# Wikipedia talk:Manual of Style/Mathematics

WikiProject Manual of Style
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.

## Scriptstyle for 'math' symbols in running text

An anon editor of Simple linear regression is under the impression that using "scriptstyle" for [itex]ematical symbols in normal running text, such as ${\displaystyle \scriptstyle {\hat {\alpha }}}$ or ${\displaystyle \scriptstyle {\hat {\beta }}}$, is some sort of convention in math articles. I don't see any evidence of this. Am I missing something? Interested parties may consider discussing this at Talk:Simple linear regression#Scriptstyle. - dcljr (talk) 05:50, 1 January 2016 (UTC)

Scriptstyle should ordinarily only be used to generate subscripts, superscripts, and other small type face. It should generally not be used to overcome the shortcomings in how Wikipedia renders mathematics into PNG. It is semantically incorrect for this purpose, meaning that what may look good for users with certain defaults (e.g., rendering to PNG) will not look good for others (e.g., MathML and SVG). I have seen mobile browsers where scriptstyle renders as an indecipherable blur. So it generally must be avoided in part for reasons of WP:ACCESS for the vision impaired. 11:42, 1 January 2016 (UTC)

## Are algorithms "invented" or "discovered"?

Are mathematical algorithms "inventions" or are they "discoveries"? --82.132.234.81 (talk) 18:09, 7 January 2016 (UTC)

Depends on who you ask. Paul August 21:54, 7 January 2016 (UTC)

## where to find info on "equation box"?

I'm looking for some info on this equation box (for instance, parameters, etc.):

 ${\displaystyle M=E-e\sin E}$

I have been perusing a lot of the WP:math type articles without much luck. All I know is that it exists, obviously. Tfr000 (talk) 16:57, 31 January 2016 (UTC)

Type "template:Equation box 1" in the search field. D.Lazard (talk) 18:54, 31 January 2016 (UTC)
Yup, that did it. Thanks! Tfr000 (talk) 19:00, 31 January 2016 (UTC)
Thank you both! I never would have thought to look under Template instead of Wikipedia. — Anita5192 (talk) 20:22, 31 January 2016 (UTC)
Opening a diff allows one to click on the template (in either diff window) as well, which takes one straight there without having to use the search widget. —Quondum 23:06, 31 January 2016 (UTC)

## Use of "\colon" vs. ":"

I think it would make sense to have a style guideline for the use of ":" and "\colon" in the [itex] tags. Namely, only "colon" should be used for expressions like ${\displaystyle f\colon X\to Y}$, while the use of ":" should be limited to the cases where the colon is to be treated by the math engine as a relation, like in set notation: ${\displaystyle \{x\in \mathbb {R} :x>0\}}$. The creators of LaTeX never intended ":" to be used in map notation, and hence "${\displaystyle f:X\to Y}$," which is found in many articles, can be regarded as bad practice encouraged by Wikepedia.--Ørsted (talk) 14:02, 29 February 2016 (UTC)

In the preceding post, the difference between ":" and "\colon" needs to be clarified. I understand, maybe wrongly, that the difference lies in the space before the colon. If this is correct, this suggests that ":" is treated by the latex engine as an operator, and "\colon" as a punctuation mark. In your both examples, the colon is a separator (punctation mark), which has no meaning by itself, and is not an operator, nor a relation (in the mathematical sense). This would induces that the spacing should be the same as punctuation in plain text. However, the colon, in both examples is a separator between math. expressions of different nature. In this case, the rule that recommends to not have two formulas separated by a single punctuation mark (for clarifying the separation between formulas), should be adapted, and this leads to insert a space before the colon. In summary, IMO, the use of ":" instead of "\colon" is not a question of good or bad practice, but a question of personal esthetic preference. D.Lazard (talk) 15:14, 29 February 2016 (UTC)
In LaTeX, one distinguishes between seven different classes of symbols: ordinary, operator, binary, relation, opening bracket, closing bracket, and punctuation. By default, ":" is treated like a relation, while "\colon" is the same symbol treated as punctuation, but with some extra spacing added by the package "amsmath." As noted by the TeX.SE user egreg (who is one of the leading figures in the TeX community), it is in general considered wrong to use ":" in map expressions like ${\displaystyle f:X\to Y}$. On the other hand, the colon in set notation, while not strictly speaking a mathematical relation, should be treated as such with regards to spacing. In particular, there should be equal spacing on both sides of this colon. This is univeral consensus in the TeX community, and it is recommended in Donald Knuth's TeXbook itself, which is the original documentation of the TeX program.--Ørsted (talk) 14:19, 1 March 2016 (UTC)
Now that we are at it, the same goes for "|" vs. "\mid": Compare ${\displaystyle \{x\in \mathbb {R} |x>0\}}$ to ${\displaystyle \{x\in \mathbb {R} \mid x>0\}}$. Here "\mid" is the right choice.--Ørsted (talk) 16:42, 1 March 2016 (UTC)
I agree to all this. This is the sort of thing that should be included in this section of the MOS. —David Eppstein (talk) 18:43, 1 March 2016 (UTC)

## Distinguishing notation for distinct concepts within an article

I would like opinion on the mixing of indistinguishable notations for, for example, dx in Leibniz's notation for infinitesimal and in the differential of the exterior derivative when both are used within the same article. I am aware that Wikipedia:Manual of Style/Mathematics § Typesetting of mathematical formulae §§ Font usage §§§ Roman_versus_italic is deliberately non-prescriptive. There are also instances where a distinction would be immaterial, such as to distinguish whether ex refers to the exponential function or to use of the constant e in exponentiation in an article on real analysis (though we've seen people tie themselves into knots in complex analysis when conflating them). Is there value in recommending distinguishing notations for distinct concepts within an article through no less than a typeface difference? —Quondum 18:17, 5 March 2016 (UTC)

Using the same notation for several concepts is, in some contexts, a standard abuse. If the abuse is standard, we do our readers a service if we explain the abuse and a disservice if we diverge from standard usage.
Distinguishing concepts using solely a typeface difference is a terrible idea. It is far too easy for editors to make an inadvertent mistake, or for readers to fail to notice the different typefaces, or even for readers to fail to notice that the article uses different typefaces. Such an article would be illegible for those who use screen readers. Additionally, there's a very good chance that someone will misunderstand the intent of the article and will blithely replace all the type changes with a single style. Ozob (talk) 19:54, 5 March 2016 (UTC)
Okay, accepting that distinguishing symbols solely though typeface difference is a bad idea (though we do this routinely in examples such as v = | v |, I actually agree with you on this point), I feel that we need some way of reducing confusion through conflation. I also agree that we should not be diverging from standard notation, though there might be some wiggle room when the notation is not really standard (as with the 'd' of the exterior derivative).
Perhaps I should rephrase my query as: should we have a guideline that encourages editors to take care to clarify through notation or explanation which of several distinct and conflatable concepts is meant in any given usage? For example, I cringe when I see dx referred to as an infinitesimal in one paragraph, and without highlighting it meaning the exterior derivative in the next (thus allowing the reader to draw the inference that they are really the same thing, or at least that some of the editors think so). In these contexts I have been tempted to make it clear through words, but then because there is no clearly dominant standard, to use a typeface as a redundant indication. —Quondum 20:44, 5 March 2016 (UTC)
Perhaps I'm misunderstanding, but I don't see v = | v | as being related to your question. The vector v and its length v are such different types of objects that even an inattentive reader is unlikely to confuse them. Whereas the distinction between an infinitesimal dx and the exterior derivative dx of the function xx is more subtle because they serve similar purposes.
I believe that we should encourage editors to write well. Your example of dx being both an infinitesimal and an exterior derivative, with no hint to the reader that the notation has changed meaning, is an example of bad writing. Such articles should be fixed, and since dx is in both instances the standard notation, the fix should be to use words. If notational confusion is a widespread problem, then I agree that the MOS should warn editors about it. Ozob (talk) 21:02, 5 March 2016 (UTC)
I can interpret the equation v = | v | perfectly well as a sensible conclusion of a logical argument (where both occurrences of v refer to the magnitude of a vector v), so I still see this as which symbol is meant as being distinguished solely by typeface (and perhaps contextually inferred intent). More explicitly: many articles rely on typeface to make the distinction between the symbol for a vector and that for its magnitude to be salient, although you appear to have labelled this as a "terrible idea".
I'm coming to think that my rephrased question should be answered as: Which symbol is intended in any potentially confusing case should be made clear to the reader, but there is not necessarily a benefit in making an explicit guideline, since this is in general obvious and not likely to result in arguments between editors.
A (possibly perverse) side of me then wants to ask whether to consider the principle that you have enunciated, namely that determining which symbol is intended in any given use, if significant, should not rely solely (or even primarily) on the typeface, mainly for the reasons you have given. But I suspect that we'll find this principle violated so often in WP and elsewhere that it'll be problematic. —Quondum 22:00, 5 March 2016 (UTC)
I think this is an important issue to address and I agree with Ozob. In well-written textbooks, the authors define their terms to make clear their meanings, especially when potentially confusing. We editors should do the same. We should use unambiguous symbols when possible. But when we must use similar or identical symbols, we should explain in words what the symbols mean and how their meanings differ when they do. We should encourage editors to write well and this should be encouraged in the manual of style. — Anita5192 (talk) 23:21, 5 March 2016 (UTC)
Again, I don't understand why the point you are making is relevant. You began this discussion with the example of dx being used to mean both an infinitesimal and an exterior derivative. I believe we are agreed that this is poor style. If I understand you correctly, you are also asserting that writing v = | v | is also poor style, and that this is contrary to my stated position that we should not distinguish concepts based on typeface alone.
But in your initial comment you brought up the choice of Roman versus italic type style. I interpreted that to mean that you were considering the merits of letting (for example) dx be an infinitesimal and dx be an exterior derivative. When I said that using typeface to distinguish concepts was a terrible idea, that was the example that I had in mind. I maintain that it is a terrible idea because of the risk of confusion. But, as I tried to clarify above, a vector and its length are obviously different types of objects. The equation v = | v | does not use different typefaces to distinguish concepts; it uses them to distinguish objects (the object v has the type "non-negative real number" and the object v has the type "vector"). So while I don't think that v = | v | is especially good style, I don't think it's so horrible, either. Ozob (talk) 02:45, 6 March 2016 (UTC)
My initial comment used roman vs. italic typeface as an example; bold vs. non-bold is another instance of the same thing. It is also a matter of opinion as to whether an infinitesimal and the exterior derivative are "obviously different types of objects"; I'd say they are utterly so: the former may be regarded as a hyperreal number or similar, the latter as a mapping between functions on a manifold. We now seem to be getting ourselves tied up about a peripheral issues, since I'm in agreement with your larger perspective. I think we should rather refocus on Anita5192's very neat encapsulation above. —Quondum 03:58, 6 March 2016 (UTC)

Another example of the problem is the polynomial notation: in many textbooks, and some of our articles, P(X) denotes a polynomial P in the indeterminate X, while P(x) denotes the same polynomial with the indeterminate substituted for x. Moreover, the polynomial is denoted indifferently by P of by P(X). Although this may be confusing for the reader, this is mathematically perfectly correct: if the functional notation is clearly defined as representing the substitution/evaluation operation, the substitution of the indeterminate by itself results in the polynomial itself, and this allows writing P = P(X). IMO, the clarification of the notation for polynomials is important, and I have tried to make it explicit in Polynomial § Notation and terminology. This has been reverted as unhelpful by this edit. I have not reverted this edit, because I am unable to provide a reference, but I think that this deserves discussion. D.Lazard (talk) 10:12, 6 March 2016 (UTC)

## HD formulas

Is there any way to see formulas with higher resolution? The PNG formula images are quite low res, and they look really ugly on a high resolution screen such as an iPad. Is there any way to use SVG or higher resolution PNG? --IngenieroLoco (talk) 17:26, 17 April 2016 (UTC)

Yes, in your preferences, in the "appearance" pane, set the "Math" preference to "MathML with SVG or PNG fallback". Then, if your browser can handle it, you should either get MathML or SVG. However I don't know whether that works in the specific case of the iPad. —David Eppstein (talk) 19:09, 17 April 2016 (UTC)
Thanks! They look great now! They do indeed work on iPad. --IngenieroLoco (talk) 19:25, 17 April 2016 (UTC)