Wikipedia talk:WikiProject Mathematics/Archive/2016/Aug

Math DAB links

There are four articles linking to the DAB page Pushforward (or to redirects to it); those links need to be disambiguated. Several of us at WP:DPL are scratching our heads over what to do with them. If anyone here is willing to tackle them, we'd be most grateful.

The articles are:

• Contraction principle (large deviations theory)
• Hodge bundle
• Rate function
• Composition operator

Many thanks for your attention! — Gorthian (talk) 07:17, 4 August 2016 (UTC)

It seems that in the Hodge bundle article "pushforward" refers to Direct image of a sheaf and in all others to Pushforward measure. I changed the links accordingly. jraimbau (talk) 08:24, 4 August 2016 (UTC)

Thank you for such quick action! — Gorthian (talk) 09:11, 4 August 2016 (UTC)

Slowly varying function

Under "Karamata's characterization theorem", β need not be non negative, see Theorem 1.4.1 of Bingham, Goldie, Teugels. Accordingly, ρ can also be negative. — Preceding unsigned comment added by 62.141.176.1 (talk) 11:23, 4 August 2016‎

Not knowing about that theorem, I won't attempt to correct any problems with the article. But I wonder why you don't. Michael Hardy (talk) 04:03, 6 August 2016 (UTC)

Measurable and μ-measurable functions

I posted a question in over at the measurable function talk page some time ago. Is there any sense to it? YohanN7 (talk) 11:46, 10 August 2016 (UTC)

Torsion coefficient (topology)

Article needs attention from an expert in algebraic topology. I posted a set of questions and objections on its talk page: Talk:Torsion coefficient (topology) 67.198.37.16 (talk) 20:16, 10 August 2016 (UTC)

Programmatic examples

Coming from a programming background, and not having much formal math schooling since high school, I find it difficult to translate the abstract mathematical notation into a language I can actually programmatically calculate. I would hazard a guess that I am not alone in this regard, although this is a bit anecdotal. Therefore, it would be awesome if a Wikiproject was started that had programmatic examples, in addition to the more abstract ones written in mathematical notation. It might even be possible to have this translation be automatic (sympy.org?). I think it would be much easier to learn complex mathematics if it was taught using python rather than Greek. --Aaron E-J (talk) 18:02, 6 August 2016 (UTC)

Can you be more specific? Which article(s) do you have in mind? Many mathematical topics cannot be programmed. For many topics that can be programmed, programming them is a difficult task, which can still be an active subject of research (a typical example is integer factorization), and the programs may be so complicate that they can be read only by specialists. On the other hand, many math. articles provide pseudo-code, which is the standard method for describing programming methods in a way which is independent of a specific programming language. Nevertheless, I agree that too many articles contain complicate descriptions of algorithms, which would be much easier to understand, by simply providing pseudo-code. Also, too many articles can be understood only by people that already know the subject. This is not because of the lack of programming examples, but, simply because they are badly written. Please improve them if you can. D.Lazard (talk) 20:13, 6 August 2016 (UTC)

I agree with D.Lazard. Many mathematical theorems use non-constructive existence proofs. The "non-constructive" part means that no algorithm is offered. I'm sure that there is a place for concrete algorithms in specific articles, but to ask Wikipedia to include an algorithm for converting mathematical proofs to algorithms is far too ambitious. Mgnbar (talk) 00:55, 7 August 2016 (UTC)

I guess what I am suggesting is programmatic examples of how you would utilize the theories, not complete proofs. Computer programs, when it comes down to it, are math. Obviously you cannot prove everything with only 1 and 0, but then an encyclopedia article is not a theorem, but an explanation of a theorem. --Aaron E-J (talk) 02:20, 7 August 2016 (UTC)

Some theories are easy to illustrate with programs, while others are not. There are topics that are well-understood from certain theoretical viewpoints but whose implementation is very subtle. For example, mathematical optimization of, say, a smooth real-valued function of several real variables is easy in theory: Find where the derivative of the objective function vanishes, compute the values of the function at those points, and also compute the function values along whatever boundary the problem might have. In practice this is so difficult that people devote their lives to it.

Whether or not providing pseudocode is feasible depends on the article. I'm sure there are articles that would benefit from pseudocode, or maybe even more than pseudocode. If you have some particular articles in mind, there are experts here who could take a look. Ozob (talk) 02:37, 7 August 2016 (UTC)

Perhaps this might help -- there are multiple books on category theory, with all the concepts illustrated in ML (programming language) or CaML. Since category theory undergirds the syntactic content of mathematics (e.g in the guise of topoi) then perhaps that could be an aid to understanding. As to actually putting program snippets into WP math articles -- thats a terrible idea -- its basically original research, unless you do it a la the aforementioned books. (The ML/CAML books are interesting precisely because ML adds types to lambda calculus, which then gives a nice bridge from category theory to type theory which is a HoTT topic these days). 67.198.37.16 (talk) 20:25, 10 August 2016 (UTC)

Mivar-based approach

This article, which is being translated from ru:Миварный подход, may be of interest. JohnCD (talk) 09:41, 11 August 2016 (UTC)

Mean value problem

Mean value problem is an article about a problem posed by Stephen Smale. I needs work. Michael Hardy (talk) 19:52, 12 August 2016 (UTC)

. . . and I've done a bit more work on it. But more is needed. Only one page links to it: the one on Smale's problems. Michael Hardy (talk) 01:59, 13 August 2016 (UTC)

Binary function

Binary function (i.e. a bivariate function, not a function with binary variables or values) has been proposed for deletion. It's been a problem article (e.g. no sources) for years, but maybe someone wants to take the effort to save it? —David Eppstein (talk) 06:35, 14 August 2016 (UTC)

Hi, I've done some work on it, but a lot of the sections are things I really don't know much about. Have removed the prod for now. Happy Squirrel (talk) 02:37, 17 August 2016 (UTC)

Convolution quotient

I've created a severely stubby new article title Convolution quotient. Clearly it needs work, but I'm done with it at least until morning. Michael Hardy (talk) 05:29, 19 August 2016 (UTC)

Josip Pečarić

• Josip Pečarić (edit | talk | history | protect | delete | links | watch | logs | views)

Two tags have been added to the article, apparently based on the description "a great name in the theory of inequality" based on this source. Is the source sufficient for the claim? Is it a reasonable statement? Please offer opinions at the article. Johnuniq (talk) 00:57, 20 August 2016 (UTC)

MoS indentation

Hi, I started a conversation regarding proper indentation of LaTeX formulas at Wikipedia talk:Manual of Style/Mathematics#Indentation which could use more voices to reach a consensus. Opencooper (talk) 12:29, 20 August 2016 (UTC)

Cyclic function up for deletion

The article Cyclic function has been proposed for deletion.  --Lambiam 22:25, 20 August 2016 (UTC)

Zermelo's navigation problem

Editor did 1/2 the math equations correctly, the rest show up garbled in the text. I haven't a clue what's going on. The creating editor is rarely on Wikipedia. Could somebody figure it out. Bgwhite (talk) 05:40, 20 August 2016 (UTC)

Now equations are not garbled. Boris Tsirelson (talk) 08:06, 20 August 2016 (UTC)

Thank you Boris Tsirelson. Boy, the page looks completely different with the equations displayed properly. Bgwhite (talk) 06:40, 22 August 2016 (UTC)

Dixon's elliptic functions

I have created a new article titled Dixon's elliptic functions.

The phrase "have regular hexagons as repeating units" may not be the most felicitous, but it's what I've got so far.

It is an amusing and slightly edifying exercise that takes a few seconds to show that "having hexagons as repeating units" in no way conflicts with the fact that the fundamental domains that repeat can be taken to be parallelograms. Michael Hardy (talk) 18:53, 23 August 2016 (UTC)

Mathematical model of flow processes

A new article titled Mathematical model of flow processes is incredibly messy. Whoever feels like cleaning up a mess should consider this one. Michael Hardy (talk) 13:01, 25 August 2016 (UTC)

I suspect we already have these documented at e.g. fluid dynamics and possible subsidiary articles. Should probably redirect there. --Izno (talk) 13:13, 25 August 2016 (UTC)

Infobox for operators

I was thinking it would be good to have infoboxes for operators such as the addition, division, dot product, cross product, &c. These infoboxes would have information on commutativity, associativity, &c. What do you think?

Sorry if this is the wrong place for this question. George Makepeace (talk) 14:17, 10 August 2016 (UTC)

I think you might mean operations, not operators. Gandalf61 (talk) 15:41, 10 August 2016 (UTC)

They do, but it isn't the most unambiguous language: operations are frequently called operators, especially in the context of programming. Terminology aside, I think an infobox is a pretty good idea — could contain properties of the operation itself (commutativity, associativity, arity, as well as some details on the normal representation/text encoding (unicode, ascii (and alternatives if applicable like ^ for exponentiation)). —  crh ₂₃  (Talk) 18:30, 10 August 2016 (UTC)

I think it's a great idea. Once you get the basic structure done, though, post a link here and give it 2–4 weeks for people to comment/improve before adding it to articles, since it will be used mostly on high-importance heavy-traffic pages. SamuelRiv (talk) 13:31, 25 August 2016 (UTC)

Math symbol code

Hi. I wonder how come the Greek alphabet letters are not independently coded like the regular coding of Anglo-Latino alphabet? Why write <math>\alpha</math> and not <math>α</math>? These letters are used so much.

And the same with symbols like ∅ instead of {\empty,\emptyset,\varnothing}, ℕ instead of \N and so on.

In any way there is no consistency in many codings, like \N is $\mathbb {N}$ but \A isn't $\mathbb {A}$ but rather undefined.

Can someone change all this? יהודה שמחה ולדמן (talk) 15:05, 17 August 2016 (UTC)

As long as we use (a version of) TeX, this is not immediately possible. Probably, a preprocessor could help. Anyway, programmers of Wikimedia are needed for such job. Boris Tsirelson (talk) 16:06, 17 August 2016 (UTC)

But could\will this be changed? Why wasn't the Greek alphabet coded like this in the first place?

I think every single symbol should be coded. That way we will not need long code words, <math>≤</math> instead of <math>\ge</math> . The clumsiness will me moved to the software, which is anyway clumsy.

Why do we refer to these symbols just as 'characters' but not letters? יהודה שמחה ולדמן (talk) 16:48, 17 August 2016 (UTC)

Why? Because TeX was written at a time long before Unicode was invented, when we still used more limited character sets. (I would say ASCII, but I seem to remember that SAIL used its own idiosyncratic character set.) —David Eppstein (talk) 17:35, 17 August 2016 (UTC)

In the English alphabet there are 26 letters, in upper- and lower-case versions. We use many other symbols, such as digits and punctuation, that are not letters. We use the term "character" to encompass all of these symbols, including the letters. Is that what you were asking? Mgnbar (talk) 18:18, 17 August 2016 (UTC)

I was asking what is the real differene between the letter <math>a</math> to the greek letter <math>α</math> , and from here I'm asking about <math>≤</math> .

Did the computers decide which to accept? No. The people inventing computers did - by what we call 'programming'. The people. Is it that hard to get? יהודה שמחה ולדמן (talk) 18:28, 17 August 2016 (UTC)

Yes, and the people (mathematicians, computer scientists, physicists) settled on TeX as the lingua franca for mathematical typesetting 30 years ago. In academic publishing, it remains the dominant way to write math to this day. Wikipedia allows for alternative encodings, but TeX is not going away any time soon. On WP, there have been many discussions of HTML vs Unicode vs TeX, and there is never a consensus to adopt any one system to the exclusion of others. I prefer everything to be in TeX, but that will never happen and I respect the consensus. If you want to learn more about the consensus and recommended style, check out MOS:MATH#Typesetting of mathematical formulae. --Mark viking (talk) 19:09, 17 August 2016 (UTC)

To reply to your original question, the TeX math alpha is considered to be an italicized version of a Greek alpha. With respect to a Unicode representation, is it better to italicize a unicode "greek small letter alpha", or use the direct unicode "mathematical italic small alpha"? See Alpha#Computer_encodings for what I am referring to. --Mark viking (talk) 19:28, 17 August 2016 (UTC)

Template:Math is usually recommended for individual symbols, variables, and short equations/expressions, instead of <math/>. I even recommend using it to enclose all numbers and operators for things like 1+2=3α, which is {{math|1+2{{=}}3''α''}}. The central advantage goes to your primary objection: the template is coded by us for us, so we can make changes and adjustments as needed, since the needs of Wikipedia and web formatting are rather different from what TeX was designed for.

TeX of course can be modified and expanded as is done all the time (WP's <math/> is based on LaTeX). There are already projects for unicode and web, e.g. XeTex and MathJax, but they haven't been combined yet. SamuelRiv (talk) 14:51, 25 August 2016 (UTC)

Just look...

...what is happening to the article "Measure (mathematics)" (note its recent history). Boris Tsirelson (talk) 10:37, 25 August 2016 (UTC)

Maybe you could just tell us what's happening. Someone is vandalizing/spamming the citations? Mgnbar (talk) 10:54, 25 August 2016 (UTC)

Well, 49.147.175.127 insists that "Radon measures have an alternative definition in terms of linear functionals on the locally convex space of continuous functions with compact support. This approach is taken by Bourbaki (2004) and a number of other sources." and tries to exterminate the other (topology-free) approach (and replace references accordingly). Boris Tsirelson (talk) 13:20, 25 August 2016 (UTC)

I haven't followed this particular discussion, but of course everybody knows that some people erroneously think that Bourbaki is God. Michael Hardy (talk) 04:05, 27 August 2016 (UTC)

In fact, I like Bourbaki (at least, in some aspects); and indeed, Radon measures are beautiful. But I have two objections. First, measure theory is invariant under (invertible) measurable transformations (which was also emphasized in clumsy words by the anon: "Let composition of measurable functions is measurable, making the measurable spaces and measurable functions a category."); but topology is invariant under homeomorphisms, – much less. Second, an infinite-dimensional Gaussian measure (maybe the most useful probability measure) is not a Radon measure (since in infinite dimension every continuous function with compact support is identically zero). Boris Tsirelson (talk) 05:07, 27 August 2016 (UTC)

Deletion discussion for Alexander Kuznetsov

Alexander Kuznetsov (mathematician) has been nominated for deletion. Please participate in the discussion at Wikipedia:Articles for deletion/Alexander Kuznetsov (mathematician). —David Eppstein (talk) 18:55, 28 August 2016 (UTC)

Template:Statistics

Someone is going around adding {{statistics}} to a bunch of articles in mathematics and statistics. The template is very large: when subst'ed, it takes up about 14kb, and is being added to articles with only a passing significance in statistics, like Lp space. Two questions: (1) is it really helpful to the reader to have the entire outline of statistics in a navigation template, even on somewhat peripheral articles? (2) Do navigation boxes this large and complex really have any legitimate use in article space, outside of (say) portals, outlines, lists, and similar kinds of organizational media? Sławomir
Biały 14:40, 23 August 2016 (UTC)

I'm not a big fan of these navigational boxes and this is a good example of why. I think there ought to be some criteria for when and where they should be used. Restricting them to certain types of articles makes sense to me. --Bill Cherowitzo (talk) 17:14, 23 August 2016 (UTC)

Rather than immediately stripping navboxes from pages, I posted a suggestion to break up the Statistics template at their talk page. SamuelRiv (talk) 16:37, 25 August 2016 (UTC)

Count me as a vote that the answer to Sławomir's question 2 is "no." At the very least, the template should be collapsed by default. --JBL (talk) 16:53, 25 August 2016 (UTC)

User:Slawekb raised several issues.

1. The template is being added to ["a bunch of"?] "articles with only a passing relevance to statistics", for example, "Lp space".

First, regarding "articles" (plural). Please name another example of a mathematical article with "only a passing relevance to statistics" to which the box was added? I know of none.

The article Lp space explains the relevance to statistics:

Statistics

In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of L^p metrics, and measures of central tendency can be characterized as solutions to variational problems.

Indeed, when I added the statistics template to Lp space, my edit summary explained the relevance: "A standard hypothesis in mathematical statistics posits that a random variable be in an Lp space)". (Obviously the linear-space properties are crucial to averaging.) Nobody has removed the template from Lp space, the 2nd step in the BRD sequence.

2. The template is big.

A discussion of re-engineering the template at the statistics project would be reasonable. A notice on the talk page of the template alerted almost nobody.

Inserting the "state=collapsed" argument makes the template appear in one-line.

162.250.169.162 (talk) 11:47, 28 August 2016 (UTC)

I'm astonished that you would think that just because an article mentions statistics means that it should carry a complete navigation box for all things statitical. What conceivable purpose does this serve? Whether it is one line or not, it does add considerably to the page-load time. This is also particularly a concern for dialup or mobile users. Sławomir Biały (talk) 12:40, 28 August 2016 (UTC)

Astonishment at things I did not write and do not thing is your prerogative. :) I shall delete the template, following the BRD sequence.

Would you please state the (plural) mathematical-articles unrelated to statistics to which I, as you wrote before, added the template or please withdraw that statement 162.250.169.162 (talk) 13:59, 28 August 2016 (UTC)

Latin square and Fourier analysis are two obvious ones. It's unclear to me that this template is really appropriate even in many statistics articles, like covariance, since these are not top-level articles. Arguably, detailed navigation templates like this only belong on top-level articles like statistics (if anywhere). Sławomir
Biały 15:26, 28 August 2016 (UTC)

Thanks for replying. You must have used "someone" for several persons. :)

Please remove infoboxes where they don't belong (and add them where they help). Latin square could use an experimental or combinatorial design infobox, if one exists. Latin squares do not appear on the statistics infobox.

162.250.169.162 (talk) 16:00, 28 August 2016 (UTC)

@Slawekb: To say that Latin squares are unrelated to statistics is to be ignorant of statistics. Latin squares are used in the design of experiments. And in fact, that is stated in the first sentence of the article. Fourier analysis is of course used in statistics because Fourier analysis is used in just about everything. Michael Hardy (talk) 19:52, 28 August 2016 (UTC)

Pardon me, but this is just an irrelevant straw-man argument. I did not say that Latin squares have nothing to do with statistics. I did, however, question whether they are a sufficiently top-level statistical article to warrant having a huge template that contains an outline of all statistics placed on it. Addition is also used in statistics. Are we to put {{statistics}} on the article addition? Fourier analysis is used everywhere, so does every mathematics navigation template we can imagine belong on the article Fourier analysis. I'd be interested in how you weigh in on these relevant questions, rather than irrelevant ones of your own invention. 21:13, 28 August 2016 (UTC)

It wasn't an argument at all, and I wasn't suggesting that those infoboxes should be there. I was just saying that it's not true that Latin squares are unrelated to statistics. You had said they were obviously unrelated. Michael Hardy (talk) 05:18, 29 August 2016 (UTC)

I did not say this, although I see that you could have come to that conclusion. Do you have anything relevant to say, or is this going to degenerate into a discussion of who said what? Sławomir Biały (talk) 10:16, 29 August 2016 (UTC)

One-line template: "State=collapsed"

Indeed, as the documentation explains, the template is easily collapsed to one line

as is the probability distributions infobox

which is more relevant for this project. 162.250.169.162 (talk) 11:47, 28 August 2016 (UTC) 11:54, 28 August 2016 (UTC)

Collapsing does not reduce the size of the file which is downloaded when reading the article. Thus the objection about the size of the template remains valid. D.Lazard (talk) 13:01, 28 August 2016 (UTC)

The size is a valid concern, while at least another stated concern was shown to be invalid.

Are you proposing a maximum-size guideline for infoboxes (for the mathematics project)? If so, the large probability-distribution infobox should be discussed along with the statistics infobox? 162.250.169.162 (talk) 13:59, 28 August 2016 (UTC)

I removed the statistics toolbox from Lp spaces, following BDR.162.250.169.162 (talk) 14:06, 28 August 2016 (UTC)

Negative-dimensional space

I tripped over negative-dimensional space and ideas like reduced homology and K-theory sprang to mind, when I realized that the entire article seems to be some sort of non-mathematical, pop-sci original-research effort to grapple with the contents of one specific paper on arxiv. (The other citation in the article is to an art project mounted by a mathematician, who does mention reduced homology.) The whole thing is dazed and confused, as a result. Should this WP article be expanded into some sort of pop-sci exploration of "negative dimension", like some fun blog post somewhere? Is a pop-sci review really encyclopedic? Turning it into a review of a single arxiv article seems wrong; its not really notable. I don't see how to rescue this article. Perhaps someone can prod for deletion? Or something? 67.198.37.16 (talk) 21:22, 28 August 2016 (UTC)

(p.s. I've recently started stumbling over articles of this kind: they're always pop-sci attempts, blog-like in structure and approach, written primarily by a single non-expert author, containing confusing, inaccurate, misleading information, or maybe containing no workable information at all. Not just in math. I find them kind-of irritating, but am not sure what to do, if anything at all. Is there some general policy about this? I'm not mean-spirited enough to just start proding and afd'ing things...) 67.198.37.16 (talk) 21:22, 28 August 2016 (UTC)

Just as an aside, the only useful and mathematically valid concept involving negative dimensions that I'm familiar with is that (particularly in the context of the face lattices of polyhedra) it is convenient to define the dimension of the empty set to be −1. But that's not enough to form the basis of an article, and probably too far removed from the topics the one you point to is wrestling with. —David Eppstein (talk) 21:43, 28 August 2016 (UTC)

I think the article seems pretty fishy. I'll add to Eppstein's observation that sometimes negative dimensional tensors are considered in connection with the theory of spin networks. Roger Penrose wrote a paper about them in 1971. It's not clear to me in what sense they describe spaces. Sławomir Biały (talk) 21:53, 28 August 2016 (UTC)

Negative dimensional spaces have been around for a while and have been considered using different approaches. Mandelbrot considered spaces of negative dimension 26 years ago in the context of multifractals, e.g, Negative fractal dimensions and multifractals. May's book on algebraic topology discusses K-theory and negative spectra, A Concise Course in Algebraic Topology, apge 231, which seems the approach used in this article. Cvitanovic and Kennedy considered spinors in negative dimensions, Spinors in Negative Dimensions. Spin glasses and random fields also have a notion of negative dimension, e.g., Parisi's 1979 Random Magnetic Fields, Supersymmetry, and Negative Dimensions. A little research shows no pop science required. --Mark viking (talk) 23:51, 28 August 2016 (UTC)

Yes, except that all of those concepts of negative dimension are more or less completely unrelated to one-another. Its a fair bit of original synthesis to put all of those things into a single article. Now, maybe its excusable in a "list of negative-dimensional concepts", or some kind of disambiguation page. But simply rattling off all the places where one has ever thought of negative dimension is .. well, its still original research. Its still pop-sci. No one is actively crossing over from one field into another based on the fact that the word "negative dimension" got used in the papers. 67.198.37.16 (talk) 21:08, 29 August 2016 (UTC)

I refuted your assertion that the K-theory approach to negative dimensions is only based on a single arxiv paper; May's discussion is a tertiary RS that suggests this may be a more widely discussed and possibly notable approach. I also showed that the concept of negative dimensions have been considered by different people over decades; the concept seems broader than just a K-theory extension. But I never claimed these should be put all into the same article; that is your synthesis, not mine. If there are reviews out there comparing and contrasting the various approaches to negative dimensions, we can write a general article comparing and contrasting the the various approaches. Otherwise, it would be better to write articles on the individual approaches according the the availability of reliable sources. We describe, not prescribe. --Mark viking (talk) 02:31, 30 August 2016 (UTC)

I think you misunderstood my comments. I was about to *add* K-theory to that article, when I realized that doing so would be "original synthesis". So I pulled back and posted here. That article, as currently written, *is* based on a single arxiv paper that has nothing at all to do with K-theory. So, rather than refuting, you seem to be "violently agreeing" with me ... as far as I can tell, there are *zero* "reviews out there comparing and contrasting the various approaches to negative dimensions", which is why I suggested prodding that article. 67.198.37.16 (talk) 23:26, 30 August 2016 (UTC)

Font Size Of All Math Formulas

All the mathematical formulas in the "Rodrigues Rotation Formula" article appear in very small type; I'm guessing 8 point type on my computer. The text appears normal as 10 or 12 point type. This is only a problem for some of the math articles in Wikipedia. This should be an easy fix.

68.100.252.138 (talk) 15:45, 30 August 2016 (UTC)Maurice Daniel68.100.252.138 (talk) 15:45, 30 August 2016 (UTC)

That article looks normal to me. Are you viewing it in an ordinary browser, or on a mobile device? Is it only the inline mathematics formulas that look small, or the ones that display on their own lines? Sławomir Biały (talk) 16:34, 30 August 2016 (UTC)

That article has normal size math symbols for me, too (Latest Chrome on a modern Mac). I don't see any unusual math markup. --Mark viking (talk) 18:58, 30 August 2016 (UTC)

The article consistently uses the math template for inline math and Tex for displayed math. It is the combination that has produced the best average visual result, and looks fine for me too."Should be an easy fix..." is undue optimism. It will surely take another fifteen years to get right, and it is not the articles themselves (the source text) that constitute the problem. YohanN7 (talk) 14:24, 31 August 2016 (UTC)

Yes, the fact that the article uses two different styles of math formatting makes me question whether "All the mathematical formulas..." can possibly look uniformly wrong. If one set, those using {{math}} or those using <math>, was wrong, then we might be able to propose a fix. I have noticed that, on the mobile interface, <math> tends to render the equations much smaller than the surrounding text. (This is the reverse of how things used to look with PNG rendering on the desktop site.) Sławomir Biały (talk) 15:42, 31 August 2016 (UTC)