as wrong. They are simply facilitating progress by providing a standard for people to follow should they choose to. A choice seems to have been not to and I do not yet see an answer to my question "What is the benefit in departing from the ISO standard?" Dondervogel 2 (talk) 21:43, 27 July 2015 (UTC)
The benefit is using the same notation all mathematicians elsewhere use, and thereby being more readable to people used to that notation. That is, we follow the de facto standard, not the false standard imposed by non-mathematicians and ignored by mathematicians. Other lesser but still significant benefits include much greater ease of formatting these symbols within <math> formulas (upright Roman characters are possible in <math> but not particularly easy, and I don't even know whether there is an upright π that works across all of the multiple options for rendering <math> in Wikipedia) and avoidance of edit wars with editors who prefer the usual format and have no inkling that the ISO might have suggested anything different (i.e. probably the majority of mathematics editors). —David Eppstein (talk) 23:25, 27 July 2015 (UTC)
I don't see ISO's efforts in this area as facilitating progress. There were de facto standard typographic conventions. They chose to flout them. Adoption of their notation has been limited; the upright d is seen occasionally, but it's been a variant usage for a long time; upright e and π are essentially unused. If anything, I think the appropriate questions to ask are, "Why adopt ISO notation contrary to standard usage?" and "Why does ISO persist in its non-conformity?" Ozob (talk) 00:55, 28 July 2015 (UTC)
So, in a nutshell: the familiarity of following existing (ambiguous) conventions is preferred over a standard that distinguishes between eccentricity and Euler's number? Dondervogel 2 (talk) 09:32, 28 July 2015 (UTC)
Or with the fundamental charge, or the elasticity, or the identity element of a group? I can't say that's ever been a problem. We deal all the time with possible conflicts between one variable and another. One solution is to use a different letter, or emphasize that this variable is not the same as the one that appears elsewhere if there is a real risk of confusion. A small change in typeface between \mathrm{e} and e does not seem like the best way, and it is certainly not the only way, to handle such a possible collision.
The purpose of a typesetting standard is (or should be) to enhance communication. It fails to do this if it does not already to a large extent agree with standard practices. One cannot enhance communication by insisting that the way people have been communicating for hundreds of years now needs to be changed. One still has to be able to read the papers that were published before the ISO standard went into effect. So, yes, "familiarity" is certainly a more important aspect in a standard than an illusion of unambiguity. Sławomir Biały (talk) 12:42, 28 July 2015 (UTC)
There are only 26 letters in the modern Roman alphabet; when you include capitalization and standard variations, like blackletter and calligraphic type or the Greek alphabet, you still only get a few hundred characters. The sophistication of modern mathematics and science makes it impossible to assign every concept its own symbol without using characters that nobody knows; even letters that people ought to be familiar with, like ξ, get muddled on blackboards all the time. So for purely practical reasons ambiguity is unavoidable.
Moreover, mathematics is not a collection of formulas; it's a rare math paper that has page after page of formulas (and those that do sometimes apologize to the reader). Written mathematics is done using written language, and it's both natural and expected that the writer will make statements like, "Let M be a manifold" or "Let M be a module" just so that the status of M does not have to be inferred from context. Ozob (talk) 13:56, 28 July 2015 (UTC)
@Slawekb. I agree it is not the only way. It might not be the best way either (how can one tell?), but it is better than not bothering to distinguish at all. If all changes were discarded because they lead to unfamiliarity we would still be counting with our fingers, we would not have computers, and we would certainly not be having this exchange on Wikipedia.
@Ozob. I agree that ambiguity in written language is unavoidable, if that's what you mean. I do not agree that ambiguity in mathematical equations is unavoidable, though it can require hard work. Distinguishing between variables and constants by means of italicization can only help.
Dondervogel 2 (talk) 15:14, 28 July 2015 (UTC)
"If all changes were discarded because they lead to unfamiliarity we would still be counting with our fingers, we would not have computers, and we would certainly not be having this exchange on Wikipedia." That's a strawman. I never said that all change from the familiar is bad. Instead, departing from existing standards of communication, instead of trying to codify best practices, actually leads to poorer communication rather than better communication. It's hopefully obvious why that is true. This very discussion is a living example of why. Sławomir
15:51, 28 July 2015 (UTC)
If I read you correctly, you're suggesting that we can assign each distinct mathematical constant or concept its own unique symbol. While I agree that such an assignment would eliminate ambiguity, it can't be done in practice. You are asking people to change good notation, in which M might stand for a manifold or a module or plenty of other things beginning with the letter "m", for an essentially arbitrary assignment where the symbols have no linguistic associations. Current mathematical practice may not be perfect, but it maintains some amount of order because people see the symbols as meaningful. Ozob (talk) 05:01, 29 July 2015 (UTC)
All I am saying is that I see an advantage in following the conventions of ISO 80000-2. There is nothing in ISO 80000-2 about assigning a unique symbol to each and every concept - that would be absurd. What I see there is a very sensible convention to italicise symbols that represent variables, while operators and mathematical constants are upright. Simple. I do not perceive a serious attempt to discuss the pros and cons of this convention, and therefore prefer to end this discussion. Good day. Dondervogel 2 (talk) 08:12, 29 July 2015 (UTC)