# Wikipedia talk:WikiProject Mathematics

 This is a discussion page for WikiProject Mathematics This page is devoted to discussions of issues relating to mathematics articles on Wikipedia. Related discussion pages include: Please add new topics at the bottom of the page and sign your posts.

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## Should display equations be centered?

Screenshot of the displaystyle proposal.

The update to the MathJax code means MathJax display equations are now centered as opposed to Texvc equation and previous versions which were left-aligned. Should display equations be left-aligned, centered or configurable using the displaystyle feature?--Salix alba (talk): 14:24, 11 February 2014 (UTC)

### Survey

When I looked at some off wiki sources I was surprised to find that in many the display equations are centered, These include blogs[1], arXiv [2] and LaTeX documents. So it not so much a technical problem, fixing the formatting looks like a simple change to the MathJax config, more a style issue. Do people have views on how thing should be displayed: left, centered or configurable using the displaystyle feature mentioned above?--Salix alba (talk): 21:00, 9 February 2014 (UTC)

• Left (with an indent, please). Centered-anything looks so weird in A.D. 2013. No such user (talk) 22:32, 9 February 2014 (UTC)
• centred. I had not thought of this before, but switched to MathJax temporarily so I could ignore the align problem until it was fixed, and noticed formulae were centred and liked it. More than that it looked so incredibly natural and like most mathematical sources. Even the spacing seems better: sometimes with left-justified formulae the white space above and below formulae looks excessive when there are many of them. So I'd like it to be available. I can understand it not being a default as any change like that can be seen as disruptive, to people who prefer it as it is, and in a small number of articles where formatting/layout is worse with it on. But as an option, so voluntary, it would be a great addition. Problems then could be fixed so they look fine in both cases, left and centre justified.--JohnBlackburnewordsdeeds 23:14, 9 February 2014 (UTC)
To boil it down: Currently good old pure [itex] behaves differently from [itex] displayed using MathJax. No good, behaviour should be identical.
If there is a need for new features, it would be wise to implement any changes in a way that the old behaviour won't be broken. I'm not telling anybody anything new. :-) --Pyrometer (talk) 16:21, 10 February 2014 (UTC)
• Left, with indent. Centered looks fine in mathematical Journals with their often rather limited column width, but on Wikipedia pages which can be displayed in all kinds of widths it's likely to break the text flow. In many cases there are rather short phrases of text between displayed formulae, and the need to jump between the left-aligned text bits and the centered formulae doesn't help readability. I'm fine with an option (preference, gadget or script) to change the default behavior to centered on a per-user basis. — HHHIPPO 19:44, 10 February 2014 (UTC)
• Worth pointing out that the way pages are laid out is going to change, and one change being proposed (currently in the beta - one of the things available from the 'Beta' link at the top of each page) is to make body text fixed width. This may be one reason why I support the centred option; I've had the the typography refresh beta enabled for a couple of weeks, so the formulae were centred in 715px wide text.--JohnBlackburnewordsdeeds 11:45, 11 February 2014 (UTC)
+1. Helder 16:53, 11 February 2014 (UTC)
Hmm, that's complicating things. Both that participants in this discussion are using different interfaces, and that the standard user interface will change at some point (is there a roadmap?). My suggestion would still be to go back to left-aligned for now, for continuity. Once the typography refresh is rolled out, shouted at, fine tuned and stable, we should re-visit this question, then with all participants and also the typical readers being used to the same new boundary conditions. — HHHIPPO 21:40, 11 February 2014 (UTC)
Template:Ping maybe the change in the alignment of math formulas should also be added as part of the typography refresh? Helder 15:53, 13 February 2014 (UTC)
Helder Thanks for looping us into the conversation, my gut tells me centered looks better purely from a layout point of view, but I think this is more about comprehension, I don't know if alignment in this case helps comprehension, e.g. if formulas are on two consecutive lines, and are of different lengths, does the fact that elements from the first may more closely align with those in the second when left aligned vs centered have an effect on understandability? if so, left aligned might be more ideal. Jared Zimmerman (talk) 18:21, 13 February 2014 (UTC)
Jared Zimmerman, I think in the cases where alignment of formulas is desired, one should use a single [itex] tag and use the align environments in LaTeX. See Help:Displaying a formula#Fractions, matrices, multilines and b:LaTeX/Advanced Mathematics#Text in aligned math display ("Multiline equations") for a few examples. Helder 19:02, 13 February 2014 (UTC)
• Consistently for PNG and MathJax. Default Left, personal option for Centered. - DVdm (talk) 21:20, 10 February 2014 (UTC)
• Make it configurable either on a per-wiki basis or even per equation basis. I could see cases that in some articles with a sequence of equations on multiple lines left aligning can make things line up better. The displaystyle option could be used for this. The CSS rule .MathJax_Display { text-align : left !important; } can be used to override the default.--Salix alba (talk): 10:07, 11 February 2014 (UTC)
• Left This is a bug not a feature. We can still center an equation with <center>. -- Taku (talk) 14:37, 11 February 2014 (UTC)
<center> is deprecated. Use CSS instead. Helder 16:53, 11 February 2014 (UTC)
It should be possible to use class="center" - that works on most (all?) block-level elements on Wikipedia. --Redrose64 (talk) 19:17, 11 February 2014 (UTC)
You can use {{center}} which works for maths equations.--Salix alba (talk): 19:59, 11 February 2014 (UTC)
• Center, as is the usual style in mathematical publications, and no more user preferences, please (those who want to change the default can use their personal CSS). Helder 16:53, 11 February 2014 (UTC)
• Indented Left. There is no usual style in mathematical publications that I am familiar with; about 50-50 on centered vs. indented left. With equation numbering, centered looks better, with short textual interludes between equations, indented left looks better. Since we have lots of the latter and little of the former, the choice is clear for me. Bill Cherowitzo (talk) 18:53, 11 February 2014 (UTC)
• Left. In a perfect world, all equations will look the same to all users. Aside from obvious technical reasons why that is not the case, including the different (and across the board better) rendering of mathematics in MathJax compared with PNG, I don't think changes that cause MathJax to depart further from the style that PNG presents are a good idea at the moment. I'm willing to be convinced otherwise, provided centering equations with MathJax enabled doesn't unintentionally break anything and makes equations always look at least as good as the left-justified manually indented versions. But consensus doesn't seem to be going in that direction. Sławomir Biały (talk) 19:06, 11 February 2014 (UTC)
• Indented Left In books (or journals, or similar), I much prefer centered equation, but on Wikipedia, this doesn't make sense to me. I have a large screen (as I'm sure, many others have), and left-aligned equations just work infinitely better. 13:42, 12 February 2014 (UTC)
• Left, but a comment on indentation: By the principle of WYSIWYM inherent to wiki markup, an equation should follow the same formatting defaults as regular text until otherwise specified. Of course, in practice one must consider that any extra step (like inserting the colon before each equation every time) an editor must take is another place for an error to occur, and indentation is by far the norm. SamuelRiv (talk) 14:07, 12 February 2014 (UTC)
• Indented left goes best with layout style of the encyclopedia. ~KvnG 17:45, 18 February 2014 (UTC)
• Indented left. Apart from its other merits, it might well go best with layout style, and aesthetically I do prefer it, but that cuts very little ice because aesthetics are subject to fashion and whim. In the case of short, isolated kids' stuff like e=mcc, the presentation should hardly matter, except for consistency, although possibly because of my computer background I am prejudiced in favour of indented left anyway.
However, this SHOULD not be a matter of aesthetics and preference, but of considerations of clarity, functionality and lack of distraction. So for example, when theorems and expressions are listed in context with each other, or when a single long expression won't fit onto a single line, or when it is better broken up into segments to show internal relationships or logical patterns, then nothing else works as well in general as indented left, sometimes multiple levels of indentation at that.
Even more strongly, getting beyond primary school level, when one lists derivations and proofs, particularly with interspersed corollaries, comments and lemmata then there simply is no contest; the use of indentation becomes as functionally important as the use of parentheses. Polish notation and centering have their uses, but they are not much good at exploiting real estate for conveying structured logic. JonRichfield (talk) 14:21, 20 February 2014 (UTC)

• A conceptual question. Can we do a poll how it should look like. It would be great to have a page that I can link to for the code review and say "look this change implements the rendering in the way it was requested from the community." My propsal (which is already implemented looks like that
Screenshot of the displaystyle proposal.
You can view it live at http://math-test2.instance-proxy.wmflabs.org/wiki/Displaystyle (probably you don't want to log in).--Physikerwelt (talk) 09:45, 11 February 2014 (UTC)
• Yes we could. We could make this an WP:RFC ideally it should be publicised widely as it effect other language projects.--Salix alba (talk): 10:07, 11 February 2014 (UTC)
• Great! @User:Salix alba can you make a WP:RFC or a draft for that? @User:pkra can you spread it?--Physikerwelt (talk) 13:51, 11 February 2014 (UTC)
• For the record, the changed behavior has little to do with MathJax being updated. It's a heuristic written specifically for MediaWiki's math extension. Pkra (talk) 22:35, 11 February 2014 (UTC)
• Mathematical typography has been worked on for a very long time, not least by such luminaries as Donald Knuth, and there is a very mature body of expertise on how to optimise the appearance of mathematics on the printed page. There is a smaller but growing body of research into layout for tablets and mobiles. I do hope that WMF and its large and well-funded staff will investigate and make use of this body of knowledge rather than redesigning on the basis of "gut instinct" and an unscientific poll. Deltahedron (talk) 19:51, 13 February 2014 (UTC)
@Deltahedron: It sees as I'm the only person working on the Math extension in my free time. I'm a PhD student with a lot of other tasks. I'd be really interested in that research field. Maybe you can point me to publications, or people. In an optimal case we could find someone of that crowd who could also help on the Math extension. i.e. people testing and code review are really needed.
Try this page for an introduction to Knuth's papers on digital typography. His paper in the AMS Bulletin (1979) is quite inspirational. Handbook of Typography for the Mathematical Sciences by Steven Krantz also contains references to earlier works. As far as reading text on tablets, mobile devices and so on is concerned, I am not aware of the status current research but there is a huge literature on human-computer interaction. I don't want to disparage your efforts in any way but surely the WMF can afford more support one part-time student? Deltahedron (talk) 17:34, 14 February 2014 (UTC)
• Currently the automated tests for Math are broken, but a fix for that is announced for next week. So if I did a larger change there is a risk of breaking something. The change that broke the align command for example was reviewed by at least two people ... and nobody realized the error. As a workaround I could add an invisible whitespace in MathJax mode. Would that be a solution for now?--Physikerwelt (talk) 13:55, 14 February 2014 (UTC)
I think that would be fine for now. Ozob (talk) 15:26, 14 February 2014 (UTC)
• Now that we are on it, can we switch the mathcal font from default one in tex to one used by topologies such as Lurie? see, for example, the notation for the line bundle, L in [3]. It is fairly standard today. If the switch is not desirable (conflict with some other area in math, say), then can we at least provide a topologist mathcal font as an option? -- Taku (talk) 13:49, 15 February 2014 (UTC)

## Euler's identity?

I think this is a prime example of a mathematics page which needs to communicate with a general readership [4]. I have posted some strictly editorial concerns on the talk page which I think deserve some response. Thank you in advance, 109.157.83.88 (talk) 11:46, 13 February 2014 (UTC) [previously 109.158.185.136 and 81.147.165.192]

• I have tried to address (in this edit) some of the issues I've encountered as a layperson coming to this page. The more general disambiguation problem in the page header (and at List of things named after Leonhard Euler) imo remains. While fully recognizing that we're all volunteers and that nobody is obliged to make any particular contribution I find it hard not to express some disappointment that my appeals for feedback appear not to have elicited any response (so far) either here or on the article talk page. 86.173.146.3 (talk) 14:14, 18 February 2014 (UTC)
Probably you have gotten no response (until today) for the following reasons:
(1) The number of people confused by the issue troubling you is well approximated by 0.
(2) The source of your confusion is your not very good source, which draws distinctions that mathematicians do not (either in the formal or informal setting).
You can see my more detailed comments on the talk page of the article in question. --JBL (talk) 20:10, 18 February 2014 (UTC)
(1) Your forcefully worded statement "The number of people confused by the issue troubling you is well approximated by 0" implies that the present Wikipedia editor does not belong to the set of people? (I do request you to be civil to your fellow gf Wikipedian.)
(2) I will certainly reply on the article talk page. As a general principle I think it is courteous in such circumstances to source your assertions. (My understanding is that Wikipedia does not contemplate argument from authority.)
86.173.146.3 (talk) 21:25, 18 February 2014 (UTC)

## List of mathematical symbols as TeX codes

There is a new article called List of mathematical symbols as TeX codes. I haev commented at Talk:List of mathematical symbols as TeX codes and put a factual-accuracy-dispute tag at the top of the article. So some work is needed. Michael Hardy (talk) 17:33, 14 February 2014 (UTC)

Why not include TeX commands (and for that matter HTML codes and Unicode code points) as separate columns in List of mathematical symbols (as I did in de:Liste mathematischer Symbole)? Best wishes, --Quartl (talk) 18:13, 14 February 2014 (UTC)
My thoughts as well. There seems to be no clear reason for having what is just a copy paste of List of mathematical symbols with nowiki tags thrown in. Sławomir Biały (talk) 18:57, 14 February 2014 (UTC)
I have nominated the page for speedy deletion as an A10, "recently created article that duplicates an existing topic". Ozob (talk) 20:35, 16 February 2014 (UTC)

## Conflict in Rotation group

Short history:

1. Template:Diff; ensuing discussion led to a stalemate.
2. JohnBlackburne initiated a requested move where sophisticatedly hid the question of WP:PRIMARYTOPIC of the term “rotation group” in a nominal topic, what to do with a dab page.
3. Two persons threw their “Support per nom” votes without any supplementary arguments about the particular primary topic problem.
4. JohnBlackburne used these two votes to press for redirecting Template:Pagelinks to orthogonal group, a confusing solution as a good mathematician should realize.

Template:Serif hope local frequenters will demonstrate a more thoughtful approach than the WP:RM people and so. Incnis Mrsi (talk) 11:12, 15 February 2014 (UTC)

You are disputing the outcome of the move: Talk:Rotation group (disambiguation)#Requested move. But the outcome is clear. I proposed a move, with reasons and referring to previous discussions which prompted the move, so there had already been plenty of argument. It's understandable in such cases when editors don't feel they need to restate the arguments. Of the responses two supported my reasoning, so there is consensus for the move as described in the request.
You only disagree what the primary topic for rotation group should be. In addition to the reasons given in the RM I can give two more if it helps. First the orthogonal group is known as the rotation group. See the first line of that article – I added that with a source after looking for a suitable target, before proposing the RM. The other reason is rotation group used to refer to an orthogonal group, Rotation group SO(3). That was moved from rotation group two years ago. So for much of its existence "rotation group" referred to an orthogonal group, just a particular one not a general one. — Preceding unsigned comment added by JohnBlackburne (talkcontribs) 12:45, 15 February 2014‎
This conflict is based on a big mathematical error. Please, correct it ASAP: It is said at several places (at least at the first lines of orthogonal group and of rotation group (disambiguation)) that rotations and orthogonal transformations are same thing. This would imply that the symmetry with respect to a line in the Euclidean plane would be a rotation! The correct wording is that the orthogonal group is the group of the isometries of a Euclidean vector space (that is a real vector space equipped with a positive definite quadratic form, such as the dot product). In dimension 2 and 3, the rotation group is SO(2) and SO(3) (in higher dimension, I do not remember if the rotation group is SO(n) or if the rotations have a more restrictive definition). D.Lazard (talk) 13:25, 15 February 2014 (UTC)
I don't see the errors you refer to. It says in orthogonal group and in the disambiguation page that orthogonal group and rotation group (usually) refer to the same thing, which is the reason for the move, supported by the arguments in the RM and above. rotation group, not rotations, which are something different and much less formally defined. But if you think it could be improved go ahead, or describe what changes should be made here.--JohnBlackburnewordsdeeds 14:15, 15 February 2014 (UTC)
It is wrong that "orthogonal group and rotation group (usually) refer to the same thing". "Rotation group" is the same thing as "special orthogonal group". D.Lazard (talk) 14:30, 15 February 2014 (UTC)
I see what you mean. The problem is that's the same article: special orthogonal group redirects to orthogonal group. I would say it's less clear cut which is the rotation group – the special orthogonal group is the group of all proper rotations, so the group of all (proper and improper) rotations is the orthogonal group. But the outcome of the move would be the same: rotation group would redirect to orthogonal group (if it's made to redirect to special orthogonal group a bot will quickly change it back as that's a double redirect). Any subsequent problems should be addressed by editing the article and disambiguation page.--JohnBlackburnewordsdeeds 15:00, 15 February 2014 (UTC)
Will creation of the special orthogonal group article be an acceptable compromise? Template:Serif am willing to settle on it, but John’s abomination in the present form can’t be tolerated. Incnis Mrsi (talk) 14:55, 15 February 2014 (UTC)
They were merged a long time ago. I don't think so old an article is a useful guide but it's hard to see how a separate article will help. There's almost no content in orthogonal group unique to the special orthogonal group, so you end up either with a stub with almost nothing in that's a disservice to readers, or largely duplicating orthogonal group with all the problems that involves of extra maintenance, articles getting out of sync.--JohnBlackburnewordsdeeds 15:10, 15 February 2014 (UTC)
 Pin → O ⊂ U Spin → SO ⊂ SU
You are not right: there are some correspondences (see the table) that could be spelled separately for G- and S-cases; note that [each other two columns have // my grammar mistake: should read “each of two other columns has” Incnis Mrsi (talk) 17:34, 15 February 2014 (UTC)] a pair of separate articles. Also, the orthogonal group virtually excludes the indefinite orthogonal group case, whereas the Template:Pagelinks should not do it and may consider all determinant-1 matrices/operators that are orthogonal with respect to certain quadratic form, including SO(3;1), as well as relevant subgroups such as SO(3;1)+. Incnis Mrsi (talk) 15:32, 15 February 2014 (UTC)
It should be obvious that SO(3) is the rotation group and that nobody thinks of O(77) as a group of rotations and that SO(n) is rotations in n dimensions. It is also obvious that SO(3) (whatever you call it) deserves an article of its own. YohanN7 (talk) 15:44, 15 February 2014 (UTC)
And it has one: Rotation group SO(3). As can be seen from that, and Rotations in 4-dimensional Euclidean space the interesting properties of SO(n) are most apparent from considering them for particular values of n. Circle group completes the set of low-index special orthogonal groups. The names could be more consistent but there's not an obvious right thing to call them.--JohnBlackburnewordsdeeds 16:02, 15 February 2014 (UTC)
No big problem then, good. (I didn't read the above too carefully apparently.) I wouldn't oppose a split of Orthogonal group into O(n) and SO(n) (or whatever we choose to call them). I believe that there is enough "substance" in the two to make up two separate articles, at least in the long term. YohanN7 (talk) 16:58, 15 February 2014 (UTC)

Template:Ping stop to push your “SO(2), SO(3) and SO(4)” crap into the lead section of the orthogonal group: it reintroduced a confusion between real numbers and an arbitrary field that Template:Serif once worked hard to eradicate. Re-join the discussion and express your opinion: would a new article be a solution, or ? Incnis Mrsi (talk) 16:52, 15 February 2014 (UTC)

Template:Ping Undoubtfully, the primary meaning of orthogonal group refers to the reals. I have carefully rewrote the lead of orthogonal group for making this clear, by describing the generalizations (to other fields of other quadratic forms) after the main meaning. My so called "crap" has been introduced in a paragraph clearly (maybe not enough clearly) devoted to the real case, and these links, as well as the fact that these case have been widely studied, are important form an encyclopedic point of view. In my opinion, this is the confusion between the primary topic and its generalizations which is confusing. D.Lazard (talk) 17:18, 15 February 2014 (UTC)
@Incnis: This kind of pettifogging is unconstructive. Wikipedia articles often proceed from the specific, but common, to the general but uncommon. Even most professional mathematicians would consider the orthogonal group to be over the real numbers. When referring to groups over an arbitrary field, it is always either explicitly said, or is in the context of linear algebraic groups or similar. Sławomir Biały (talk) 17:21, 15 February 2014 (UTC)
Template:Serif consider this as an implicit support for splitting. One hardly can substantiate such heavy emphasis on S groups in the lead section about a non-S group. Incnis Mrsi (talk) 17:34, 15 February 2014 (UTC)
If a split should occur, it should be by restricting Orthogonal group to the real case (related to Euclidean distance), and creating Orthogonal group over a field. Similarly, we have already Indefinite orthogonal group. D.Lazard (talk) 18:52, 15 February 2014 (UTC)
Which problem will be solved? The lead became bloated with the S-related stuff after your late edits, and it will remain bloated regardless of whether “non-standard” fields will be expunged or not. Incnis Mrsi (talk) 20:26, 15 February 2014 (UTC)
I don't have strong opinions about a split one way or another (implicitly or otherwise). I was merely responding to your apparent point that the case of the reals needs to be de-emphasized. Sławomir Biały (talk) 19:45, 15 February 2014 (UTC)
Template:Serif meant primarily that Daniel’s three links through redirects are self-contradicting: the article says there are O groups over any field, but sends the reader to articles about real groups via unspecific O(n) titles. Template:Serif didn’t say the real case has to be specially de-emphasized, but the lead section become bloated and a bit confusing after late D.Lazard’s edits. Incnis Mrsi (talk) 20:26, 15 February 2014 (UTC)
Much of the content in the current lead in Orthogonal group should really be in Classical group. That article could well serve as an umbrella for articles on particular classical groups. See also Talk:Classical group#Not B-class. YohanN7 (talk) 22:02, 15 February 2014 (UTC)
It may be worth noting that the Encyclopaedia of Mathematics article Orthogonal group begins "An orthogonal group is a group of all linear transformations of an n-dimensional vector space V over a field k which preserve a fixed non-singular quadratic form Q on V" while Reflection group begins "A discrete group of transformations generated by reflections in hyperplanes". I personally prefer the more general definition of orthogonal group. Deltahedron (talk) 22:09, 15 February 2014 (UTC)
Will it help to solve the current problem, or it is an independent suggestion? Incnis Mrsi (talk) 20:26, 15 February 2014 (UTC)
It will not help solve the problem with the disambiguation page (if that is what is the current problem), but it can be taken into consideration if Orthogonal group is split. The stuff about bilinear forms need not be repeated in each classical group article, it is common to all of them except for SL(n, C) (and the exceptional ones if you count them as classical). By the way, I don't think we need to have such a broad interpretation of what a rotation is, SO(3) as the rotation group and SO(n) as a generalization would work. "Improper rotations", "rotations in spacetime" and the like serve no purpose really. YohanN7 (talk) 22:02, 15 February 2014 (UTC)
And by extension of my above reasoning, it would be strange to have "rotation group" redirect to "orthogonal group" or for it to have "orthogonal group" as the main dish. YohanN7 (talk) 22:14, 15 February 2014 (UTC)
The exceptional ones are not classical by definition. There is also a broad concept rotation (mathematics) article. Template:Ping please, explain yet a time: which articles should, in your opinion, serve the O(n, F) and SO(n, F) topics? Incnis Mrsi (talk) 12:58, 16 February 2014 (UTC)
Template:Ping I haven't explained even one time which articles should serve the general field topics. I'm thinking about the definition and classification of the classical groups in terms of bilinear (sesquilinear) forms. This should in my opinion go into Classical group in a more thorough way than today. I frankly have too little knowledge about groups over general fields to even have an opinion about where they should be treated. But I do feel that the fields R, C and H should be treated within the same article for each "abstract" group we treat separately. Probably then, the O(n, F), etc, should each have a section in the general O(n), etc, articles. Some people (the real connoisseurs) count the exceptional groups among the classical groups (but I don't). Yes, I have references supporting that statement, but this is not important. YohanN7 (talk) 16:00, 16 February 2014 (UTC)
Quaternions are a division ring, not a field. There is the GLn (although with two incompatible natural representations), but there isn’t neither SLn nor O(n). You must reserve special clauses to define the determinant that isn’t matrix multiplication-invariant at last, you must care about the order of factors everywhere (such as in bilinear forms), and you can’t define orthogonality as a symmetric relation. One would be more successful in generalizing these groups to commutative rings than over structures where the multiplication does not commute. Incnis Mrsi (talk) 16:29, 16 February 2014 (UTC)
Division ring, non-commutative field, whatever. See Wulf Rossmanns Lie Groups - An introduction through linear groups for a thorough treatment of GL(n, H), SL(n, H), (S)U(p, q), Sp(p, q) and (S)O*(2n). These are groups over the quaternions, very successfully generalized to them. YohanN7 (talk) 17:42, 16 February 2014 (UTC)
See a follow-up at talk: Classical group #Matrix groups over non-commutative rings. Incnis Mrsi (talk) 12:20, 18 February 2014 (UTC)
But you are right about symmetric bilinear forms. They don't yield anything interesting (I think they are automatically degenerate, not sure, can check this out later) in the quaternionic case. I was thinking more generally in terms of all classical groups. YohanN7 (talk) 17:52, 16 February 2014 (UTC)

We must not forget that the orthogonal group (over the reals) is not only a concept of pure group theory, but also an important geometrical concept, widely used in mathematics, physics and mechanics. On the other hand, as far as I know, the generalization over other fields is considered only in pure group theory. As the article must be accessible to a much wider audience than only group theorists, this must help to give a due weight to the primary topic (over the reals) and its generalizations. D.Lazard (talk) 23:06, 15 February 2014 (UTC)

The orthogonal group for a general quadratic form over a general field is certainly not "considered only in pure group theory", although it is indeed important there. It is important in, for example, number theory and field theory (see for example the books of O'Meara, or Lam, or Cassels). Deltahedron (talk) 07:24, 16 February 2014 (UTC)

## user Wachipichay

I noticed that the user Wachipichay is making many edits to mathematics pages. It seems the purpose of all edits is to include references to a mathematician called István Mező. As far as I can tell, these are typically very recent minor results that have no place in an encyclopedia. Perhaps someone who reads this can have a look at his edits and clean up as needed. I apologize if this is the wrong forum, I am not active on Wikipedia and have no idea how these things work. 129.16.126.117 (talk) 08:43, 18 February 2014 (UTC)

At least, not all edits; Gamma function#Raabe's formula is not. But most of them are. Boris Tsirelson (talk) 09:36, 18 February 2014 (UTC)
FYI: Sławomir Biały (talk) 12:50, 18 February 2014 (UTC)

## Eigenvalues and eigenvectors - Illustration

What am I missing? The rationale for depicting vectors as "line segments" floating on a stretchy background rather than as unique elements of a vector space is eluding me, including that these are "an elementary concept in vector spaces" not even needing to be mentioned in that article, and intuition can be relied upon for underlying concepts in WP. —Quondum 02:41, 20 February 2014 (UTC)

## Popular pages tool update

As of January, the popular pages tool has moved from the Toolserver to Wikimedia Tool Labs. The code has changed significantly from the Toolserver version, but users should notice few differences. Please take a moment to look over your project's list for any anomalies, such as pages that you expect to see that are missing or pages that seem to have more views than expected. Note that unlike other tools, this tool aggregates all views from redirects, which means it will typically have higher numbers. (For January 2014 specifically, 35 hours of data is missing from the WMF data, which was approximated from other dates. For most articles, this should yield a more accurate number. However, a few articles, like ones featured on the Main Page, may be off).

Web tools, to replace the ones at tools:~alexz/pop, will become available over the next few weeks at toollabs:popularpages. All of the historical data (back to July 2009 for some projects) has been copied over. The tool to view historical data is currently partially available (assessment data and a few projects may not be available at the moment). The tool to add new projects to the bot's list is also available now (editing the configuration of current projects coming soon). Unlike the previous tool, all changes will be effective immediately. OAuth is used to authenticate users, allowing only regular users to make changes to prevent abuse. A visible history of configuration additions and changes is coming soon. Once tools become fully available, their toolserver versions will redirect to Labs.

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## "Template:Noredirect"

A recently created redirect, Template:La, currently points to Bifid cipher, is this correct? -- 70.50.151.11 (talk) 10:15, 23 February 2014 (UTC)

As far as I know, numerical ciphers are just ciphers that translate a message into a sequence of numbers. So Bifid cipher isn't equivalent. The redirect may have come from Numerical_cipher in the cryptography wikia. --Mark viking (talk) 13:33, 23 February 2014 (UTC)
I wouldn't trust anything coming from Wikia. What should we do with this redirect then? -- 70.50.151.11 (talk) 04:02, 24 February 2014 (UTC)
I've nominated it for deletion -- 70.50.151.11 (talk) 08:05, 27 February 2014 (UTC)
I've proposed at WP:RFD#Numerical_cipher that this be changed to redirect to Cipher (disambiguation). As far as I understand it, the use of the word cipher was common in the 16th and 17th centuries to mean zero, and often spelt cypher before English spelling got standardised (if we can call it that) in the late 18th to mid 19th centuries. I think it is perfectly reasonable to have it as a DAB (doesn't Isaac Newton in his Principia Mathematica on the differential and integral calculus calling the cheat of dividing by zero "the cypher"? Or was it John Napier doing logarithms? I forget which and most of my books are in store so can't check it from RS, and obviously Wikipedia is not in itself an RS so there's no point looking up what Wikipedia says about it. Si Trew (talk) 14:09, 1 March 2014 (UTC)

## Template:Noredirect

FYI, Template:La has been nominated for deletion. -- 70.50.151.11 (talk) 10:28, 23 February 2014 (UTC)

## Upright versus italic d

I am in a dispute with Template:User-multi on Fundamental theorem of calculus. The issue is whether a roman or italic letter d should be used for differentials. Formerly, the article used italic d, as in:

${\displaystyle \int f(x)\,dx.}$

Bub250 changed these to roman, as in:

${\displaystyle \int f(x)\,\mathrm {d} x.}$

I firmly believe that this is wrong, regardless of the interpretation of d, and accordingly I reverted him. He reverted me, citing the IUPAP Red Book and ISO 80000-2 standards. We have both hit WP:3RR, and neither of us seems to be budging, so I think it would be helpful to have some outside input.

In the past, the community has applied WP:RETAIN to the question of upright versus italic d. That may still be the consensus, but since it has been a while since we had this discussion it may be worth reopening the issue. Ozob (talk) 18:23, 23 February 2014 (UTC)

Might I suggest the following process that each of you might follow:
• Come back here and explain why your preferred choice improves the encyclopaedia from the point of view of the reader
or (better)
• Laugh ruefully, realise how extremely unimportant this issue really was, and put it all behind you.
Deltahedron (talk) 19:00, 23 February 2014 (UTC)
I have reverted the last edit of this user and left a warning on his talk page with references to MOS:MATH and our previous discussion here. D.Lazard (talk) 19:06, 23 February 2014 (UTC)
The consensus here in the many times this has come up before is that the italic d is by far the one more commonly used in sources, and that we should stick to that convention. Sławomir Biały (talk) 21:09, 23 February 2014 (UTC)

I should note that "upright d" is mathematically incorrect. (I know some students use them, but the usage is incorrect.) The reason is simple: "dx" means the diffenrial or the exterior derivative of x. Here, d is a function (from the space of functions to the space of one-forms). One can write d(x), but since d is linear, one can drop parathesis; like one writes Tx instead if T(x). Whenever you see the "upright d", the order is to eliminate them. -- Taku (talk) 03:25, 25 February 2014 (UTC)

I agree that upright d is mathematically incorrect, but I disagree that dx exclusively refers to an exterior derivative. It can also refer to a measure. In some sense this is more fundamental, because integrals of differential forms are ultimately defined by integrating in coordinate patches, and the integrals in coordinate patches are defined in terms of a measure. In a measure-theoretic context, for a function f, df is the Lebesgue–Stieltjes measure associated with f; in a sense this is the pullback of Lebesgue measure of R. Since d is still an operator on functions, it is still correct to italicize it and incorrect to romanize it. For measures like Lebesgue or Hausdorff measures which are defined directly (not as a Lebesgue–Stieltjes measure), the d is simply notation, but consistency seems to demand that it still be italic.
There is also the interpretation of dx as an infinitesimal (in the sense of Newton, Leibniz, and so on). Here the d is again an operator, so again it should be italicized. Ozob (talk) 05:34, 25 February 2014 (UTC)
This is a perennial problem. In things like differential topology the upright will always be used but in straightforward calculus learnt for hundreds of years the italic is used. I don't think we can decide that one form should be used everywhere, it depends on the circumstances. Dmcq (talk) 16:21, 25 February 2014 (UTC)
I think we should generally stick to what most sources in the relevant subject use. It bothers me that the argument for using an upright d almost always refers exclusively to a (paywalled) ISO standard, as if that should somehow trump every other mathematical style guideline. Sławomir Biały (talk) 16:39, 25 February 2014 (UTC)
This should be in WP:MOSMATH; I've been told that the upright d should be used in integrals, but it's often too difficult to implement. I don't have any elementary textbooks to determine the current usage in print. — Arthur Rubin (talk) 20:13, 26 February 2014 (UTC)
It is in the section WP:MOSMATH#Choice of type style, where both roman and italic forms of the differential are claimed to be correct. --Mark viking (talk) 22:23, 26 February 2014 (UTC)

## Global analysis?

We have no article titled global analysis. Michael Hardy (talk) 20:08, 23 February 2014 (UTC)

That was my thought exactly too. I don't feel qualified to create the article myself, but this is such a terrible oversight. -- Taku (talk) 20:22, 23 February 2014 (UTC)
Is this the only omission from the top-level MSC categories, as listed here? Deltahedron (talk) 20:47, 23 February 2014 (UTC)
Judging from Mathematics Subject Classification, the two red links are Expansion (approximation theory) and Mechanics of deformable solids. I think we have the latter covered in articles such as Deformation (mechanics) and Elasticity (physics). I don't know about the former. We have articles like Taylor expansion, Perturbative expansion and Asymptotic expansion, but I don't see offhand a general article on the subject. --Mark viking (talk) 00:28, 24 February 2014 (UTC)
I just created a short stub for the topic. Contributions welcome. --Mark viking (talk) 21:13, 23 February 2014 (UTC)

## Requested articles/Mathematics/Logic‎

The subpage Wikipedia:Requested articles/Mathematics/Logic‎ is not picked up by the bot that maintains Wikipedia:WikiProject Mathematics/Current activity and so new entries there are not flagged up. Is it possible to get that changed? And is there any special necessity to maintain this separation anyway? Deltahedron (talk) 07:37, 24 February 2014 (UTC)

I think what probably is useful is to keep the organization into mathematical logic, and subfields. I would be fine with having an L2 heading of "Mathematical logic" in the main page, with the subfields as L3 headings, and get rid of the subpage altogether. (There are probably several other fields that could benefit from such a structure as well.) --Trovatore (talk) 15:42, 24 February 2014 (UTC)

## Catching up on accessibility issues/debate?

I have never edited or looked at a talk page of any Math article. I haven't even browsed the archives of this page yet. I am a naive and innocent passerby. A simple user who happens to have an editor account from other interests. I see the FAQ above and I know my questions and opinions are familiar and well-worn territory. However the FAQ doesn't sate my curiosity. Is there perhaps a famous thread or talk page or external blog post or something that really digs into the issue of accessibility of math articles?

My own feeling isn't about a specific article, but it can be summed up by my own behavior: if I'm searching on google for most topics and I see a result from wikipedia, I'm happy and always check it out, and often that is the end of the search. If I'm searching for something Math related and I see a wikipedia result, my first reaction is to avoid clicking on it, and if I click on it I'm _always_ disappointed by what I read. I _always_ have to keep digging for an alternate explanation. Why this is exactly is a bigger topic, but I wanted to just get some pointers first before I trot out the same old complaints. Silas Ropac (talk) 01:30, 25 February 2014 (UTC)

Here are some recent thoughts on this subject.
Wikipedia_talk:WikiProject_Mathematics/Archive/2013/Nov#A_couple_general_ideas
Wikipedia_talk:WikiProject_Mathematics/Archive/2013/Jun#Linear_function.2C_Linear_Equation.2C_Linear_Inequality_full_of_errors_and_inconsistencies_and_.22matheese.22
Wikipedia_talk:WikiProject_Mathematics/Archive/2013/Jun#A_wild_idea:_multi-tiered_maths_articles_to_match_the_target_audience.3F
Wikipedia_talk:WikiProject_Mathematics/Archive/2013/Feb#Linearly_ordering_the_mathematics_articles
I, too, have thoughts on why this is a perennial issue, but I'll save those for another time. Ozob (talk) 01:45, 25 February 2014 (UTC)

I think Wikipedia is more successful in its coverage of mathematics than in any other subject. (Nonetheless, I think there are vast areas of imperfection in Wikipedia's coverage of mathematics.) Michael Hardy (talk) 06:32, 25 February 2014 (UTC)

I think there is a middle territory between the elementary and the advanced that we don't generally do very well. In my own experience, areas like differential equations, special functions and to some extent linear algebra seem to be very incomplete and not well-done. Sławomir Biały (talk) 12:24, 25 February 2014 (UTC)

This has been said many times before, here and elsewhere, but the fundamental problem is that "math cannot be explained". In mathematics, you have to put real efforts to understand a concept you didn't know before. Wikipedia does not/is not meant to solve this. For example, I've always thought the definition of spectral sequence is very dry; the concept made sense "only after" doing concrete computations with simple and not so simple examples. Our spectral sequence is, not surprising, dry and didn't help much when I was learning the subject. (Coincidentally, if I were writing it, I would stress the exact couple of a filtered complex). -- Taku (talk) 14:03, 26 February 2014 (UTC)

Template:Tq Has there ever been an objective poll done by the wikimedia foundation or someone external? Comparing satisfaction on various subjects? I'm not asserting that I'm right or you're wrong, but just wondering if there is any objective data out there? Particularly that focuses on users and not editors.
However I guess I have to back pedal some. As I click through many dozen Math articles I see a much tamer situation than I had in my head. In my head based on math articles viewed over the last few years, and some recent clunkers, I was concluding that the math articles were allowing and encouraging the content to simply be pretty much all equations. That a pile of equations was seen as a reasonable explanation for any math concept.
While I feel there are various levels of domain knowledge required to understand articles throughout wikipedia, equations are a special case because they are essentially another language. It's as frustrating as if you looked up an article on Chinese literature, in the English wikipedia, and found a wall of Chinese characters. And then on the Talk page you read the editors insisting "only Chinese can adequately explain Chinese literature". That clearly would not fly.
However I'm not really seeing that as an endemic problem here. I do see tons of equations, but I'm assuming math people expect and require that. But I also see lots of attempts to explains things with words. I think when I see an article that I feel does not achieve a good split, I should just comment on that article's talk page. I was sort of jumping to the conclusion that it was a lost cause to address a specific article, that the whole math ship was going down, but perhaps not.
Here is a funny example though: Bayesian network. That article actually has plenty of explanations later on, but they make a concerted and heroic attempt to scare off the reader before they get to the prose.
Since I can't find the examples I was thinking of, here is a more obscure one: Volume of an n-ball. The lede is only 43-words but there are 50+ lines of equations. I read on the math style guide that you should realize people generally will skip over equations and write accordingly. But reading just the words here there is zero sense of flow or explanation of anything. It feels like a laundry list of facts. Perhaps that is what mathematicians expect in wikipedia articles? I can imagine volunteers cheerily typesetting all these equations for hours, then grumbling over spending 20-30 seconds on the lede. It wouldn't be a big deal except the article is B-class. I'm guessing "number of equations" is pretty high on the assessment criteria for math articles?
I do wonder if equations should be banned from the lede: Linear independence, Cross correlation, the style guide says "It is even more important here than in the rest of the article that the text be accessible".
Now of course the really advanced stuff is incomprehensible but that is it's own problem: Hopf fibration, Special unitary group. I highly wonder if it's possible to write anything interesting and accessible about really high level math, I have never seen it done.
I don't buy that Template:Tq, you have to truly work and understand it. I can read about Math without understanding it. I think that is a problem with a lot of the advanced math articles, they don't have enough about the thing. The history of its discovery and use, the importance, what concepts does it relate to. These are things any reader should be able to take away.
But I don't see the broad sweeping problem I thought. I see articles mostly attempting to be accessible, succeeding or failing to various degrees, but not a conspiracy by any means. Perhaps there are ways to steer the overall a little better, like requiring non-trivial and accessible ledes for C class and above. I think that would be a good gesture towards the average reader. 14:20, 26 February 2014 (UTC)
I don't think Volume of an n-ball is really that bad. It's not a great article, but it conveys the necessary information. In article like that, there are naturally going to be quite a few formulas, and this one is not even all that heavy. I don't think that all articles must be pitched at "any reader". We should pitch articles at likely readers. An article on the volume of an n-ball should not be targeted at readers who don't know what an n-ball is to begin with. I generally think that equations should not dominate the lead, although it would be a mistake to rule generally on that matter. For instance, obviously articles that are about an equation should be permitted to have that equation in the lead. I do think that generally equations in the lead, and to a lesser extent the text, should be minimized wherever that is reasonable. As to the history of the subject, it can be surprisingly difficult to find good accounts on the history of mathematics. Often one has to go so far as to track down and consult original articles, obscure papers in the history of mathematics, and so forth. Mathematics is unfortunately not a subject where it is common to refer to the original papers of Cauchy or Riemann or Poincare or whomeve, and unfortunately there is nothing Wikipedia can do about that. I can count on one hand the number of mainstream mathematical textbooks I have read that actually give a thorough and well-researched account of the history if their subjects. Sławomir Biały (talk) 15:25, 26 February 2014 (UTC)
I agree Volume of an n-ball is kind of an oddball case. I don't see how it's a B-class article, but it's not worth belaboring that example. I was really just using it to point out what I think are some less-good features which occur often in Math articles: inaccessible ledes and over-reliance on equations. However as I said above I was actually really impressed to see these problems are much less common than I thought, really I think there are tons of articles, I'd say definitely the majority, that do a good job on these points. However I think these are common pitfalls that should be actively warded off. It's like over-summarizing in book articles, it's just a common mis-step that is endemic to the topic.
I disagree that "likely audience" should be the goal.The FAQ above says the target is "the interested layman" except then it immediately punts and says "this is not always possible". That is way too vague. When is it not possible? How do we determine if it's not possible or the article is just not written well? Importantly: if it's not possible do we then give up completely and accessibility becomes a non-goal? Or is it still useful to strive for a somewhat accessible lede even if the article itself is super advanced?
I sympathize with the difficultly of doing any of these things for math articles, especially advanced ones. It's a really really hard problem. I just feel like the wikipedia math community has somewhat punted by saying "we are special, we just can't do it, it's impossible". I think that's a mistake, I think the goal should be to do much better, and that this can be done without removing the technical content for expert readers.
One way to improve things is just to tell people "try harder to make things accessible" but of course that will accomplish nothing. I think it would take systematic change and strong leadership to declare that accessibility is a huge goal for all articles, and to work towards that goal. It might take many years or a decade to really effect that kind of change. But I think future-wikipedia would be a much better thing if it were done well.
I'm not a math editor and not likely carry this flame. So really I don't expect much to change from my comments. But I just wanted to give my two cents since to me the problem is crystal clear. I suspect I represent a decent chunk of people who use math articles, but I'm sure math-intensive people are a bigger faction, and that is why the problem is not seen as a problem. Silas Ropac (talk) 19:53, 26 February 2014 (UTC)
I think you'll find us in agreement on the broad points. Quibbling over "general reader" versus "likely reader" isn't terribly constructive. The bigger picture is that there are many mathematics articles that need to be improved (both in terms of accessibility and otherwise). I don't mean to diminish the achievement of editors who have struggled to prove the many articles that are very good. Even the articles on special functions that I love to gripe about seem to have improved substantially in the last few years. I still think we have major weaknesses in core mathematical areas like linear algebra and differential equations. Progress in those areas hopefully comes in fits and starts. "Carry the flame" is an apt analogy. Sławomir Biały (talk) 22:15, 26 February 2014 (UTC)
I am broadly in agreement with both of you, but I have something specific to add. I wrote most of Volume of an n-ball, starting about a year and a half ago (here) and I have some insight into why it is the way it is.
I got interested in the subject because I decided that this formula was a basic computation that I should really understand; I wasn't satisfied anymore with nodding my head at every step of someone else's derivation. In a very strong sense, I wrote the article for myself. And it shows; I don't know anything about the history of the computation of these volumes, and I don't know who needs volumes of n-balls in their work (I don't), and since the article had neither of these before, it has neither of them now. I don't know much about volumes of n-balls. I just felt like learning about them. I did demand of myself, however, that I knew how and why the formulas worked, and in the process I converted the article from a pile of equations to something that, perhaps despite appearances, has exposition.
My feeling was that the primary reason why someone might read the article was because they would either want to know how the formula was derived or they would want to look up the formula. I realized that it would be easy for me to make the article useful reference, so I put quite a lot of formulas at the beginning. I added all the derivations I could find (I think the one using Gaussian integrals is really the "right" one in a sense). And I added a little other content, like the asymptotic formula in high dimensions. I don't think it's a stellar article, but I achieved my goals for it, and I'm pretty happy with how it turned out. But it's not, and never was, intended for a general audience. Ozob (talk) 03:29, 27 February 2014 (UTC)
I too write for people like me who want to know something about certain rather specialised topics in mathematics, the ones I happen to be interested in. It seems reasonable to assume that those readers already have some mathematical background. If other editors feel that articles need more explanation to make them easier to access by readers with less background than I'm assuming, then they are perfectly free to add that material. I'm not very interested in being told by other people that I should be doing what they themselves are free to do. Deltahedron (talk) 07:31, 27 February 2014 (UTC)
Well, I don't always write for myself, and I do believe that the "interested layperson" is the right audience to aim for. When I work on an article like Derivative or Chain rule, I try to aim for a less sophisticated reader; but I don't think I always succeed, and I certainly haven't written much, if any, brilliant prose. I don't know if I could ever produce an article of the quality of Homotopy groups of spheres, which I think is really outstanding. Good exposition is a very hard problem which I don't know how to solve. Ozob (talk) 15:15, 27 February 2014 (UTC)

Ozob and Deltahedron make excellent points. The fact that everyone is a volunteer with their own intentions and goals for adding content is a huge factor in all of wikipedia. As is the fact that articles get built over time. I imagine it's well documented that editors who participate at different stages of an article's development have different personalities and motives. Perhaps my criticism of Math articles is as simple as: wikipedia is not done yet. I'm having deja vu that I've come to that realization more than once, that incompleteness looks like bias. Maybe articles which are inaccessible and equation-heavy today will be fleshed out over time. Certainly the best Math articles on the most common subjects seem really good today, so maybe it's just a question of time and resources.

So long as people are additively contributing all is well. However if there are edit wars or turf battles where people trying to make articles more accessible are beaten down by those trying to keep them "pure" and expert-centered, then that is bad. I haven't edited Math articles or read many talk pages, so I can't say whether this is a problem or not. Like I said before my main take-away from this thread is if I wanted to help I should address a specific article not the whole project, which I think is a wikipedia-wide rule of thumb.

One Math-specific issue I didn't raise yet. Does WP:NOR apply to equations? I see sources cited in Math articles, but I rarely see citations on specific equations. Like in Volume of an n-ball do those 50+ equations appear verbatim in the one cited reference? Or, as seems more plausible, do Math editors take the liberty to derive or produce original content? Is there some kind of official exception to WP:NOR for Math, or is it sort of just understood that one wouldn't get very far writing about Math if one didn't do some Math in the process?

I don't really don't have a pre-conceived opinion on that one. My guess is the cat is so far out of the bag and the tide of new equations spewing forth from editors minds so torrential it would be impossible to ever enforce a strict citation policy.

However going back to my "wikipedia isn't done" comment it does lead to point. In most subjects common topics have copious references but as one narrows scope, the number of sources dwindles and the amount of content in those sources dwindles until there is simply nothing to write about. But if Math editors are allowed to more or less generate content then the natural taper goes away.

This is speculation, but it suggests the lifecycle of a Math article is just different from other types of articles and can be mis-interpreted. Rather then getting built a tiny bit a time, as cited facts are bolted on, Math articles can be quickly inflated with content, but then they have to be whittled down and framed with explanations. Again I'm making this all up, does this ever happen? Silas Ropac (talk) 15:04, 27 February 2014 (UTC)

Re WP:NOR: there is a provision WP:CALC for simple calculations and derivations, which was left deliberately vague to allow some leeway for mathematics editors to supply simple proofs. It has been extensively debated (see Wikipedia_talk:No_original_research#Counting_--_possible_addition_to_WP:CALC, Wikipedia_talk:No_original_research/Archive_58#Routine_calculations and possibly elsewhere (?)). I sort of recall it was a subject of a big hassle few years ago, about an editor who was supplying a ton of original proofs, but I don't recall the details (was it User:Mathsci perhaps?). Maybe it's worth pursuing for further refinement. No such user (talk) 15:59, 27 February 2014 (UTC)
Gosh they are talking about counting and arithmetic. My gut is people are doing major derivations and elaborations and enumerations and manipulations of formulas. But I don't know at all for real, I just get that impression looking at the articles, it looks like some of the people kind of say "well what else can I say about this" and just kind of come up with stuff which is mathematically true, but isn't sourced. But this could be "don't ask don't tell" in that 99% of editors are not going to be able to call anyone out on these transgressions. Or maybe there are no transgressions I'm one of the 99% here I really can't say. Silas Ropac (talk) 05:24, 28 February 2014 (UTC)
Why would it be necessary for all of the equations to appear verbatim in one single source? That's not even a reasonable standard for nonmathematical articles. There is of course some leeway in how things are presented, but this is the same leeway that is afforded to articles in any other subject. Regarding citations in mathematics articles, there has generally been resistance to over-use of inline citations (so you will seldom see references attached to every single equation) in favor if the recommendations of WP:SCICITE. While many mathematics article would certainly benefit from more citations or clearer attribution, it doesn't necessarily mean that original research is being committed. This is especially true of content that can be found in essentially any textbook in the relevant subject area, which actually covers quite a lot of our mathematics content. It's not unusual for a single textbook to serve as a general reference for an entire article. (The opposite situation, where a single textbook is referred to assiduously at every line if the article really looks quite amateurish and silly.) Sławomir Biały (talk) 16:29, 27 February 2014 (UTC)
Template:Tq It's not necessary in general, but in this case there were 50 equations and one source, therefore my own rudimentary math skills lead me to believe all the equations must be verbatim from that source. I mean that's the general idea, that facts are from a source and not the editor's fertile imagination? Now I can't really read any of this stuff, but my guess just from glancing at the squiggly lines, and the quantity of squiggly lines, is that there is rampant "don't ask don't tell" policy in play with Math articles. Forbidding Math editors to come up with their own equations would go over about as well as forbidding humming at a song-writers convention.
And the WP:NOR question was just out of curiosity anyway, my main concern was accessibility. I think I've more or less bottomed out on the issue by admitting there isn't a big anti-accessibility cabal which is going around obfuscating all the articles so beginners can't understand them. Instead I feel that math is hard, or at least advanced math is hard, and without a lot of effort no math article is going to be super friendly. And so a lot of the big and popular articles are in fact quite friendly, but a lot of the advanced and less common articles are not. That that's just the state of things in 2014, and maybe it will get better over time.
I pulled over thinking there was a big injustice being done and all I saw was a bunch of mathematicians working on a construction site, with one yelling "move on, nothing to see here". Silas Ropac (talk) 05:18, 28 February 2014 (UTC)
I wholeheartedly agree with this sentiment, especially that "without a lot of effort no math article is going to be super friendly". Speaking from personal experience, it is really hard (for me at least) to write articles that are both suitable for an encyclopedia and accessible to a wide audience. I don't even claim to be all that successful at it: there are some articles that I have worked on that I am quite happy with, and others less so. The latter have to be just good enough, unless and until someone makes a better attempt. It's comforting to know that Wikipedia is a work in progress. Sławomir Biały (talk) 18:30, 1 March 2014 (UTC)
In a way, you're right, there's no natural taper for mathematics. No matter what problem you're considering there is always more to say; Henri Poincare once said, "There are no solved problems in mathematics, only problems that are more or less solved." But there is a natural taper for mathematics articles. Not everything that you can say about a subject is interesting, and not everything is notable enough to be the subject of an article. Because we are supposed to be able to cite everything to a secondary source, the scope of Wikipedia is vastly more limited than that of mathematics itself.
Regarding Volume of an n-ball, no, at some point I looked at the one cited source and it didn't have all of those equations or even most of them. The article is sorely lacking references. However, it ought to be possible to find references for all the facts in the article (equations or otherwise; remember that equations are just a kind of fact). Ozob (talk) 03:21, 28 February 2014 (UTC)
Right I agree that WP:N saves us from a library of babel of Math articles. I was relieved when I realized that. So instead I think what you have is just the quirk that for Math articles one can fairly easily inject completely true but unsourced information. That's pretty hard to do in non-Math articles, unless you just happen to have the first-person knowledge. But I don't see that as a showstopper by any means. I can imagine debating WP:NOR and fighting against each and every non-sourced equation, but that doesn't interest me. I feel as long as more mature articles are more accessible and rely less on equations, I'm not sure there is anything to argue about, the bottom line seems to be just that having more mature articles is better for everyone, which is a milquetoast platform. Silas Ropac (talk) 05:38, 28 February 2014 (UTC)
WP:V is also important. Everyone makes mistakes, and I've certainly written things that I was convinced were true but in fact were false. Once you've seen yourself make enough mistakes (on Wikipedia or otherwise) the necessity of verifiability becomes clear.
Also, many (but not all) of the equations in Volume of an n-ball fall under WP:CALC. The very first one does not, and I think the next two probably do not either. But the three after that are manipulations that could be done by a high school student; I think they are covered by WP:CALC. While everything in the section "Recursions" can be derived in an elementary way from the previous section (and so I think WP:CALC might apply), I'm sure that citations for the first two formulas exist, and the article would benefit from them. I believe the two following formulas fall under WP:CALC; certainly the second equality in each does. The entire table in the "Low dimensions" section is covered by WP:CALC. The formulas in the "High dimensions" and "Relation with surface area" section need citations (but the last four in "Relation with surface area" go together; any source with one will have all four). Then we are in the proofs section. The proofs themselves need citations, but those citations will cover all the formulas that appear. The "Balls in Lp norms" section needs a citation for its first equation (though WP:CALC might cover it in light of the equation cited below), but then most of the rest counts as routine calculation. The last two displayed equations are both covered by the article's one reference. Altogether, I think that if the article were to have inline citations, it would need about fifteen more citations than it does presently to cover all the equations. Many of these would be citations to the same source or sources.
I've just added one citation to the article. Ozob (talk) 15:19, 28 February 2014 (UTC)
If an able editor makes a derivation in a math article to make it clearer to the "intended audience" it is usually not original research in any reasonable sense. It might be original, but there is typically nothing that warrants the research label, even if it is a derivation that is not to be found anywhere in the references. Straightforward application of everyday mathematics to obtain (even new) formulas just isn't research.
My 2c: Sourced equations (and derivations) are preferable to unsourced ones, but unsourced equations (and derivations) are better than no equations (and derivations). Errors (unavoidable whether the material is sourced or not) are quite likely to be caught. Now, Wikipedia has a different definition of original research, see WP:NOR. The term "research" is tied to that something isn't in print (or it is simply unknown where it is to be found) in "reliable sources". If editors just use their good judgement (they usually do that), I think they strike a fine balance. YohanN7 (talk) 17:56, 1 March 2014 (UTC)

## Help needed with eight links to Index (mathematics)

Index (mathematics) is a disambiguation redirect, and happens to be one of the last links needing to be cleared for the February 2014 list of most linked disambigs. The seven pages linking to this title are:

If someone with the requisite knowledge could go correct the link to Index (mathematics) in these seven pages, that would be most appreciated. Cheers! bd2412 T 15:48, 25 February 2014 (UTC)

All done - thanks! bd2412 T 23:35, 25 February 2014 (UTC)
To BD2412: Unfortunately, the correction was erroneous in the articles 2 and 5, linking to indexed family instead of winding number. I have corrected these. In the 7th article, I do not know what is a "resource allocation theory index", but the link to indexed family is certainly wrong. The link to winding number in the first article seems also dubious. D.Lazard (talk) 12:18, 28 February 2014 (UTC)
I assume someone from this project applied those fixes after I posted this request - so to the extent that fixes were erroneous, that is a matter to take up with whichever editor made that edit. bd2412 T 13:12, 28 February 2014 (UTC)
Article 1 and 7 are not mathematics articles. Thus I have replaced the controversial wikilinks by {{clarify}} templates. Now, all are done. D.Lazard (talk) 16:16, 28 February 2014 (UTC)

## K(n,n) equation

Anybody here acquainted with the K(n,n) equation? -- Crowsnest (talk) 07:02, 26 February 2014 (UTC)

It's a variant of the KdV equation used for studying compactons, a variety of soliton with compact support. See for instance, [5]. --Mark viking (talk) 01:11, 27 February 2014 (UTC)

## Miss-matched <sub> and <sup> tags

I've been doing a scan of wikipedia articles for miss-matched <sub> and <sup> tags. Things like e<sup>x</sub>. Anyway there are a fair number of maths articles (357) with such problems. You can see a list at User:Salix alba/subsup. For the most part the normal renderer works fine and manages to correct the problem, however the Visual editor makes different assumptions so things look a bit odd. If anyone fancies fixing a few of these that would be great.--Salix alba (talk): 08:08, 26 February 2014 (UTC)

I fixed Dirac equation and Zero sharp which are on my watch list. I could not find the error in Mass in special relativity. JRSpriggs (talk) 10:03, 26 February 2014 (UTC)
Found it. — HHHIPPO 10:23, 26 February 2014 (UTC)

To help spots these things I written a bit of javascript which displays lines with errors. To use add the line

importScript('User:Salix alba/SubSup.js');


to your Special:MyPage/skin.js. This will add an entry 'SubSup' to your toolbox. Clicking on that link will open a window showing the lines where the tags don't match.--Salix alba (talk): 13:30, 26 February 2014 (UTC)

There's enough of them so a general mismatched tags check and fix should be stuck into some robot and standard checks somewhere. Dmcq (talk) 14:03, 26 February 2014 (UTC)
I fixed several more articles and your tool was a very great help. However, it sometimes indicated that there was no problem in one of the articles even though that article was on your list and the revision history indicated that no one had previously fixed it. JRSpriggs (talk) 08:40, 27 February 2014 (UTC)
There is now a discussion at Wikipedia talk:WikiProject Check Wikipedia#Mismatched sub and sup tags. Sees like a check for these may be added to some bots, AWB etc. My list is a bit dated being generated from dumps rather than live versions. There are some cases like <sup id="foo">ref</sup> correct markup which get listed in the dumps but the javascript tool does not report.--Salix alba (talk): 10:06, 27 February 2014 (UTC)

## AfC submission no 2

Wikipedia talk:Articles for creation/Multivariate metamodelling of mathematical models. FoCuSandLeArN (talk) 15:47, 26 February 2014 (UTC)

This seems like original research to me. At least there appears to be no identifiable reference that supports the topic of the article as a whole. But this is far outside my area of knowledge, so YMMV. Sławomir Biały (talk) 17:46, 26 February 2014 (UTC)
We already have an article on this general topic using the more familiar name of surrogate model. This AfC article seems like a perhaps unintentional POV fork of surrogate model; it spends most of the prose extolling the advantages of using such a model, but doesn't acknowledge that almost all systems requiring a surrogate model are multivariable in nature. Right now, I cannot see how this fork is notable--most of the refs are primary refs about examples of surrogate models rather than discussing the subject directly. Note that the article metamodeling is about metamodels in software design, which is a different concept than that presented here. --Mark viking (talk) 19:16, 26 February 2014 (UTC)
I concur with this evaluation. Also, there is the whole book dealing with the subject, The simulation metamodel. I would suggest the author to rework/expand "surrogate model" page, rather than write a separate essay, as well as browse wikipedia for the subject/keywords, to draw the connections, make cross-links. I don't know how communication in AFC is carried out (the afc page does not have a talk page: it is a talk page itself). I will point the user in his talk page to this discussion. Staszek Lem (talk) 23:07, 26 February 2014 (UTC)

## Fibred category -> Fibered category

I've started a requested move at Fibred category. Participations are very welcome. -- Taku (talk) 12:55, 28 February 2014 (UTC)

## Total free access to Royal Society History of Science journals for 2 days on March 4th and 5th !!!

As Wikipedian in Residence at the Royal Society, the National Academy for the sciences of the UK, I am pleased to say that the two Royal Society History of Science journals will be fully accessible for free for 2 days on March 4th and 5th. This is in conjunction with the Women in Science Edit-a-thon on 4 March, slightly in advance of International Women's Day, on Saturday March 8th. The event is fully booked, but online participation is very welcome, and suggestions for articles relevant to the theme of "Women in Science" that need work, and topics that need coverage.

The journals will have full and free online access to all from 1am (GMT/UTC) on 4th March 2014 until 11pm (GMT/UTC) on 5th March 2014. Normally they are only free online for issues between 1 and 10 years old. They are:

The RS position is a "pilot" excercise, running between January and early July 2014. Please let me know on my talk page or the project page if you want to get involved or have suggestions. There will be further public events, as well as many for the RS's diverse audiences in the scientific community; these will be advertised first to the RS's emailing lists and Twitter feeds.

I am keen to get feedback on my personal Conflict of Interest statement for the position, and want to work out a general one for Royal Society staff in consultation with the community. Wiki at Royal Society John (talk) 12:17, 28 February 2014 (UTC)

## Four-paragraph leads -- a WP:RfC on the matter

Hello, everyone. There is a WP:RfC on whether or not the leads of articles should generally be no longer than four paragraphs (refer to WP:Manual of Style/Lead section for the current guideline). As this will affect Wikipedia on a wide scale, including WikiProjects that often deal with article formatting, if the proposed change is implemented, I invite you to the discussion; see here: Wikipedia talk:Manual of Style/Lead section#RFC on four paragraph lead. Flyer22 (talk) 15:09, 28 February 2014 (UTC)

## Cramér's conjecture

Template:User-multi and a set of anonymous editors (or one editor acting from multiple IP addresses) have been trying to add a 2014 paper published by Marek Wolf, and a conjecture named by Wolf after himself, to the Cramér's conjecture article. Template:User-multi and I have reverted for now but more eyes would be helpful. There is also a discussion of this issue on the article talk page for which additional contributions would be welcome. —David Eppstein (talk) 23:14, 1 March 2014 (UTC)

I note that similar material appears in Prime gap. There is also a Marek Wolf-generated figure in each article. --Mark viking (talk) 23:32, 1 March 2014 (UTC)
And in Cousin prime. YohanN7 (talk) 01:38, 2 March 2014 (UTC)
There is also a mention of Wolf in Riesz_function, which someone who knows something about the subject should assess for relevance. --JBL (talk) 02:04, 2 March 2014 (UTC)
I am far from an expert in the subject but (without an error term) the equality asserted in this mention looks nonsensical. —David Eppstein (talk) 02:22, 2 March 2014 (UTC)
Indeed, and on reading the paper by Wolf it appears that the RHS is indeed the leading term in a series for the Riesz function, not the function itself. Deltahedron (talk) 07:41, 2 March 2014 (UTC)
I've reported the IP that has been the source of most of the recent edits for edit-warring. --JBL (talk) 01:49, 2 March 2014 (UTC)
In spite of all this, I do hope that it will be possible to explain the local customs to User:Marek Wolf: the best possible outcome would be to have him join as a constructive editor contributing content in his field of expertise. Deltahedron (talk) 09:57, 2 March 2014 (UTC)
New ip user around: 46.205.82.65 YohanN7 (talk) 14:36, 2 March 2014 (UTC)

User:Marek Wolf has now been blocked for a week. I do not think that was the best way of dealing with this situation. Deltahedron (talk) 17:44, 2 March 2014 (UTC)

An ip user is at it again. This time at Prime gap. YohanN7 (talk) 21:58, 4 March 2014 (UTC)

## Insertion of Original research in several articles

Template:U has recently edited several articles for inserting in them some texts supported by unpublished Bensimhoun's articles. I have reverted one of these edits. However some of these edits may be partially constructive, and some other eyes would be welcome. These edits include edits in

D.Lazard (talk) 09:36, 2 March 2014 (UTC)‎

At least one consists of adding as a reference a link to a PDF file uploaded onto Commons. This is obviously not a reliable source. Deltahedron (talk) 09:54, 2 March 2014 (UTC)
These results are so elementary that they do not need "reliable sources". They can be recognized as exact in few seconds by any person sufficiently experienced in algebra. The links to the documents with the proofs are a "bonus" here. If you think that these links are irrelevant, you could at least keep the corresponding assertions in the Wikipedia pages without linking to their proofs. Michael Bensimhoun (talk) 21:58, 2 March 2014 (UTC)
An interesting view, and one I am not entirely unsympathetic with, but Wikipedia has a policy on verifiability from independent reliable sources for a number of reasons. Firstly, so that readers, and other editors, can have some reasonable degree of confidence that the results are correct. Secondly, so that there is some degree of confidence that the results are worth mentioning. Thirdly, to prevent debates among editors, that would generate more heat than light, over points one and two. Deltahedron (talk) 22:09, 2 March 2014 (UTC)
If I'm not wrong, the problem is in the fact that I mentioned an unreliable source. What about not mentioning nothing at all, and to insert the assertion? Please, consider this paradox : on one hand, no conventional (reliable) journal would accept to publish elementary results. But on the other hand, Wikipedia do not accept publishing things that are not "explicitly" mentioned elsewhere in peer reviewed journals or books; so, there are mathematical truths and interesting observations that will be ignored for ever. Is it what you call "expansion of the knowledge"? In my opinion, a more intelligent point of view would be to "give a chance" to these mathematical truths, and to require a vote in the case where it is thought the result is suspect. Surely, for such elementary assertions, the exactness or inexactness would emerge very quickly. Michael Bensimhoun (talk) 22:42, 2 March 2014 (UTC)
It's not thought entirely polite to mention it, but here's the real issue. We're forced to hold a fairly tight line on "original research" (this is a Wikipedia term of art; it doesn't imply that anything is particularly original or research-like), because otherwise we would be overwhelmed with submissions from cranks and crackpots. We're not supposed to give much (theoretically, we're not allowed to give any) weight to an editor's credentials, so if it weren't for the OR policy, it would be very hard to prove that crankish submissions ought to be removed.
Unfortunately, it does sometimes create an obstacle non-crank editors adding useful material. But once you've been around a while, you'll probably agree that that's a necessary tradeoff. --Trovatore (talk) 23:11, 2 March 2014 (UTC)
As you might have noticed, proof outlines and supporting arguments with "unreliable references" will be challenged. But nothing prevents you from being bold. Proof outlines and supporting arguments without references may be challenged, but will not be challenged with certainty. YohanN7 (talk) 23:31, 2 March 2014 (UTC)
Let me clarify. Other editors may know of a "reliable" reference, or they may accept the argument as it stands or endow it with a "citation needed tag" for future improvement. Best is to drop a note in the articles talk page when adding unsourced material. Finding acceptable references on your own for every claim is notoriously difficult (and potentially expensive). Use your judgement. YohanN7 (talk) 23:41, 2 March 2014 (UTC)
I agree, this requires a common sense approach rather than enforcing rules for rules' sake and remembering the policies exist as a tool to serve a goal and are not really (primary) goals in their own right (and we have WP:IAR for that reason). So if you come across some obviously true material (as in easily recognizable to be true for anybody with some domain knowledge), simply don't challenge it. Of course if it gets challenged nevertheless sources will need to be added or in exceptional cases proof reading/verification by people with domain knowledge (in particular regulars of this portal) might suffice. Note that the latter only applies to things being obviously true for people with domain knowledge and may be considered an application of WP:IAR. The latter however cannot serve as an excuse for editors making unsourced edits all over the place or to cite their own unpublished results.---Kmhkmh (talk) 09:03, 3 March 2014 (UTC)
I agree with Template:U. This is for this reason that I have not reverted myself all Template:U's edits: some of them did contain not only reference to his original research, but also some text which may be useful. I had not the time for checking if this text needed or not to be challenged. D.Lazard (talk) 09:29, 3 March 2014 (UTC)

## Little orphan Annie

(No pun intended. Except that actually, I couldn't resist.)

Anne's theorem is currently an orphan: no other articles link to it. Michael Hardy (talk) 17:17, 2 March 2014 (UTC)

## AfC submission - 04/03

Wikipedia talk:Articles for creation/AMS Centennial Fellows. FoCuSandLeArN (talk) 14:17, 4 March 2014 (UTC)