Wikipedia talk:WikiProject Mathematics/Archive/2013/Jun

Mathematician categories
As I was adding some into non-gendered parts of the tree, I noticed that, and several others, have by-century trees, but that are sparsely populated. What would think about making those century trees (like diffusing on the head category, and move all mathematicians into those trees, by century, out of the head cat? Something similar was done recently at  (though there is still some controversy about it). What about here? If not, I might suggest otherwise to delete those cats, as having them as non-diffusing is a bit non-standard (by-century cats are usually diffusing elsewhere in the tree). Best --Obi-Wan Kenobi (talk) 23:24, 21 May 2013 (UTC)
 * Any thoughts? --Obi-Wan Kenobi (talk) 16:33, 3 June 2013 (UTC)

Yurii Reshetnyak
The new article Yurii Reshetnyak has been proposed for deletion under WP:BLPPROD. Reshetnyak is a very influential figure in geometric analysis and mathematical elasticity. We should have an article about him, even if it's only a stub. Unfortunately most biographical sources appear to be in Russian. Please help to improve the article! Sławomir Biały (talk) 23:02, 2 June 2013 (UTC)

Six operators
The new article titled Six operators definitely needs work! Including links, context, and some explanation of the role and importance of the concept. Michael Hardy (talk) 21:38, 4 June 2013 (UTC)

L. E. J. Brouwer
Someone moved Luitzen Egbertus Jan Brouwer to Bertus Brouwer. I've always heard him called L. E. J. Brouwer, and I'd never heard Bertus Brouwer before. I've moved it to L. E. J. Brouwer. Michael Hardy (talk) 21:59, 4 June 2013 (UTC)

Disambiguation help needed.
Greetings! Expert mathematical help is needed in determining the correct targets for links to the following disambiguation pages:


 * 1) Facet (mathematics) and Facet (geometry) both redirect to Facet (disambiguation), for a total of 138 links. ✅ D.Lazard (talk) 16:31, 3 June 2013 (UTC)
 * 2) Normed algebra: 24 links
 * 3) Sum of squares: 18 links
 * 4) Lie bracket: 17 links
 * 5) Primitive polynomial: 17 links ✅ D.Lazard (talk) 09:41, 3 June 2013 (UTC)
 * 6) Simple root: 17 links ✅ Mark M (talk) 12:55, 3 June 2013 (UTC)

Please also double check to make sure that these terms are indeed ambiguous, and are not susceptible to being presented in a substantive article as a topic an and of themselves. Cheers! bd2412 T 00:18, 3 June 2013 (UTC)


 * I got to ask: why is Lie bracket a disambig page? Not just a redirect to Lie algebra. (maybe I don't have a good perspective.) -- Taku (talk) 00:54, 3 June 2013 (UTC)


 * "Lie bracket" by itself is often used to refer to the Lie bracket of vector fields. Although a disambiguation doesn't seem to be necessary.  We can do that with a hat note or, even better, mention the algebra of vector fields in the lead of the Lie algebra article, with a link to the relevant notion of Lie bracket.  Sławomir Biały  (talk) 03:04, 3 June 2013 (UTC)


 * I agree, per WP:TWODAB; so I redirected Lie bracket to Lie algebra, and put a hatnote. Though the Lie bracket of vector fields is also mentioned later in the article, so I'm not sure if a hatnote is even necessary. Mark M (talk) 08:27, 3 June 2013 (UTC)
 * Thanks, I appreciate the solution. bd2412  T 12:04, 3 June 2013 (UTC)

For Simple root, there is a strange situation: All articles linking to this dab page are intended for the meaning in group theory (root system), while, IMO, for most people the main topic refers to a root of a polynomial. Both links of the dab page are redirects to sections. Thus I suggest to redirect Simple root to Polynomial (the target of Simple root (polynomial)) and to add a hatnote to the target section. I believe that it will be more useful for the readers than the symmetric action, which would need less editing work. D.Lazard (talk) 09:41, 3 June 2013 (UTC)
 * Incoming links can be a tricky indicator, since editors may link to an article merely because it is the existing target, rather than being a primary topic. If "real world" sources on the internet and in print indicate that Polynomial is the primary target, then this can be redirected per WP:TWODABS. Ideally, a disambiguation page should only exist if there are too many meanings of a term to fit neatly into a hatnote, or if the few meanings that do exist are in equipoise. Cheers! bd2412  T 12:08, 3 June 2013 (UTC)


 * Okay, I've fixed all of the incoming links to Simple root, and sent all but one to Simple root (root system) (which is a redirect). Only one incoming link was actually intended for Polynomial, which is where Simple root is now redirected. Mark M (talk) 12:55, 3 June 2013 (UTC)

I have moved the geometric content of Facet (disambiguation) to Facet (geometry), which is now a stub, and redirected Facet (mathematics) to Facet (geometry). There is no reason to tag Facet (geometry) as a dab page, because the different meanings are strongly connected, and a part of the content does not appear elsewhere. D.Lazard (talk) 16:31, 3 June 2013 (UTC)
 * Fantastic! That leaves only Normed algebra and Sum of squares in the top 500 disambiguation pages. bd2412  T 17:25, 3 June 2013 (UTC)
 * BTW, I did not find [] a good move. Unfortunately there are some users who say: if this is a dab page with inbound links, then let us… to disguise a dab page as an article, and disambiguators become happy. I do not think it improves an encyclopedia. Moreover, Bubka42’s edit actually concealed the Normed associative algebra red link which, unlike the current piece of crap, could be a valid encyclopedic topic. May I revert this? Incnis Mrsi (talk) 09:59, 6 June 2013 (UTC)
 * The over-riding question is whether there is a topic here that is capable of being discussed as an article, or whether there are merely a collection of unrelated terms that happen to share the same name. So far as I can tell from the previous version of the page, there are no title matches at all. It is not as though there is an album titled "Normed Algebra" and bird called the "Normed Algebra" and a person named "Normed Algebra" in the mix. "Normed associative algebra" and "Normed division algebra" are partial title matches, and are therefore not ambiguous to one another. What is left, then, but a single mathematical concept which is merely applied in different ways? bd2412  T 13:24, 6 June 2013 (UTC)
 * I don't think that your original dab page was truly a disambiguation page either. A normed algebra after all is an algebra with a norm.  So the links there were all topics related to this.  So I'd suggest reverting the edit if you like, but removing the disambiguation template.   Sławomir Biały  (talk) 13:51, 6 June 2013 (UTC)
 * A dab or a stub, but “normed associative algebra” is a more concrete structure which the (ambiguous) wording “normed algebra” usually, but not always, denotes. Recent edits plays this circumstance down. And in any case… fix what occurred at, please. I hoped to fuse two dabs into one, but if there is no support for it, then it would be better to restore its original tiny dab page or do something else but redirecting to a strange stub. Incnis Mrsi (talk) 15:23, 6 June 2013 (UTC)
 * I note that neither Gelfand–Mazur theorem nor Hurwitz's theorem (composition algebras) mention the term "Normed division algebra", which means that they can not be included on any disambiguation page for the unmentioned term (see WP:DABMENTION). To the extent that the phrase "Normed division algebra" is used with respect to either article, it must be discussed in that article before it can be included on a disambiguation page, because disambiguation pages only disambiguate content that is already in the encyclopedia. Without that restriction, we could not be sure that the disambiguation page itself is strictly reporting notable uses. However, since those are the only two links claimed to be associated with the exact phrase, "Normed division algebra", WP:TWODABS also applies. Why not redirect Normed division algebra to whichever of those two links is more likely the primary topic of the term, with a hatnote pointing to the other link? (I take it no one would look for Banach algebra or Composition algebra under the name "Normed division algebra"). bd2412  T 15:40, 6 June 2013 (UTC)
 * This is because you are preoccupied with a formal (link-structural, mention rules, etc.) well-being of Wikipedia, not semantic one, and push forward your “WP:TWODABS” on any pretext or even without one. If there is no clear WP:PRIMARYTOPIC, then do not enforce your dreams that there should be a primary topic. Let experts to decide it, please. There will be numerous links to a dab and you will be slightly unhappy, but eventually it would be better for readers, believe me. Incnis Mrsi (talk) 17:01, 6 June 2013 (UTC)
 * If there are distinct and different topics, then it should be no problem to fix the links themselves, so that they point to the intended article, and not to a disambiguation page. Remember, disambiguation pages are a means to an end, not an end in and of themselves. They exist to clear up confusion where a term can mean different things, and should not exist if this confusion can be cleared up without creating an extra page to do it. bd2412  T 17:05, 6 June 2013 (UTC)

Ambox-throwing to sections
(notified) was already well-known to me thanks to his “interesting” work with redirects. Recently he turned attention [ to mathematics], where can see: Of course, there may be original researches in mathematical articles, but unlikely a reasonable person could claim that a section consisting of disjoint examples, most of which can be found in textbooks, is an WP:original research. Does anybody think that these edits actually helps to improve 10 affected articles? Incnis Mrsi (talk) 06:14, 6 June 2013 (UTC)
 * 1) [ Placing] unreferenced section to Real number  section, which unlikely contains anything beyond textbooks on mathematical analysis;
 * 2) [ Cluttering] Quotient ring  with &#123;{unreferenced section}} and original research(!)
 * These unreferenced sections should be verified by external sources, if possible. I found several lengthy unreferenced sections, and decided to tag them as needing additional references. Adding additional references to these sections would be helpful to readers, since it would enable them to confirm the validity of the statements that are made. Jarble (talk) 06:26, 6 June 2013 (UTC)
 * How this makes the list of examples an original research? And how do you imagine an intended “externally verifiable” Real number where most statements are backed by hundreds of textbooks? A dozen of &lt;ref>s on each statement? With page numbers for each instance, or only a chapter name/number? Incnis Mrsi (talk) 06:39, 6 June 2013 (UTC)
 * I noted a similar phenomenon at Transcendental number. The section begins We will now follow the strategy of David Hilbert and ends For detailed information concerning the proofs of the transcendence of π and e see the references and external links.  In the references, the first item is David Hilbert, "Über die Transcendenz der Zahlen e und $$\pi$$", Mathematische Annalen 43:216–219 (1893), which is precisely to the point.  It seems clear that the section is adequately supported by a reliable source and that any reader would be able to identify the source being relied on.  Spectral sequence (talk) 06:42, 6 June 2013 (UTC)
 * In that case, an inline citation to that particular article should be added to the section, using the tag. Jarble (talk) 06:55, 6 June 2013 (UTC)
 * Pointing out what is hopefully obvious: inconsistent citation style and lack of references are two different things. In this case, there was a reference and a citation to that reference contained in the text.  If you don't find the citation adequate, then WP:SOFIXIT becomes an issue.   Sławomir Biały  (talk) 13:20, 6 June 2013 (UTC)

It is not necessary to give citations for each individual statement in an article provided the material is uncontroversial and widely available in general sources. For such kinds of information, general sources are sufficient. WP:SCICITE has more details about this. The "original research" tag pointed out above is obviously ridiculous. Very likely all of these examples will appear in either the textbook referenced by Lang or the textbook by Dummit and Foote. It seems to me that the onus is on the person placing the template to check the references, and I think there is little likelihood that this happened here. I don't really think that these kind of templates in general improve articles. It's more likely that a fact tag here or there, preferably accompanied by an explanation on the discussion page, will lead to a reference. The placement of large and disruptive templates to articles seems to have more to do with social psychology than with encyclopedia building. Sławomir Biały (talk) 13:44, 6 June 2013 (UTC)

Those tag-tacking edits should be undone. Mct mht (talk) 16:04, 6 June 2013 (UTC)

For a section with uncontroversial knowledge, WP:SCICITE recommends a citation or two for the entire section, often placed in or after the first sentence. So if a section is completely unreferenced, is it within policy guidelines to ask for a citation for the section, but it is also easy to fix this problem. Such a citation can show a reader where to find more information about a section topic; doing so is in my opinion an important part of encyclopedia building. --Mark viking (talk) 10:46, 8 June 2013 (UTC)


 * Actually it's sufficient to provide a general reference for an entire article. It isn't strictly necessary to have footnotes to the general references in each section.  Most (all?) of the articles under discussion include such references already.  I do think that citations generally improve the overall quality of the articles, but I disagree very strongly with the application of templates to enforce what is actually just a style issue (especially templates placed without any discussion on the talk page).   Sławomir Biały  (talk) 12:55, 8 June 2013 (UTC)


 * Where is the policy that it is sufficient to provide a general reference for an entire article? Again, WP:SCICITE says this is fine for articles of a few sentences, but longer articles should have citations. I agree with you about the drive-by tagging; when I see uncited sections where the material seems fine and I want to know more, I usually either contact the dominant editor, if there is one, or I post a query on the talk page. --Mark viking (talk) 19:21, 8 June 2013 (UTC)


 * WP:SCICITE specifically says that general references are adequate when most of the content of an article appears in multiple general sources (e.g., textbooks on the subject), regardless of article length. It may be appropriate in some cases to include a citation in the section, the lead of the article, or in a list of references at the bottom.  This has all been standard practice in mathematics articles for a long time.   Sławomir Biały  (talk) 20:39, 8 June 2013 (UTC)

In general examples should not have original research tags stuck on them because they are counted as illustrations and come under WP:PERTINENCE. They may be made up by an editor and don't need citations however if so they must not bring in any new ideas but simply be an obvious demonstration of what has been said around them. Any new idea in them would of course be subject to the verification policy. For instance if in the addition article we say 5+7 is an addition giving the result 12 that does not need a citation showing an example of 5 and 7 being added. Citations can be good if people want to follow up but that is not the purpose of an example. If someone thinks an example is not straightforward from what has been said then a citation can be called for but sticking in block tags is not the way to get clarification of an example. After all one can always say an illustration doesn't seem right but you don't put in tags saying all the images in an article need citations. Dmcq (talk) 13:38, 8 June 2013 (UTC) +WP:IUP we must not copy peoples examples straight as they are copyright even if they involve mathematics. Dmcq (talk) 13:53, 8 June 2013 (UTC)

Parity of zero is up for peer review
Peer review/Parity of zero/archive1

That's right, folks, I'm getting back on this horse. Please feel free to chime in! Cheers, Melchoir (talk) 22:17, 8 June 2013 (UTC)

Long-time requests
Looking at the dates embedded in Requested articles/Mathematics, I see there are some 40 requests dating back to 2005 and one to 2004. Perhaps we should try to clear the backlog? For reference, they are listed below. Spectral sequence (talk) 17:15, 3 June 2013 (UTC)


 * IMHO, this list is obsolete and the best is to destroy it. There are many topics of much larger importance which are not, or badly, described in WP and which deserve to have a much higher priority, like Multivariate resultant or D-finite function. D.Lazard (talk) 17:59, 3 June 2013 (UTC)


 * The traditional approach would be to archive very old entries. Charles Matthews (talk) 15:17, 9 June 2013 (UTC)

Calculus of variations

 * Deformation theorem

Category theory

 * Atomic topos
 * Coquasitriangular Hopf algebra
 * Ribbon category
 * Semi-abelian category (with redirect from Semiabelian category)

Coding theory

 * Coding lemma -

Convex analysis / Optimization

 * Constrained conjugate gradient / Conjugate gradient with barriers (how does the barrier effects the conjugate gradient solution) -
 * Waterfilling theorem -

Cryptography

 * Multilinear modular hashing

Differential geometry and topology

 * Natural bilinear concomitant -

Dynamical systems

 * Zeeman catastrophe machine -

Functional analysis

 * Codistribution -
 * Convenient analysis -
 * Nonlinear operator theory -

Geometry

 * Diametral circle
 * Diametral lens

Graph theory

 * Intrinsically linked graph
 * Restriction scaffold problem

Group theory

 * Recoupling theory

History of mathematics and other cultural aspects

 * Etymology of mathematical notation —

Lie groups, Algebraic groups / Lie algebras

 * Primitive invariant -

Mathematical analysis

 * Percent recovery

Algebraic number theory

 * Brandt module -

Numerical analysis

 * Model order reduction -
 * Nested dissection algorithm -

Order theory

 * Continuous poset -
 * Ideal completion -

Probability theory

 * Bayesian mapping -
 * Luders rule -
 * Marked point process -
 * Threshold function and their relation to combinatorics/graph theory, number theory, etc. -

Real analysis

 * Maharam theorem -

Statistics

 * Burstiness -
 * Gap statistic -
 * Ryan Einot Gabriel Welsch method -
 * Tukey B method -

Algebraic topology

 * Witt space -

General topology

 * Contiguity space -
 * Double fibration -

Uncategorized

 * Dynamic subtraction -
 * Eigenfilter -

Transformed redirect Cartesian tensor into an article
This should be an article. Cartesian tensors are the first approach to tensors and index notation (at least in my experience).

I wrote this from the perspective of someone with a firm grip on basic vector algebra, and some possible exposure to linear algebra and tensor index notation, but not lots, so there is some preamble on notation and terminology.

It is hoped to bridge the gap between basic (Gibbsian, as it were) vector algebra and tensor analysis.

Feel free to complain about the potentially trillions of typos, or anything, on the talk page and we can improve the article.

There is room for more sections and expansion also. M&and;Ŝc2ħεИτlk 23:56, 8 June 2013 (UTC)
 * Could you explain better what does it mean: a tensor in an Euclidean space? There is no such thing as a “tensor which exists in Cartesian coordinates” because a tensor must have a representation in any basis, by its very virtue to be a tensor. Incnis Mrsi (talk) 09:43, 9 June 2013 (UTC)


 * Fixed, any more specific inaccuracies please take it to the talk page. M&and;Ŝc2ħεИτlk 09:56, 9 June 2013 (UTC)

Links to fractional-order system
Fractional-order system is a new article. No other articles link to it. Creating some links to it from other articles, and other work, should get done. Michael Hardy (talk) 18:15, 9 June 2013 (UTC)
 * Sorry if it is a dumb question, Chaos in fractional order system is another new article. Should they not be merged? Solomon  7968  18:24, 9 June 2013 (UTC)
 * Perhaps. Michael Hardy (talk) 19:05, 9 June 2013 (UTC)
 * Merged. No significance to the example, so I removed it.  It might be required to determine whether the statement makes any sense, even if there is insufficient information in the reference to locate it.  — Arthur Rubin  (talk) 19:49, 9 June 2013 (UTC)
 * Proposing a merge into fractional dynamics; same subject, that's almost an orphan, as well, but it's better-connected. — Arthur Rubin  (talk) 20:59, 9 June 2013 (UTC)

Equality, identity and equation
I have recently rewritten the leads of equality, identity and equation. Before my edits, none of these articles contained any understandable definition of their topic. Instead, either they were too technical (introduction of Peano and extensionality axioms in the first line of the lead) or they contained silly assertions like "An identity is a relation which is tautologically true" or "An equation, in a mathematical context, is generally understood to mean a mathematical statement that asserts the equality of two expressions". Editing these leads, I was faced with the problem of lacking of sources providing general definitions of these basic concepts. In fact, they are too difficult to be accurately defined in elementary textbooks. And more advanced studies, such as in mathematical logic, usually deal with only one aspect of these questions.

Therefore I have tried to write down what I believe to be commonly meant by these words. But I may have omitted some important aspect. More important, the lack of convenient sources makes that a consensus is needed on these fundamental questions. Also, I have not edited the bodies of these articles which need also some attention. D.Lazard (talk) 10:15, 8 June 2013 (UTC)
 * [ Your edits] were partially wrong. An equation does not differ from an equality, it uses the equality binary relation but has a sense different from that of an identity. An (equality-based) identity is a statement of the form $∀⋯: F(⋯) = G(⋯)$, where $F$ and $G$ are terms, which must be a theorem in certain theory. An equation is a predicate expression of the form $F(⋯) = G(⋯)$ on one or more variables with the equality as the upper (outer) logical relation, and is not a theorem. Incnis Mrsi (talk) 10:44, 8 June 2013 (UTC)


 * While "equality" may merely mean that two expressions happen to have the same value (extensionally), "identity" is usually taken to mean that they have the same meaning (intentionality). That is, two things are identical if they are necessarily equal, not merely contingently equal.
 * Equality is characterized by reflexivity and the substitution property of equality. The substitution property implies symmetry and transitivity among other things. However, the article on equality (mathematics) misstates the substitution property as "For any quantities a and b and any expression F(x), if a=b, then F(a)=F(b).". The correct statement would be "For any quantities a and b and any predicate P(x), if a=b and P(a), then P(b).". JRSpriggs (talk) 12:18, 8 June 2013 (UTC)


 * This explanation is quite enlightening.  Sławomir Biały  (talk) 12:43, 8 June 2013 (UTC)


 * Intention and contingency have their own hard to pin down philosophical definitions. From the point of view of mathematical logic, are you saying that identity is like logical equivalence, something that holds in all models, and that equality is more like material equivalence, which is model-dependent? Thanks, --Mark viking (talk) 18:59, 8 June 2013 (UTC)
 * First of all, I think the desired word is intension, not intention.
 * I don't really agree with either JR or Incnis here. Two objects are identical just in case they are the same object; necessity or contingency doesn't enter into it, and axiomatic theories still less (Incnis's claims seem to assume a formalist POV).  There is an older usage whereby two expressions are said to be "identically equal" if their values are equal for all values of the free variables, whereas just saying they're "equal" may leave open the possibility that you have a particular set of values in mind for the free variables, and the values are equal for that particular assignment.  But this is mostly a convenience in exposition, and shouldn't be overinterpreted. --Trovatore (talk) 19:46, 9 June 2013 (UTC)
 * As a non-expert in these things, I found your version of the leads to be clear and easy to read. Leads are necessarily summaries and approximations of main articles; I don't think one can address all the mathematical and philosophical subtleties of these concepts in a lead, keep a lead short enough for MOS, and keep a lead understandable for non-experts. Equivalence may be a related concept to deal with. --Mark viking (talk) 19:12, 8 June 2013 (UTC)
 * I have some concerns about them, frankly.
 * The first point is cosmetic: The changes use boldface repeatedly, which is contrary to Wikipedia style.  The article title, and synonyms redirected to it, should be bolded at first occurrence, but not thereafter.  Similarly, be careful of WP:OVERLINK.
 * More substantively, I doubt that some of the proposed distinctions are really standard, specifically the supposed distinction between equation and equality. The distinction I would make is rather that an equation is a syntactic object, something you can write down, whereas equality is a property or relation.  --Trovatore (talk) 21:33, 9 June 2013 (UTC)
 * I agree with Trovatore. I'm not convinced there is a widely held distinction between "equation" and "equality" (in the same way that "inequality" and "inequation" should probably be merged). I understand there are two uses of two similar words, but I'm not convinced mathematicians (or anyone else) actually use these words in the way described. Mark M (talk) 12:34, 10 June 2013 (UTC)
 * The difference between equation and equality in the leads seems reasonable to me, at least in common usage. We solve for unknown variables in quadratic or differential equations, and the solutions make both sides satisfy an equality or make both sides equal. Also in computer languages, we test variables or objects for equality, which comes down to determining the truth value of a predicate expression whose variables are already determined or bound at the time of testing. --Mark viking (talk) 15:54, 10 June 2013 (UTC)
 * Several posts are about the difference, if any, between equation and equality. I agree that opposing them, as in equation is too strong. I am thinking to a better formulation. I agree also that, from a formal point of view there is no syntactic difference between the two notions. But this does not means that they have the same semantic. If the notions would have the same semantic, the two words would be synonymous, and one could find sources talking of the equation $$(x+1)^2=x^2-x+1$$, presenting $$x^2+y^2=1$$ as the equality of the unit circle or $$ax^2+bx+c=0$$ as the quadratic equality. As these articles are not intended for specialists of formal logic, not even for experimented mathematicians, it is essential to explain the distinction between these two notions that the mathematicians (not the logicians) make in their common usage . And this explanation must not involve high level notions. I have tried to solve this difficult equation :-), but this may certainly be improved. D.Lazard (talk) 18:20, 10 June 2013 (UTC)
 * I don't think this use of equality as a count noun is very usual. Equality is generally a property; one ordinarily does not speak of an equality at all, and there is certainly no bar against talking about the "equation describing the unit circle".  Is it possible that you are being overly influenced by French usage here? --Trovatore (talk) 18:31, 10 June 2013 (UTC)
 * I think it may be helpful to some readers to draw a distinction between the two concepts.. but I don't see the point in having two separate articles, equation and equality (mathematics). I think this gives the impression that the concepts are more different than they actually are (and the false impression that it is a really important distinction). It think it would be better to explain terminology in a single article. Mark M (talk) 22:17, 10 June 2013 (UTC)

I continue to find this situation problematic. I simply do not believe the purported distinction between "an equality" and "an equation" is standard in English-language mathematics (or, indeed, that it is usual to speak of "an equality" at all). D.Lazard, Mark viking, anyone else who makes this distinction, can you back this up? --Trovatore (talk) 18:23, 12 June 2013 (UTC)
 * I personally am quite comfortable with the phrase "an equality" as a partial synonym for "an equation", and I am more comfortable with "an inequality" than I am with "an inequation". It seems to me that in good encyclopedic fashion the appropriate thing to do here would be to find one or two reliable sources that either do or do not draw distinctions between these terms, and report on what they have to say, rather than trying to formulate the rules ourselves from scratch.  --JBL (talk) 21:43, 12 June 2013 (UTC)
 * I can believe some sources will use the terms in such a way, but I think the main thrust of the articles should follow common scholarly usage, which I think uses equality primarily as a mass noun rather than a count noun. I agree with you about inequation, a very ugly word that is probably attested somewhere but is definitely not standard. --Trovatore (talk) 21:45, 12 June 2013 (UTC)
 * You are free to dislike "inequation", but, please, remember that in the context of system of equations solving and real algebraic geometry, both inequation and inequality are commonly used with different standard meanings: $$A\ne B$$ is an inequation, while $$A>B$$ and $$A\ge B$$ are inequalities. D.Lazard (talk) 11:40, 13 June 2013 (UTC)
 * Can you source that? I do not think the term inequation is really standard at all, in any field.  But I don't know all fields of mathematics, so I could be wrong.  Oh, MathWorld doesn't count, of course, especially in this sort of case, as it frequently seems to borderline make stuff up in regards to terminology, or at least pull it from idiosyncratic sources. --Trovatore (talk) 16:27, 13 June 2013 (UTC)
 * Not exactly in reply, but syntactically "inequality" much more resembles "identity" than "equality" or "equation". Sławomir Biały  (talk) 18:25, 13 June 2013 (UTC)
 * In common practice in English-based reliable sources like scholarly articles and books, these terms are in no way interchangeable. In Google scholar, "differential equation" nets 1,810,000 results but "differential equality" nets 593 results. In the other direction, "test for equality" nets 31,300 results but "test for equation" nets get 454 results and most of the first page results are bogus. "Equality predicate" gets 4200 results and "equation predicate" gets 24. --Mark viking (talk) 22:52, 12 June 2013 (UTC)
 * None of that surprises me. As I said, in my usage, "equality" is a property (or predicate), so it's used as a mass noun.  I don't have a problem with treating the property of equality separate from the syntactic object of an equation (or the semantic object of the proposition intended by the equation).
 * What I don't find convincing is talking about an equality, and distinguishing that from "an equation". It's not implausible that such a distinction could be made, and some authors probably do, but I don't believe it's standard. --Trovatore (talk) 23:52, 12 June 2013 (UTC)

Anatolii Alexeevitch Karatsuba
There is a request for further input at Talk:Anatolii Alexeevitch Karatsuba. Spectral sequence (talk) 21:25, 10 June 2013 (UTC)

New article: Spherical basis
I started it for now. It is incomplete and probably full of typos/inaccuracies, and I intend to finish it soon, but it's been sitting in my userspace for a very long time so for now it's been moved into mainspace allowing others the freedom to edit it, if inclined. M&and;Ŝc2ħεИτlk 08:30, 12 June 2013 (UTC)


 * I also redirected spherical tensor, spherical tensor operator, and tensor operator to spherical basis for now. Do people think they should have their own articles? Spherical tensor and Spherical tensor operator makes sense to redirect since the literature seems to explain spherical basis and spherical tensors and spherical tensor operators together. So tensor operator should have its own article? M&and;Ŝc2ħεИτlk 14:16, 12 June 2013 (UTC)


 * Would some slightly more concrete examples and material, presumably relating the abstract content you develop to the concrete set of spherical harmonics as perhaps the simplest and well-known such basis, be appropriate? (And then perhaps discussing other possible such concretely-realised basis sets?) Or have I missed the point? Jheald (talk) 18:01, 12 June 2013 (UTC)


 * Yes, as said, more work is needed, including examples and other applications will be added as I learn them in time. M&and;Ŝc2ħεИτlk 18:08, 12 June 2013 (UTC)


 * While tensor operator seems to be used by physicists mostly in the context of tensors under rotation in quantum mechanics, the concept is used in other ways, too. For instance, in image processing, there is the concept of tensor operators for energy tensors, e.g., Energy Tensors: Quadratic, Phase Invariant Image Operators and also in the more general concept of structure tensor. Neither of these necessarily involve 3D rotational invariance/covariance. Tensor operator algebras have also been created for other groups, e.g., Tensor Operator Algebra for Point Groups. I don't think the redirect from tensor operator to spherical basis is a bad move, but if an editor wanted to do so, creating a standalone tensor operator article seems reasonable. --Mark viking (talk) 20:24, 12 June 2013 (UTC)


 * Yes, I suspected tensor operator would potentially have it's own article for the reasons you mention. It's easy to overwrite a redirect. Thanks, M&and;Ŝc2ħεИτlk 20:34, 12 June 2013 (UTC)
 * In the end I split the tensor operator stuff from spherical basis to overwrite tensor operator, for reasons explained here and at Talk:Spherical basis, Talk:Tensor operator. The redirects are changed as stated on these articles. M&and;Ŝc2ħεИτlk 08:56, 13 June 2013 (UTC)

3x12 = ?
I have a different opinion about [ what (or who) was silly] in Hexadecimal. Incnis Mrsi (talk) 04:09, 9 June 2013 (UTC)
 * Perhaps you could explain what you think the purpose of the link is? --JBL (talk) 15:52, 9 June 2013 (UTC)
 * Perhaps, an inhabitant of Unicodified worlds needs a hint to understand the “humour” invented by ASCII-based tribes in prehistoric times before the advent of HTML? Incnis Mrsi (talk) 16:13, 9 June 2013 (UTC)
 * This is why the "joke" is followed immediately by an explanation, is it not? --JBL (talk) 17:51, 9 June 2013 (UTC)
 * Sławomir Biały (talk) 19:38, 9 June 2013 (UTC)
 * Is there a reliable source which supports anything at all in the section Hexadecimal? Spectral sequence (talk) 20:54, 10 June 2013 (UTC)
 * There are a lot of sources (but of dubious reliability) in the main article on this topic, hexspeak. Apparently the original source for this is Kernighan and Pike The Practice of Programming (1999) but I don't have a copy to check. —David Eppstein (talk) 20:54, 12 June 2013 (UTC)
 * As far as I can see, hexspeak is a random collection of mildly amusing jokes that can be or have been made using hexadecimal notation, sourced only to primary sources, and with no single reliable secondary source to suggest that the list is complete, or representative, or significant. The section Hexadecimal mentions a few of those jokes and recounts some others, all without any sources at all.  It seems completely undue.  Spectral sequence (talk) 21:17, 12 June 2013 (UTC)
 * In the absence of any further comment I have boldly deleted the section. Spectral sequence (talk) 18:56, 20 June 2013 (UTC)

An instance of erroneous eponymy
I have created this new section, explaining that the so-called Weierstrass substitution was used by Euler long before Weierstrass was born. I don't know how this came to be called the Weierstrass substitution by respectable authors, but Google Books confirms that it is. Maybe the answer to that last question should be included in the article if it can be found. Did Weierstrass even used this substitution? Where, specifically, is it found in Weierstrass' work. If it isn't there, what source could be cited to confirm that it isn't there? Would this warrant renaming the article? How best should the topic of erroneous nomenclature be treated in Wikipedia? Michael Hardy (talk) 13:06, 17 June 2013 (UTC)
 * I have never heard of this name for the tangent half-angle substitution and I would never find this article by myself. I have created the redirect Tangent half-angle substitution, and I support to move Weierstrass_substitution to this new page. Also it could be worth to merge this page with Tangent half-angle formula. D.Lazard (talk) 13:58, 17 June 2013 (UTC)
 * Is there an independent reliable source stating that this substitution was used by Euler? So far, all we have is a reference to Euler E342.V.261 where a substitution equivalent to this appears for one specific case.  Michael Hardy may be correct about Euler, and in deed I personally think he is, but we go by what the sources say.  It seems to be at best original research by way of synthesis to suggest from this reference alone that Euler was aware of the substitution for general rational functions.  It is also unwarranted to assert that the assignment to Weiesrstrass is "erroneous".  There may be a good historical reason for it -- we just do not know, because there are no sources cited to support the assertion either way.  Whereof one cannot speak, thereof one must be silent.  Spectral sequence (talk) 17:03, 17 June 2013 (UTC)
 * Euler knew that

\begin{align} \text{if }y & = \tan\frac\theta2 \\[8pt] \text{then }\frac{2y}{1+y^2} & = \sin\theta \\[8pt] \text{and }\frac{1-y^2}{1+y^2} & = \cos\theta \\[8pt] \text{and }\frac{2\,dy}{1+y^2} & = d\theta. \end{align} $$
 * Certainly he was aware of that substitution. Whether he knew it could be applied to all or to only some rational functions of sin &theta; and cos &theta;, I can't say for sure.  Whether Weierstrass knew that, or ever wrote anything about this substitution, I don't know.  What we can say is erroneously attributed to Weierstrass is the first use of this substitution. Michael Hardy (talk) 22:51, 17 June 2013 (UTC)
 * . . . . and I should add: Secondary sources are needed to establish notability, and we certainly have those secondary sources for this substitution. But primary sources are what is needed to establish that a particular author used this substituion. Michael Hardy (talk) 22:52, 17 June 2013 (UTC)
 * "I don't know". That's exactly my point.  Wikipedia reports what reliable sources say, not our personal guesses.  Is there a reliable source that says that the name "Weierstrass" is erroneous?  The primary source indicates that Euler was aware of one particular use of this substitution.  Does any source state that Weierstrass was the first person to use this substitution, which would indeed be an error if so?  Perhaps it was named after Weierstrass because he rediscovered it, generalised it, popularised it, used it heavily, or whatever -- I don't know and it seems that you don't either.   Saying that the attribution to Weiestrass is "erroneous" appears to be synthesis at best.  Spectral sequence (talk) 06:15, 18 June 2013 (UTC)
 * Additional: I see that you have removed the word "erroneous" anyway so this part of the discussion is perhaps moot. In any event it seems to belong at Talk:Weierstrass substitution, not here.  Spectral sequence (talk) 06:23, 18 June 2013 (UTC)

The general points raised do seem worth continuing to discuss here. I prefer the term "unhistorical" to "erroneous". It seems to me that we should use the terminology most commonly used in the current literature, whether or not that happens to be historically accurate. That is what readers expect and will think it odd not to find. We are here to follow, not lead, the scientific literature. We are not here as advocates or to right great wrongs. Spectral sequence (talk) 06:32, 18 June 2013 (UTC)


 * I wholeheartedly agree with this. Of course, if a good source has a discussion of the history of the name, we can include that somewhere in the article, and that would be valuable. But the name we use in general should be the name that is commonly used. Also, we should remember that many theorems are "known" to some editors by Western names, but known to editors in other countries by completely different names, which makes historical accuracy particularly trick to judge based on personal knowledge. &mdash; Carl (CBM · talk) 02:01, 19 June 2013 (UTC)
 * It seems that "Weierstrass substitution" is not the most common name. Google Scholar provide 26 hits for these words (with quotes) and 70 hits for "tangent half-angle substitution", without taking into account other current locutions like "taking the tangent half-angle as new variable".
 * This Google search provides also the reference Jean-Pierre Merlet, A Note on the History of Trigonometric Functions, International Symposium on History of Machines and Mechanisms 2004, pp 195-200, which contains the sentence "All the authors seem to agree that this substitution was first used by Weierstrass (1815-1897) and is often called Weierstrass substitution or Weierstrass t-substitution [Stewart 94]". It seems thus that this article may be the reference that it is asked for. Unfortunately, I have not an easy access to the full text of this paper. D.Lazard (talk) 09:50, 19 June 2013 (UTC)
 * That statement is somewhat suspect. I think the referenced source there is Stewart's Calculus, not exactly the gold standard in historiography of mathematics.  Sławomir Biały  (talk) 00:43, 20 June 2013 (UTC)

It was an email from Fred Rickey that alerted me to the possibility that this substitution may be nowhere in Weierstrass' writings. In our article titled integral of the secant function, this paper that he wrote is cited, showing that the value of that integral was a celebrated conjecture in the 17th century:
 * V. Frederick Rickey and Philip M. Tuchinsky, "An Application of Geography to Mathematics: History of the Integral of the Secant", Mathematics Magazine, volume 53, number 3, May 1980, pages 162–166

Michael Hardy (talk) 23:14, 20 June 2013 (UTC)

Schwartz kernel theorem
The article Schwartz kernel theorem looks as if it could use further elaboration including concrete examples. Michael Hardy (talk) 23:00, 20 June 2013 (UTC)
 * The german version looks good de:Kernsatz von Schwartz. The Legend   of Zorro  00:44, 21 June 2013 (UTC)

Linear function
Is "linear function"
 * (a) a synonym for linear map;
 * (b) a synonym for linear equation;
 * (c) could be either (a) or (b), depending on context ?

At the moment there is considerable overlap between our articles on linear function, linear map, linear equation and a new article linear function (mathematics). Any views on what the best resolution is ? Gandalf61 (talk) 10:14, 19 June 2013 (UTC)


 * It is (c) as far as the use of term is concerned. We had an extensive discusson on that here a while back. Currently it seems to me that the main (and established) articles are linear map and linear equation. The other two in particular the new one should incorporated into them. The new one is probably well meant but essentially an undesired fork. Also to avoid such forks/redundant articles in the future we should integrate some disambiguation mechanism.--Kmhkmh (talk)
 * P.S.: The recent discussion was: Wikipedia_talk:WikiProject_Mathematics/Archive/2013/Feb--Kmhkmh (talk) 10:58, 19 June 2013 (UTC)


 * In my opinion, "linear function" is a synonym for linear map, as stated in that article. There is a relation between "linear equation" and "linear function", as discussed in the section linear equation, but they are different concepts--a linear map is a map from one module to a potentially different module, whereas a linear equation describes a relation among variables and/or a geometric object. The new article linear function (mathematics) actually has a lot of overlap with linear equation and perhaps could be merged into the latter, if there is anything useful to merge. Similarly, linear function could be redirected  and merged into linear map, but if this is done, it would be important to make sure that linear map has some sort of elementary explanation before launching into vector spaces and modules. High school students may want to learn about linear functions and the high level algebra would scare them away. --Mark viking (talk) 11:04, 19 June 2013 (UTC)
 * I think there's a misunderstanding here. Nobody suggested that linear map and linear equation are the same concept - obviously there are not. However in literature, depending on the context, the term "linear function" is used to denote either concept. That was the result of that earlier discussion, you can find concrete exmples for both usages in there.--Kmhkmh (talk) 11:36, 19 June 2013 (UTC)
 * (Edit conflict) I agree that in many context "linear function" is a synonym for "linear map". But for a polynomial function of degree one, the term of affine function seems not to have a dominant use in analysis. Moreover, it needs implicitly to understand that the field of the reals is both a vector space and an affine space. Also, affine function redirects to affine transformation, which does not consider "functions" as they are viewed in analysis. IMO, the lead of "linear function" must be rewritten as a WP:CONCEPTDAB and must begin like "Depending on the context, a linear function may refer either to a linear map between vector spaces or to a polynomial function of degree one", and link to the new article (possibly renamed linear function (analysis) or linear function (calculus)) for the second meaning. Also, a function is not an equation and linear equation refers to linear algebra, which is not the case for polynomial function of degree one. Thus the proposed merge of these two notions is a nonsense. The possible merge of the present content of linear function into linear map in another question. In any case, the present state of the "well established articles" although formally correct is confusing for the readers. D.Lazard (talk) 11:54, 19 June 2013 (UTC)
 * Sorry for the confusion. I meant to suggest that the current content of the article linear function (mathematics) has a lot of overlap with the article linear equation and could be merged, not that the two topics in general should be merged. --Mark viking (talk) 12:02, 19 June 2013 (UTC)
 * I oppose to classifying such stuff as linear function as CONCEPTDABs – there are two sharply distinct meanings. Yes, there is a lot of inbound links and placing a disambiguation tag would make certain people unhappy, but there are other such cases and, more important, diverging clearly distinct senses via dabs makes Wikipedia better in a long-term perspective. BTW, linearity is another interesting “article”. Incnis Mrsi (talk) 07:35, 20 June 2013 (UTC)
 * So you oppose what exactly now?--Kmhkmh (talk) 03:02, 21 June 2013 (UTC)

I have been bold, and have rewritten the lead of linear function to take the two meanings into account. If I am not reverted, as I hope, it remains to decide which merges are worth. IMO the present body of linear function duplicates linear map and could be suppressed (linear map is already linked to in the lead). Thus the body may be used to develop the "calculus meaning", that is to merge from linear function (mathematics), but with emphasis on the functional aspects rather than on the various equations of the graph of a linear function, as it is presently done in linear function (mathematics). D.Lazard (talk) 14:13, 19 June 2013 (UTC)


 * I agree with D.Lazard's approach. There remain several problems with the linear function (mathematics) article. There is the POV problem. The "polynomial" definition is referred to as mainstream mathematics, while the linear map view is considered advanced mathematics (does that editor really think that mainstream mathematics is elementary?). There is considerable confusion in the article between the concepts of function, equation and geometrical lines (for instance, at one point he calls a line a function). After fixing these problems (further discussion will be on the article's talk page) I would also suggest moving the article to linear function (calculus) if there is enough material left to make a viable article. Bill Cherowitzo (talk) 15:00, 19 June 2013 (UTC)

At the moment we have this: Now, here is my opinion: Since this affects numerous articles, I am not sure where else to discuss it centrally. Thoughts? &mdash; Carl (CBM · talk) 15:09, 19 June 2013 (UTC)
 * Linear function (calculus) redirects to Linear function (mathematics). The latter article is very new and in very rough shape
 * Linear map
 * Linear function
 * Affine function redirects to Affine transformation. Focuses on maps between affine spaces
 * Linear function (mathematics) is an awful way to disambiguate the title because both concepts (linear map, affine function) are in mathematics
 * Make Linear function have a lede and two sections, which are summary-style paragraphs about the two versions
 * Make Affine function be the page that is now Linear function (mathematics). This can then link to affine map as a more advanced topic lower down.
 * Sounds good. What fate do you plan for linear equation ? Gandalf61 (talk) 15:59, 19 June 2013 (UTC)
 * Since essentially everyone (at least in the US) learns about linear functions (i.e., first-degree polynomial functions) in primary or secondary school and no one calls these objects "affine functions" in this context, it seems to me inappropriate to make affine function the main article about this object. I agree that "linear function (mathematics)" is a useless title; "linear function (calculus)" or "linear function (elementary mathematics)" is very much preferable.  Otherwise, I think this is a very good suggested arrangement.  --JBL (talk) 16:54, 19 June 2013 (UTC)
 * Since my above post, the article was moved to linear function (calculus). I also edited linear function itself, any feedback on the talk pages of those articles would be valuable. &mdash; Carl (CBM · talk) 20:30, 19 June 2013 (UTC)
 * BTW, I added the link to affine transformation. But the thing “linear function (calculus)” still misses is functions of several variables. Incnis Mrsi (talk) 13:46, 22 June 2013 (UTC)

Spin matrix (and plural: spin matrices)
Not terribly important, but this term could refer to a number of things, so I created a DAB page. The plural spin matrices used to redirect to Pauli matrices, so I removed double redirects from articles, to spin matrices, to Pauli matrices.

If anyone can think of other "spin mattrices" within pure/applied mathematics (not just the Pauli matrices for quaternions, Clifford/geometric algebra, etc.) then add the article there, higher spin alternating sign matrix is the one and only example.

If anyone disagrees with a DAB page and there is widespread consensus to redirect it somewhere, we could overwrite the spin matrix and spin matrices back towards Pauli matrices, presumably. M&and;Ŝc2ħεИτlk 22:28, 20 June 2013 (UTC)
 * Commented at Wikipedia talk: WikiProject Physics ‎. Incnis Mrsi (talk) 13:46, 22 June 2013 (UTC)

Empty sum
The statement in Summation


 * $$\sum_{n=s}^t f(n) = \sum_{n=t}^s f(n)$$, for finite s and t.

seems to contradict the article Empty sum and Summation. Best wishes, --Quartl (talk) 05:11, 21 June 2013 (UTC)


 * Indeed. I deleted that line. Boris Tsirelson (talk) 05:46, 21 June 2013 (UTC)


 * As it says in that section,
 * $$\sum_{n=s}^j f(n) + \sum_{n=j+1}^t f(n) = \sum_{n=s}^t f(n) \,.$$
 * If we replace t by s&minus;1, then we get
 * $$\sum_{n=s}^j f(n) + \sum_{n=j+1}^{s-1} f(n) = \sum_{n=s}^{s-1} f(n) = 0 \,$$
 * which implies
 * $$\sum_{n=s}^j f(n) = - \sum_{n=j+1}^{s-1} f(n) \,.$$
 * Right? JRSpriggs (talk) 06:01, 21 June 2013 (UTC)


 * That is basically the argumentation of . The problem seems to be: what is
 * $$\sum_{n=s}^j f(n)$$
 * when j ≤ s-1. The case j = s-1 is defined as zero. Is the case j < s-1 also zero or better left undefined? The WP articles don't answer that question. Best wishes, --Quartl (talk) 06:41, 21 June 2013 (UTC)


 * I doubt you will find any satisfying answer to that, because it comes up so rarely in practice, and few authors spend time talking about conventions that they will never use. &mdash; Carl (CBM · talk) 14:22, 21 June 2013 (UTC)


 * @Quartl: Can I convince you that the following look different from each other?
 * s-1
 * s - 1
 * s−1
 * s − 1
 * Only the last one is correct according to WP:MOSMATH. Michael Hardy (talk) 17:12, 22 June 2013 (UTC)


 * Sorry, I thought the MOS applies to articles only and you can be a bit less formal on talk pages as long as the meaning is clear. Best wishes, --Quartl (talk) 18:40, 22 June 2013 (UTC)

File:Megaprime found.png
This image is being used at the top of the article megaprime. The description says the image is based on the information at http://primes.utm.edu/primes/lists/all.txt. I don't understand this image. The Y-axis appears to be the number of megaprimes found in a particular year. I don't understand the labeling of the X-axis. As is, I find this image highly confusing. I posted at but haven't received any response yet. Can someone who understands the image explain this to me please and perhaps improve the image description in the article? --  Toshio   Yamaguchi  07:48, 20 June 2013 (UTC)
 * Requiring the reader to add 1998 to the label is just silly. The last but one revision of the image (http://upload.wikimedia.org/wikipedia/commons/archive/9/94/20130318131035!Megaprime_found.png) is more sensible, I have no idea why it was immediately reverted by the author, but I’m inclined to rerevert it.—Emil J. 11:14, 20 June 2013 (UTC)
 * I went ahead as there were no objections.—Emil J. 12:53, 23 June 2013 (UTC)

J. Laurie Snell
Someone has proposed deletion of the article titled J. Laurie Snell. I heard of this guy a lot in the '90s and '00s, and I thought there must be some reason for that. Michael Hardy (talk) 03:42, 21 June 2013 (UTC)
 * I find this trend highly concerning to ignore. User:RadioFan proded this article twice both time contested, with the rationale "No indication of how this might meet notability guidelines for academics. Lacks citations to significant coverage in reliable sources". A simple Google scholar search shows 4000 citations. I bet he has not done a Google search before prodding these. This type of repeated prodding is very much unconstructive. The Legend   of Zorro  04:10, 21 June 2013 (UTC)
 * Irrespective of the merits of the article, it should not have been proposed for deletion twice, . If a PROD is contested, AFD is the appropriate route.  Spectral sequence (talk) 11:11, 23 June 2013 (UTC)

Linear function, Linear Equation, Linear Inequality full of errors and inconsistencies and "matheese"
These articles are SO badly written, so inconsistent, so incredibly unhelpful .. AND so important to regular people. Just to mention my qualifications: I have over 35 years of teaching mathematics at every level and a Ph.D. in theoretical mathematics.

A. Constant function is correct.

B1. Linear function is incorrect. This is the definition of a linear mapping from linear algebra on up.

Sources:
 * http://planetmath.org/linearfunction (READ LAST LINE)

B2. Linear function (calculus) is mostly incorrect - particularly as it seeks to "include" constant functions with linear functions.

Sources:
 * http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
 * http://www.columbia.edu/itc/sipa/math/linear.html
 * http://www.math.okstate.edu/~noell/ebsm/linear.html
 * http://www.mathplanet.com/education/pre-algebra/graphing-and-functions/the-slope-of-a-linear-function
 * http://planetmath.org/linearfunction (although this article is definitely not "for the people"!)

The person who "fixed" and "renamed" my version (originally called Linear function (mathematics)) apparently did not even bother to look at Constant function and Quadratic function and incredibly where the Linear Function article refers to linear mappings of higher mathematics (linear algebra and above so usually college level), decided that a mainstream (general mathematics) definition of linear function (just put it in any browser or look in the CCSSM) was a calculus level subject. P.S. This was my first and most definitely my ONLY contribution to wikipedia; the incredible arrogance of the various responses and in the end - although I certainly did not object to his making it wikipedia format - the forced "corrections" (see talk).

C. Quadratic function is correct.

D. The article Linear equation is incredibly misleading.

This article is incredibly misleading. You are confusing linear equation (refers to the degree of the polynomial) and linear function (a function whose graph is a line).

Some sources for this:
 * 1) http://tutorial.math.lamar.edu/Classes/Alg/SolveLinearEqns.aspx
 * 2) http://www.purplemath.com/modules/solvelin.htm
 * 3) https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities (I have written to them about the "opposite inconsistency" with linear inequalities as with e.g. MathPlanet.)
 * 4) http://www.webmath.com/solver.html

As I said, the word linear here refers ONLY to the degree of the variables. It has NOTHING to do with the graph or rather the graph of the solution set! (It is implicit in the article that the graph of a linear equation is a line.) This is simply not true. A linear equation is NOT the same as a linear function.'


 * Where is a linear equation in 1 variable, e.g. 3x=6? The solution of set of a linear equation in 1 variable is a value or point on the number line, e.g. x=2.  This is the form most children see at ages 7 and they are told that they are solving a linear equation in 1 variable and do not understand why they don't "see" a line (since it is not a linear function and has nothing to do with a line).


 * A linear equation in 2 variables and a linear function in 2 variables written in general form are the same, i.e. Ax+By=C. The solution set of both is a set of order pairs (x,y) in the plane that form a line. (I note that it is EXTREMELY unfortunate that teachers in middle school insist that Ax+By=C is a linear "function", since it is very difficult after that for children to understand the idea of a function. In its "starting" form as a "mapping", the definition of a function completely separates the roles of independent and dependent variable, which is obviously not true of a linear function in general form. Unless a child goes on to higher mathematics (and we are talking about less than 10% of the entire population of the entire world), this definition of function, i.e. the explicit form, is the ONLY definition he will ever see. If one does go higher, then one sees functions of all kinds (implicit, parametric, vector-parametric) and can actually categorize linear equations in 2 or more variables as implicit functions that can be solved uniquely in explicit form (and this explanation will definitely help you use mathematics software.)


 * Where is the "clarifying" example of a linear equation 3 variables? The solution set of a linear equation in 3 variables is a plane in 3D space.  You never mention it, yet every child who completes 12 years of school must solve a system of "3 equations in 3 variables" and has NO idea that he is actually finding the intersection point of 3 planes. This is critical. Again, this is not a linear function and has nothing at all to do with a line (since it is a plane.)

Then you can go on to the general definition. But these three are critical to the definition and understanding of linear equation.

'''Where is the information that a linear equation is never unique? '''

Linear Inequality Finally, if you properly define linear equation, then you can properly define linear inequality in 1, 2, 3 variables (without mentioning linear functional OMG in the second sentence)!

Some sources for this:
 * 1) http://www.mathplanet.com/education/algebra-1/linear-inequalitites/solving-linear-inequalities
 * 2) http://www.purplemath.com/modules/ineqlin.htm

P.S. I have also written to MathPlanet (who has the opposite inconsistency of Khan):

The following article is incorrect (and inconsistent with another of your articles - see below)
 * http://www.mathplanet.com/education/algebra-1/visualizing-linear-functions/linear-equations-in-the-coordinate-plane

A linear equation is a polynomial equation of first degree so a linear equation in respectively 1, 2, 3... variables is: Ax=B, Ax+By=C, Ax+By+Cz=D... where capital letters are constants. A linear inequality is a linear equation in which the equals sign has been replaced by an inequality.

The term linear function in general mathematics is restricted to a polynomial function of first degree: y(x)=mx+b. That is, it is a function whose graph is a line in the plane. It is linear equation in 2 variables when written in general form: ax+by=c.


 * The definition in the above referenced article is also inconsistent with your article: http://www.mathplanet.com/education/algebra-1/linear-inequalitites/solving-linear-inequalities


 * Further these discrepancies confuse students who (a) have been told that they are solving a linear equation in one variable when they solve e.g. 3x=6 and (b) when they solve a systems of 3 linear equations in 3 unknowns as they think they are finding the intersection of 3 lines (and not 3 planes, which is the correct interpretation).

Thank-you for your consideration. LFS Lfahlberg (talk) 18:04, 22 June 2013 (UTC)Lfahlberg (talk) 15:58, 22 June 2013 (UTC)
 * As far as that some articles are (still) badly written, I think nobody disagrees. However I don't quite understand your complaints about "correctness" of linear function. First of all you own sources don't agree with your claim, that is http://www.columbia.edu/itc/sipa/math/linear.html includes constant functions under linear functions as well (so does any math book on that subject that I've seen so far). The PlanetMath article is not disproving anything in the WP article either, it merely shows that there is even a 3rd meaning/usage of the term, we haven't covered yet. However given that discrete geometry/linear (incidence) spaces is hardly a particularly popular math subject, WP coverage is still weak in that area and hence the PlanetMath content is still missing.


 * More importantly more or less all your sources don't really prove much regarding (alleged) "incorrectness" of WP content. They merely "prove" a particular usage of a term but do not disprove alternative usages. Aside from that logical problem they are (at least partially) not really authoritative sources either. PlanetMath is a Wiki like us, so strictly speaking it doesn't even qualify as a source. The various university websites and Khanacademy are ok to a degree but hardly authoritative sources, for that you'd need a standard textbook or some reviewed journal article.--Kmhkmh (talk) 23:57, 22 June 2013 (UTC)


 * Welcome to Wikipedia! You have brought up several perennial problems which are to be expected from such a system as ours. There are a few things to keep in mind. 1) While you might feel strongly about how certain articles should be, don't forget you are working with a community to build them. 2) Don't forget there are other editors as qualified (maybe a few even more qualified) as you. 3) Be sure to keep assuming good faith! This job requires copious amounts of it. Rschwieb (talk) 00:05, 23 June 2013 (UTC)


 * I agree with your complaint with linear equation, it sort of wades into the definition from the shallow end instead of having a clear definition section, which tends to compound misunderstanding as the article develops since encyclopedic writing communicates implicitly. It's in such bad condition because there are no users with a vested interest in the article, at least not ones with the reference material to formulate the article properly. Contrast it with Abelian group, which has a more typical structure, one in line with MOS:MATH. I don't know what your complaint with quadratic function is. Neglecting to equate a polynomial of degree at most one with a line is obscuring the concept and truth of the matter - polynomials are curves. The Planetmath article you refer to for linear function is a generalization of an affine map to other incidence structures (without a distinguished origin, the exact analogue wouldn't apply). While it can be mentioned in a generalization section of that article, it's not particularly relevant, as it doesn't inform the reader of any flexibility in the concept vs. the formalism that isn't owed entirely to the generalization from affine spaces to the other incidence structures. ᛭ LokiClock (talk) 02:03, 23 June 2013 (UTC)


 * 1) Firstly, thank you all for replying. My experience with wikipedia in this area has not been good.  I appreciate and welcome discussion.
 * 2) I have no complaints at all with either Constant function or Quadratic function and state so specifically.  In fact, I state that Linear function should take its natural place between these and not try to be all all things to all people. I do not think that it is useful to consider a constant function as a linear function and broaden the definition explicitly, particularly as there is a separate article on constant functions. To avoid this problem, one could simply state that a linear function ia a polynomial function of first degree and then say that its graph is a inclined line. (I debated about the order of these two sentencea for a long time....) There is a plethora of definitions of linear functions including allowing x=C (which i presume we all agree is not a function). Stating that a square is also a rectangle and so a linear function must include a constant function is again not useful. A rectangle is also a parallelogram and using that analogy one could consider a quadratic function to include linear and constant functions...  One could mention that some references include constant function as a linear function even though it is a polynomial of degree 0 because it is a function whose graph is a line... . I firmly object to categorizing a linear function as a calculus topic Linear function (calculus). It only serves to make readers afraid and certainly it not introduced in calculus.
 * 3) I see that the article Linear function has been changed now at least to reflect the possibility of the general math definition. No images or anything... That was my original intention in writing the article that was first utterly disdained as non-wikipedia since it dared to have images and media, then marked for speedy deletion as it supposed duplicated this article which at the time was devoted exclusively to linear mappings and which itself duplicated the article Linear mapping, then it was renamed and completely changed to the article mentioned in the above passage without any hint of allowed discussion (and no I do not consider myself the most qualified, but I certainly am qualified and so I do not consider these good intentions....).
 * 4) An aside...  Ask an engineer, what is an "affine map"? Ask him, what is a "linear function"?  (I dont dare say ask a regular adult either of these questions although presumably they all passed algebra 1 and studied this stuff for years.)
 * 5) What do you consider a good source? A commercial textbook and at what level would be acceptable here? Tthe Common Core State Standards for Math from the USA, Planet Math,  ...? I tried to find a wide variety of online sources to illustrate that fact that the generally accepted definition of a linear function is not that of linear mapping (or operator).   I only included planetmath as it tends to start from the highest level and even it considered linear functions as separate topic from linear mappings. I certainly did not mean to imply that we should go their way  in wikipedia (argh).
 * 6) Finally my point in writing here is that linear equations and linear functions are fundamental topics. They are the first topics in "algebra" where we lose so many children and hence adults. The term linear in linear equations applies to the degree of the polynomial  The term linear function applies to the graph being a line in the plane. (Questions: Would a linear equation include a constant function which is considered to be from R to R? Do we consider the e.g. parametric function of a line in 3d to be a linear function? I dont know.)  We need to make this distinction between linear equations and linear functions very clear. We extend these definitions implicitly when talking about linear inequalities, systems of linear equations, quadratic functions, ... If we are not clear and mix simple examples and complicated language, then we are just talking to ourselves.Lfahlberg (talk) 09:46, 23 June 2013 (UTC)

Some examples of "good" sources from Google books, picked at random to give you a head start, with the headings on the topic typed in the search engine (with slight variations):


 * Linear transformations


 * New Foundations in Mathematics: The Geometric Concept of Number, Garret Sobczyk
 * Advanced Engineering Mathematics, Peter V. O'Neil
 * Advanced Engineering Mathematics, Volume 1, H. C. Taneja
 * Advanced Engineering Mathematics, Alan Jeffrey


 * Linear equation


 * Linear Algebra Georgíj Evgenevítsj Shilov
 * Convergence of Interations for Linear Equations, Olavi Nevanlinna
 * Elementary Linear Algebra: Applications Version, Howard Anton, Chris Rorres
 * A First Course in Linear Algebra: With Concurrent Examples A. G. Hamilton
 * Matrices and Linear Algebra, Hans Schneider, George Phillip Barker


 * Affine transformation


 * Geometry, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray
 * 3D Computer Graphics: A Mathematical Introduction with OpenGL, Samuel R. Buss
 * Transformation Groups For Beginners, S. Sergeĭ Vasilʹevich Duzhin, B. Boris Dmitrievich Chebotarevskiĭ


 * Linear inequality


 * Systems of Linear Inequalities, A. S. Solodovnikov
 * Advances in Linear Matrix Inequality Methods in Control Laurent El Ghaoui, Silviu-Iulian Niculescu
 * Linear Programming and Extensions, George Bernard Dantzig


 * Linear function


 * Linear Functions and Matrix Theory, Bill Jacob
 * 'Linear Functional Analysis'', Bryan Patrick Rynne, Martin Alexander Youngson
 * Applied Functional Analysis: Applications to Mathematical Physics, Eberhard Zeidler
 * Mathematics as an Educational Task, Hans Freudenthal

Basically: university textbooks (undergrad, grad), research monographs, papers in peer-reviewed journals, ect. Planet math is not reliable as a wiki, as others have said.

You may also want to see cite book, cite journal, cite article, cite webpage, for uniform formatting of references (but they're not essential), in case you haven't encountered them already. Best, M&and;Ŝc2ħεИτlk 10:59, 23 June 2013 (UTC)

Excuse me, these are are sources for the topics Linear function and Linear equation? None of these, that is, not one is at the level at which these topics are introduced and at which someone looking up the topic would understand. That is my entire point.Lfahlberg (talk) 11:12, 23 June 2013 (UTC)

I am the person who "fixed" and "renamed" an original version, called Linear function (mathematics), and I already looked at Constant function and Quadratic function about half-year ago, during the previous discussion. Moving the article to linear function (calculus) was an emergency measure to prevent creating links to a nonsensical title. Probably the article would be better called linear function (mathematical analysis), linear (affine) function, constant-derivative function, or whatever: I do not object against any title which copes with the ambiguity in any meaningful way. Also, $y = b$ is a “linear” function, but $Ax = C$ is not. Look at piecewise linear function to understand why this definition have more sense than other two possibilities (i.e. excluding constants, or including implicit functions). Also, linear function is a mishap, a stuff which actually may not be an article, and I hope it is a transitional phenomenon. Incnis Mrsi (talk) 11:19, 23 June 2013 (UTC)

I knew I should give up when I gave up. It was just reading the article on Linear equation; it said "try again". Nope, now for sure I am out of it. Have at it. Definition of wikipedia math: math articles by and for mathematicians. P.S. I love that you are so certain that $y = b$ is a “linear” function, but $Ax = C$ is not. How can you tell that $y = b$ implies an independent variable and so must be a function. To a non-mathematician, they are exactly the same sentences, particularly when you substitute numbers (and not little and capital letters to confuse them). Lfahlberg (talk) 11:36, 23 June 2013 (UTC)


 * Up to you, but you shouldn't give up this soon and this easily just because one (me?) or more of us are incompetent.


 * About sources earlier - you asked what are "good" sources, so I simply (attempted) to answer you question in good faith - those are the typical types of books we add to wikipedia.


 * So you want to add schoolchildren books to WP for references? M&and;Ŝc2ħεИτlk 11:56, 23 June 2013 (UTC)
 * Your in/dependent variables do not make any sense: it was already pronounced at talk: Linear function (calculus). It is because we, mathematicians, cease to think about variables whenever a construction becomes to belong demonstrably to certain class or set. To you, a “number” or a “function” is something written on a blackboard, paper, or HTML page, i.e. some symbolic notation. To us, member of the WikiProject, a symbolic notation only represents an element. A function is something which is a function due to certain theorem, possibly rather trivial. For example, a polynomial (coefficients of which are numbers) is a function. Or: the composition of two functions, where the codomain of the right-hand one matches the domain of the left-hand one, is also a function. You cannot think as we think, and we have to make great efforts to think as you think. That’s why we do not understand you and you do not understand us. Incnis Mrsi (talk) 11:58, 23 June 2013 (UTC)

With these sentences you have absolutely proven what I said: Definition of wikipedia math: math articles by and for mathematicians. And not just mathematicians. Apparently one must be supercilious. Since I am not, that is why I don't understand you. I think that articles in wikipedia should instruct and encourage. Pity the actual reader who comes in thinking he might learn something useful (as with most non-math articles in wikipedia, thank-goodness). Lfahlberg (talk) 12:31, 23 June 2013 (UTC)
 * To instruct, but not to stuff a reader’s brain with dependent and independent variables only because someone’s dogmatic mind can’t think about functions without these surrogates. One should investigate the structure of variables when deals with coordinate systems, partial derivatives, implicit functions, and so on. Not for what we are speaking about. Incnis Mrsi (talk) 12:42, 23 June 2013 (UTC)

Just a remark: the term linear in linear equation does not refer to a polynomial degree but to the linearity of the map T in an equation T(x) = b, where x is the unknown (vector). Besides scalar linear equations there are linear differential equations, linear integral equations and so on. Feel free to consider de:Lineare Gleichung as a starting point, which I wrote some time ago. Best wishes, --Quartl (talk) 15:15, 23 June 2013 (UTC)


 * I agree that the linear equation is a bit problematic. I'm still not clear on what the problem is with linear function/linear function (calculus), in spite of all the discussion above.   Sławomir Biały  (talk) 18:24, 23 June 2013 (UTC)
 * Sorry, I must be slow on the uptake. It occurs to me that User:Lfahlberg's first attempt at an article was treated a bit unfairly by one of Wikipedia's reviewers (WP:BITE, etc), and then as if to add insult to injury (because of a post here) many mathematics editors started piling on.  His or her reaction to all that is understandable.  Sometimes that's the way it rolls on Wikipedia.  One sometimes unfortunate corollary of being the encyclopedia that anyone can edit is that "anyone makes mistakes", as we all know.  "Assuming good faith" is what we're supposed to do, but I'm a bit too cynical for that: I prefer a good sense of humor.  In any case, it would be a shame to lose an editor with an interest in improving the accessibility of Wikipedia's mathematics content.   Sławomir Biały  (talk) 19:52, 23 June 2013 (UTC)

Special:Contributions/99.241.86.114 again
Aside of well-known “latex-to-html” campaign, he is engaged in another crusade: replacing $S^{n}$ for n-sphere with Sn. See [] as a recent example. Incnis Mrsi (talk) 11:58, 23 June 2013 (UTC)
 * For clarity, in this instance it does not appear to be a change in the use of  or of math, only changing of italic S to roman bold S.  As this is a symbol and not a variable, neither is in accordance with WP guidelines – it should be simple roman (neither bold nor italic, e.g. $S^{1}$ or S1).  Since in this case I think the guidelines give a definite preference, this should be resolvable, and the IP editor should be guided rather than persecuted.  — Quondum 17:00, 23 June 2013 (UTC)

Random math article
Hi folks, I was perusing the archives, and happened upon a random math article link, maintained on a separate server by User:Jitse Niesen (operator of User:Jitse's bot). Is it worth adding this to the WP:WPM homepage? Sławomir Biały (talk) 21:38, 21 June 2013 (UTC)


 * Fun and more useful for the mathematically inclined than the Special:Random link in the sidebar. I think it would be worth adding. --Mark viking (talk) 21:55, 21 June 2013 (UTC)
 * Actually, I'm a bit pleasantly surprised of the general quality of articles that the random math link generator produces. Overall, they seem to be of a generally higher quality than the articles linked by Special:Random.   Sławomir Biały  (talk) 22:31, 21 June 2013 (UTC)


 * Sure, why not? Michael Hardy (talk) 17:16, 22 June 2013 (UTC)

I've gone ahead and added it to WikiProject Mathematics/Nav, the navbox that appears on the right-hand side of the project page, as this seems to be the most convenient place to have the link. But as always, feel free to change it (or complain about it here :-)  Sławomir Biały  (talk) 18:21, 24 June 2013 (UTC)

A wild idea: multi-tiered maths articles to match the target audience?
I fairly regularly observe the tension between those who feel math (and physics) articles should be aimed at introductory level (let's say, at least understandable to a senior school child or the non-mathematical layman), and those who feel that that it should address the topic more in line with the serious scholar, say an undergrad or postgrad studying the topic. There seems to be potential value to readers in both domains in WP, but the spread is a bit large to be addressed in a single article (even with the current formula of an "understandable" lead and introductory sections) and is getting more so. The "simple English" version may not adequately address the lower end of the WP spectrum in this sense. Only a part of the problem is that the lower end sometimes expects a pedagogical approach (e.g. linearity above). I think the pedagogical approach should be discouraged in WP, but there may still be a need for an approach with multi-tiered maths reference articles, which cross-reference and complement each other. Would it make sense for Wikiproject Mathematics to pioneer such an idea? — Quondum 17:33, 23 June 2013 (UTC)


 * There is some precedent for this, having separate "Introduction to X" articles. While this can sometimes work, for example, the two featured articles General relativity and Introduction to general relativity, more often I think what happens is that content becomes too forked and fragmented and we end up with a collection of bad articles rather than one article (which may be good or bad, but at least it's only one to worry about).  This was the case until recently for essentially all of our articles on tensors.  I think it would be better to focus on bringing existing articles up to standards, especially WP:LEAD and WP:MTAA.  If there is enough material to fork, then (and only then) should it be forked.   Sławomir Biały  (talk) 18:19, 23 June 2013 (UTC)


 * We do have some multi-tiered articles like this, for instance, Group (mathematics) and Group theory. I agree with Sławomir, however. If possible, single articles are more useful for our readers and give a better overview for the whole topic. There is nothing wrong with having an Introduction or Elememtary usage section to explain how the topic is treated in pre-college courses. More sophisticated users can use the table of contents to skip to the advanced stuff. --Mark viking (talk) 18:50, 23 June 2013 (UTC)
 * I'm going to renew my point here that that's the wrong distinction between group (mathematics) and group theory. The distinction should be that the former is about groups, whereas the latter is about the theory of groups.  That is, an article called group (mathematics) should tell you what a group is, why it's important, and what you do with one.  An article called group theory should discuss the work of mathematicians primarily interested in groups themselves.
 * Now, in practice, to some extent, the two formulations may overlap. Indeed, I think the articles are currently largely written in the way I suggest, with one exception I'll get to.  So what I'm talking about here is not so much a proposal to restructure anything, as to adjust how we think about the existing text.
 * But here's where you see the distinction: Some applications of groups come up inside group theory, some outside.  The latter ones (for example, anything from physics) belong in group (mathematics), and not in group theory, no matter how "advanced" they are, because they're about groups, but they're not about group theory.
 * Just to head off another possible confusion: No, this is not a pure-vs-applied distinction either; groups might show up in some other very pure field, say descriptive set theory.  As long as it's not from group theory, it belongs in group (mathematics).  --Trovatore (talk) 19:51, 23 June 2013 (UTC)


 * Thanks for the link to WP:MTAA – it is excellently written. From this it seems that several working options have already been identified; being familiar with these guidelines and essays is really helpful. — Quondum 18:56, 23 June 2013 (UTC)
 * This approach would be, at best, precocious when WikiProject Mathematics still has not a comprehensive content guideline for articles intended for experts (at least, professionals). Such problems as:
 * Which notation to assume well-known?
 * How to explicate/declare a notation which is not assumed well-known?
 * How to make the notation consistent across articles? (at least closely related ones)
 * How to make terminology and definitions consistent across articles?
 * How to refer to logical systems used?
 * Numerous conflicts related to “spaces” and “vectors”
 * still wait a solution. When a good content guideline “for adults” appeared, the time to develop content guidelines “for children” will come. BTW, miles of flame at IMHO shall be simply disregarded: the “problem” is not about certain article, but about disagreement of one editor with a style established here and such Wikipedia fundamental as editing of his articles by other editors. There are problems more important than to satisfy demands to explicate the content according to someone’s favorite textbook and exotic mindset. Incnis Mrsi (talk) 20:24, 23 June 2013 (UTC)
 * I agree with you on every point, and have already effectively withdrawn my proposal. My reference to the section linked above was merely a recent example of a common tension, I realize now not adequately representative of the usual goodwill request for something that may be understood by entry-level readers.  I think that the guidelines already documented are fine for the moment, and will be progressively adapted and fine-tuned through collective experience and collaboration.  — Quondum 23:18, 23 June 2013 (UTC)

I might ask why a mathematician might read an article in Wikipedia on say e.g. Linear function? If he doesn't remember what a linear function is (and that it is usually called a linear mapping or linear operator), then doesn't he have his own textbook (if he is a student) or his books in his own personal library to look it up? I certainly do (I still own Dunford and Schwartz, the bible on linear operators and it is still in print even though it is as old as I am). I never noticed the incredible uselessness of Wikipedia articles on standard math topics because of course I never used them. I do use Wikipedia all the time and I am INCREDIBLY GRATEFUL that the articles on which I needed information were written so that I could understand them and actually learn something. It is only because I have been working on creating resources for non-mathematicians (who BTW include adults) that I started reading them and this attitude here that only major-in-mathematics university level explanations are acceptable, that mathematics starts with calculus, that only "high-level" textbooks are acceptable resources and that speaking mathematics using normal words and sentences is unacceptable is not right, nor is it the purpose of Wikipedia and it is, of course, the (justifiable) reason that most people are so terrified of mathematics that they refuse to learn anything at all. They are NOT stupid - we are stupid for not explaining mathematics in ways and at a level that they can understand.

I absolutely fail to see why in a single Wikipedia article one cannot start at a basic level of explanation and proceed up the mathematical ladder. I am very sorry Quondum that you have withdrawn your proposal. As a final question I would ask those reading this to ask themselves "Who are the over 1000 people per day who access Linear equation?".

I will add a line from a letter I just received from a colleague (university professor) with a tremendous online math resource (pauls notes) that I use constantly to help me explain mathematics in reply to an email I wrote him to say that he should add the words "in one variable" to his definition where he states: a linear equation is an equation of the form ax+b=0. His response is excellent as he writes:
 * You are correct of course in your definition and I do cover linear equation in two and three variables later in the material. I suppose the reason that I didn't mention "one variable" at that point (it's been a while since I wrote the notes so I don't recall all my reasoning!) is that most of the students I would get in an Algebra class (also been a while since I've taught Algebra) had trouble doing even basic exponent operations and so I figured let's not "confuse" the issue by mentioning cases that we wouldn't be covering until the end of the semester.  Many of the students could handle it but a sizable portion would get locked into me mentioning a case that we weren't going to cover  right away and would have trouble getting past that point.  That is not to say they are "stupid" or incapable of understanding but they tend to be so "math phobic" that they would spend too much time concentrating on unimportant issues (at the time anyway) and not enough time trying to understand the topic at hand.

Lfahlberg (talk) 15:36, 25 June 2013 (UTC)


 * Articles are to some extent expected to start at a fairly basic level, see WP:MTAA. I don't think anyone here would disagree that our articles on elementary mathematics are sometimes quite inadequate (even mathematics at the college level is woefully poor in some areas).  Someone with extensive professional experience in pedagogy is a boon to the project.  I for one think that there is nothing wrong with citing good sources that are not targeted at college majors.  Some of our best articles cite a variety of such sources.  It's simply ludicrous to suggest that journal articles and higher level texts are "better" than sources aimed at a different audience.
 * But I think it may have already been pointed out that there isn't really any philosophical agreement among members of the project exactly what mathematics in Wikipedia should look like. Some would adopt a Bourbaki point of view of the subject, and attempt to create a precise and rigorous mathematical cipher.  Others may want articles to be read by their peers.  Still others want articles that are readable by their students (which may include high school students, college students, graduate students).  I also want mathematics articles suitable to be read by my children and nieces and nephews.  This is all part of the culture, and often these philosophical differences lead to conflict.  That isn't a bad thing: it's an essential part of the process.  But it does take getting used to, and sometimes there are some aggressive personalities to deal with.  Sławomir Biały  (talk) 18:23, 25 June 2013 (UTC)


 * I fully agree with Sławomir. However, there is an important class of readers that he has omitted, and that is neglected by most WP editors: the readers with a good scientific knowledge who are looking on information on subjects that are outside of their domain of competence. The information that such reader are looking for is frequently very often lacking in the WP article. Several examples that are not far from the example of linear function: In practice, many users, like engineers, use real functions of several real variables; I am unable to find any article on this subject. The article system of linear equations needs to be carefully read to learn that there are very efficients algorithms to solve huge systems (up to millions of equations and variables). An information that is essential for most users of such tools is the possibility of numerical instability. This is not even cited in this article. I could continue with many other examples. When you edit WP, please, keep also in mind this category of users (academics and engineers that need usable information outside their domain of competence). D.Lazard (talk) 22:27, 25 June 2013 (UTC)


 * Oh, so sorry to chat again here, but this is the stuff of my dreams - cooperation between the communities in writing useful articles. I am a professor of mathematics in the engineering department of my university. My degrees are in theoretical maths and I have spent most of the last 20 years trying to make math understandable and useful for engineers - but first having to learn it myself! (Just a teensy low-low-level example - engineers are always using functions involving parameters and yet this has got to be one of the least well explained areas in mathematics (including the fact that even in WP constants are referred to as parameters). Lfahlberg (talk) 10:26, 26 June 2013 (UTC)


 * Considering D.Lazard's point above that no article on real multivariable functions exists, I made a clumsy start. Anyone is more than welcome to complain on the talk page. Thanks in advance M&and;Ŝc2ħεИτlk 13:31, 26 June 2013 (UTC)
 * It may have been raised before, but is there any reason for Real-valued function when we have Function of a real variable?. Real-valued function (a two-sentence dictionary def) should just redirect to Function of a real variable. M&and;Ŝc2ħεИτlk 14:17, 26 June 2013 (UTC)
 * Ummm ... aren't they different things ? A real-valued function is a function to the reals whereas a function of a real variable is, in general, a function from the reals. Even if you restrict "function of a real variable" to be only functions from R and to R, real-valued function is still a more general concept. Gandalf61 (talk) 14:32, 26 June 2013 (UTC)


 * Whatever. Leave them separate. M&and;Ŝc2ħεИτlk 16:21, 26 June 2013 (UTC)

Euclidean space: inner product, dot product and Cartesian coordinates
I'm trying to clarify the distinction between an inner product and a dot product in a few related articles, and I want to make sure that I've got the concepts straight. I'm bumping up against the classic problem of trying to determine how much a concept has been defined too concretely (and hence has lost its generality) as a result of the pedagogical process, in this case the general concept being taught in terms of Cartesian coordinates, and being worded in WP to exclude the original, correct and more general (and more abstract) definition. Please correct the following: I intend to word the articles so that the distinction between a real coordinate space with a dot product and a Euclidean space with an inner product is respected, in general avoiding introducing abstractness. — Quondum 23:21, 23 June 2013 (UTC)
 * A Euclidean space is an inner product space in which the underlying scalars are the real numbers.
 * The dot product is defined as a coordinate-wise sum-of-products of Cartesian component vectors in Rn.
 * Since there exist many inner products on component vectors in Rn that do not fit the definition in the previous bullet (i.e. they have a positive-definite symmetric bilinear form that is not represented by a diagonal matrix), not every inner product on Rn is a dot product, even though there is always an isometry with the dot product on Rn.
 * Since a Euclidean space in the abstract sense need not be defined in terms of Rn and an associated inner product (even though it is always isomorphic with it), strictly speaking a dot product is not defined on an abstract Euclidean space, only on the Cartesian coordinate vectors of the associated decomposition in terms of any selected orthonormal basis).
 * IMHO the main distinction between “inner product” and “dot product” is that the former is a general concept (applicable to complex vector spaces, possibly also to spaces over arbitrary ordered fields and their extensions), whereas the latter is something over not wider than $R$ and usually in finite dimensions. The decision to use one or another should be bases not on coordinate/Euclidean distinction, but on the scope of an article. If the article focuses on such properties as positive-definiteness of the form and derivation of topological structure from it, then the link should be inner product space. If the article focuses on geometrical aspects of Euclidean spaces of low dimensions, physical uses of 2- and 3-vectors, as well as row and column vectors, then the link should be dot product. BTW, is a finite-dimensional $∑_{k} u_{k}v_{k}$ a “dot product” over an arbitrary field, where it is not an inner product, such as over complex numbers? Incnis Mrsi (talk) 06:15, 24 June 2013 (UTC)


 * The dot product's formula as a sum of products can be taken as its definition. The components are scalars, not vectors (vector multiplication need not be defined first). But in particular, the dot product has geometric meaning, perhaps clarified by vector projection. Hence it is also defined on abstract Euclidean space. ᛭ LokiClock (talk) 02:02, 26 June 2013 (UTC)


 * @Incnis: if defined in terms of components, I suppose the dot product would be defined over an arbitrary field. This is how it is defined in dot product, but from your description, it sounds like the Euclidian geometric interpretation is the appropriate definition, and that the component version then would only apply when the vectors have a geometric interpretation (though even geometric is hazy: vector spaces over any fields for which a symmetric bilinear form is defined sometimes seem to be called "geometric").  This would suggest that this article needs rewording, not using the sum-of-products definition.  It feels more natural to me, the way a physicist, engineer or geometer would interpret it.  The summed products definition would then be called a summed component-wise products or similar, but would not qualify as a dot product.  However, people who deal only with matrices might object.  Anyhow, the question is whether we should adopt this definition and modify the article.
 * @LokiClock: You can't have it both ways. But you can define it in terms of the component-wise sum-of-products with the restrictions that the basis is orthonormal in a Euclidean space, and then extend the definition to any Euclidean space.  But in that case, it makes sense to do it the other way around: define it geometrically, and then derive the sum-of-products in the special case of an orthonormal basis, not as a matter of definition.  My point originally was in effect that the bland component-wise definition is not consistent with the geometric interpretation in general.
 * So, I guess I should seek consensus on the correct definition of a dot product first, but I guess that discussion should be at the talk page rather. — Quondum 02:46, 26 June 2013 (UTC)
 * Well, both definitions are correct in the sense that they appear in high quality sources.  Sławomir Biały  (talk) 07:18, 26 June 2013 (UTC)
 * Nobody doubts that all three standard definitions of dot product (abstract bilinear form a.k.a. inner product, $∑_{k} u_{k}v_{k}$ in a Cartesian basis, and the product of the cosine and lengths) are applicable to $E^{n}$. The question is whether should we refer to such things as $∑_{k} u^{k}v^{k} = uT v$ for two column vectors as to a dot product, even over non-ordered fields/rings. Incnis Mrsi (talk) 08:50, 26 June 2013 (UTC)
 * In $C^{n}$ it's also called dot product by many authors, see for example . Best wishes, --Quartl (talk) 11:12, 26 June 2013 (UTC)
 * @Quartl: Unfortunately, that definition corresponds to the inner product (a sequilinear form) under the name "dot product", not to a general extension of the dot product to arbitrary fields (a bilinear form). I think that the definition corresponding to the bilinear form over complex numbers occurs as well, especially in physics, but I'd have to check.
 * @Incnis: A general definition of the dot product in terms of the components just does not make sense, except in the limited (and usually pedagogical setting) where the definition starts "Assume an orthonormal basis for a vector space...". The two definitions currently in dot product are incompatible, and I would suggest that the "algebraic" definition ("an algebraic operation that takes two equal-length sequences of numbers") should be regarded as incorrect even in a Euclidean space, because it fails to assume the orthonormality constraint. As to whether the term should be taken to be synonymous with symmetric bilinear form for arbitrary fields would require a notability check, but I suspect that it might find use over arbitrary fields, e.g. in Clifford algebra. — Quondum 12:14, 26 June 2013 (UTC)
 * One is free to regard the definition as incorrect, but this is how basically everyone does define it (not just in pedagogical contexts either). If you feel that it's an important qualification, you can add that the coordinates of the vectors are Cartesian coordinates.  It would be inappropriate to introduce orthonormal bases, not only because most sources do not, but also since the notion of orthonormality already presupposes the existence of an inner product.   Sławomir Biały  (talk) 13:10, 26 June 2013 (UTC)
 * Certainly, orthonormality is, in most general case, derived from a bilinear form, not versa. You do not need concepts of orthogonality and norm to define $uT  v$: for coordinate space (of finite dimensions) it is defined over an arbitrary field or ring. The problem is that, although the definition is universal to aforementioned conditions, it makes a thing with properties of an inner product space only if scalars possess a total order and commute. Over complex numbers there are both $uT  v$ (a bilinear symmetric form) and $u* v$ (a sesquilinear inner product). The latter is never called a dot product, but what about the former? Incnis Mrsi (talk) 13:43, 26 June 2013 (UTC)
 * I see the question with dot products in Euclidean spaces as the least difficult. Yes, it is an inner product. Yes, it matches the $∑_{k} u_{k}v_{k}$ only in orthonormal bases/Cartesian coordinates. No terminological clash: we just define the dot product in an Euclidean space as the same thing as its inner product and the dot product in orthonormal bases. I do not think one should strike through “dot product” and replace it with “inner product” wherever an article has no reference to an orthonormal basis. Incnis Mrsi (talk) 13:43, 26 June 2013 (UTC)
 * Implicit use of an orthonormal basis is often sufficient to qualify something as a dot product. I'll see what I can do to implement this discussion into the articles concerned.  — Quondum 02:20, 27 June 2013 (UTC)

Sign conventions in rotation representations
I’m tired to see numerous edits like [] in numerous articles related to 3d rotations. Could someone make a page (in Wikipedia: or User: space) with reviews and substantiations for all these sign conventions? It would become easier to revert “correctors” (although this concrete case is not typical) without searching for an inconsistency. Incnis Mrsi (talk) 07:16, 26 June 2013 (UTC)
 * Ugh, agreed! I was just looking at this. Surely enough people have been over it to ensure it was correct in whatever convention it was using. Rschwieb (talk) 13:54, 26 June 2013 (UTC)
 * It's easy enough to verify that the x, y, and z rotation matrices are consistent; it's more difficult to determine whether they are in left- or right-handed coordinate systems and whether they are covariant or contravariant representations. A page in Wikipedia:Wikipedia Project Mathematics space would be good, though.  — Arthur Rubin  (talk) 17:51, 26 June 2013 (UTC)

Mathematical abbreviations are Latin abbreviations, not English
I was told this was the place for discussing content issues concerning mathematics.

I noticed a preposterous claim as I read the page Limit: "In formulas, limit is usually abbreviated as lim as in lim(an) = a". It sounds like lim is an abbreviation of limit when it in fact is a abbreviation of limes. You could believe that this was an exception but after reading several other articles such as Natural logarithm (with ln = logaritmus naturalis), logarithm (with log = logaritmus), Sine (with sin = sinus) there seems to be a policy of denying history here. In the history section of sine the sceptic reader gets altered that sin is short for sinus and not sine, but thats about it. I think it needs to be clarified in each article what the abbreviation stands for when it's used for the first time. --Immunmotbluescreen (talk) 12:26, 22 June 2013 (UTC)
 * Are you a history of science expert? Okay, start please from explicating the tale how an ignorant Arabic-to-Latin translator invented a nonsensical term “sinus”. Incnis Mrsi (talk) 13:46, 22 June 2013 (UTC)
 * I have no problem pointing out what the abbreviations derive from, if it can be appropriately sourced. I also don't see what's wrong with the passage you quoted.  Is limit abbreviated in some other way you want to have the article point out?  Sławomir Biały  (talk) 14:19, 22 June 2013 (UTC)
 * Obviously you would want it to be "usually abbreviated as lim (for limes) as in lim...". Since everybody knows that this is the case there is no need to have a source.--Immunmotbluescreen (talk) 20:12, 28 June 2013 (UTC)
 * Because saying "usually abbreviated as lim (for limes)" is in no way confusing to a typical English reader?? Sławomir Biały  (talk) 20:50, 28 June 2013 (UTC)
 * Mathematical terms are not Latin abbreviations. Their etymology or history is not a part of their definition or expositions. Thanks, Anand (talk page) 16:08, 22 June 2013 (UTC)
 * Not there terms but the abbreviations--Immunmotbluescreen (talk) 20:12, 28 June 2013 (UTC)
 * The claim that limit is abbreviated lim is not preposterous at all: it is entirely correct. Are you suggesting that limit is abbreviated as anything else?  A discussion about why those three letters are used might be appropriate provided of course that it was supported by reliable sources.  There are other cases in natural English and in mathematics where abbreviations derive from Latin or indeed other languages.  For example, "for example" is abbreviated "e.g.".  To suggest that all mathematical abbreviations are Latin is simply incorrect.  Many twentieth century abbreviations derive directly from German (Z) or English, (glb, hcf, Tor).    Spectral sequence (talk) 16:23, 22 June 2013 (UTC)
 * Technically it is correct but as I said it confuses the reader to believe that lim is an abbreviation of limit. It only goes one way. Maybe not all but the most common and old mathematics. --Immunmotbluescreen (talk) 20:12, 28 June 2013 (UTC)

"lim" may originally have been an abbreviation of "limes", but that doesn't mean it is an abbreviation of only the Latin word. And when one writes
 * $$ \dim\ker(T) + \dim\,\operatorname{Im}(T) = n, \, $$

the abbreviation "ker" quite obviously comes from a Germanic root, not from Latin. One cannot claim any generality for a statement that there is only one language from which mathematical abbreviations are ultimately derived. Michael Hardy (talk) 17:42, 22 June 2013 (UTC)
 * Not to mention the abbreviations a.e., a.s., l.i.m. (limit in measure) which all derive from English, p.p. and cadlag which derive from French.  Sławomir Biały  (talk) 19:57, 22 June 2013 (UTC)
 * I am not sure of the correctness of the above interpretation of "ln" as an abbreviation of "logaritmus naturalis". In fact, for French mathematicians, "ln" is an abbreviation of "logarithme népérien" (Neperian logarithm). An historical research or a reliable source would be needed to decide which etymology is correct. D.Lazard (talk) 20:46, 22 June 2013 (UTC)
 * Actually, within mathematics lim only stands for limes. The face that English derives from French which derives from Latin and happen to have similar words does not alter what the abbreviation stands for. --Immunmotbluescreen (talk) 20:12, 28 June 2013 (UTC)
 * Is there a reliable source for this extraordinary assertion? Spectral sequence (talk) 20:30, 28 June 2013 (UTC)
 * Google books finds quite a few . For instance, it's in Florian Cajori's History of Mathematical Notation . —David Eppstein (talk) 20:35, 28 June 2013 (UTC)
 * There's no question about the etymology of "lim". What's debatable, however, is the assertion that "within mathematics lim only stands for limes".  How many mathematicians think of "lim" as standing for "limes"?  Should this perspective be emphasized in an encyclopedia article on the topic (outside of the history section)?  Sławomir Biały  (talk) 20:49, 28 June 2013 (UTC)
 * Immunmotbluescreen's assertion has several components: (1) that English derives from French (which is false) (2) that lim is short for limes (which is true) (3) that in mathematical writings lim derives only from Latin limes and never derives from French limite or English limit (which is extraordinary). Cajori observes that Cauchy used lim. and Cajori makes it clear that Cauchy was writing in French, not Latin.  So let me repeat my question.  We have yet to see a reliable source that supports the assertion that "lim" is an abbreviation only for Latin limes and explicitly states that it is not an abbreviation for French limite or English limit.  In the opposite direction, there are certainly English-language sources that show that limit is abbreviated lim, for example,, , , ...  The "only" part of the assertion has no demonstrated support.  Spectral sequence (talk) 20:58, 28 June 2013 (UTC)
 * Why do we even need to talk about this? I'm just going to repeat my suggestion from below &mdash; change "abbreviated by" to "denoted by" and be done with it, except maybe in the history section.  Who cares what it stands for, in a discussion of the mathematics? --Trovatore (talk) 21:00, 28 June 2013 (UTC)
 * We only need to talk about it because one particular user appears determined to advance a personal view about this subject even thought they have produced no sources to support their unusual views. Trovatore's suggestion seems perfectly adequate to me.  Spectral sequence (talk) 21:04, 28 June 2013 (UTC)
 * Good grief. I've gone ahead and implemented this minor wording change.   Sławomir Biały  (talk) 21:20, 28 June 2013 (UTC)
 * This discussion appears to be the continuation by the original poster of the tendentiously-named Village_pump_(policy). Spectral sequence (talk) 20:52, 22 June 2013 (UTC)
 * For the most part, these complaints can be resolved simply by removing any claim that the short forms are abbreviations for anything in particular. For example, rather than saying that limit is "abbreviated" as lim in formulas, say that it is "denoted" as lim.  What if anything lim is short for is not really important to understanding limits.  However, if sourceable, it could be explained that lim originally abbreviated limes, in a separate "etymology" or "history of notation" section. --Trovatore (talk) 22:29, 22 June 2013 (UTC)
 * For consensus, I agree with everything Trovatore just said. M&and;Ŝc2ħεИτlk 11:14, 23 June 2013 (UTC)

Review of trolling vandal edits requested
These edits are few in number, but seem intent on subtle (under-the-radar) and lately not-so-subtle (provocative) degradation of WP math content. The first five edits and the last (as of now) have remained unreverted. Could someone check these? I don't feel confident enough in these areas to be sure that every edit constitutes vandalism, though they seem to me to be. The very small number of edits under a named account all apparently being vandalism suggests the possibility of several socks being operated in parallel. — Quondum 01:59, 24 June 2013 (UTC)
 * , given in isolation, is anything but certainly not a good-faith edit. Let us wait for several next edits to determine whether the operator has any positive intentions. In my considered opinion, after yet one edit such as replacement of “$x$” with “65” the account shall be blocked without further deliberations and investigated by WP:CheckUsers. Incnis Mrsi (talk) 06:15, 24 June 2013 (UTC)
 * I tend to agree, but I've reverted all but one of his remaining edits, and given a final warning. (One of the edits was actually good.)  — Arthur Rubin  (talk) 08:01, 24 June 2013 (UTC)
 * FYI is his new, active sock. Feel free to track and/or block it, but I will not help anymore because I’m disappointed and upset about rampant incompetence and dickery of the people related with sock hunting. Note that I do not refer to CheckUsers themselves. Incnis Mrsi (talk) 06:56, 25 June 2013 (UTC)
 * Incnis Mrsi has reverted a closure by an SPI clerk on an SPI report page (started by me). He added the editor above. When Incnis Mrsi reverted the close, only one of three edits was odd, so there was no clear pointer to sockpuppetry, beyond circumstantial evidence (recently created account, same section of article). However, they seemed to have some mathematical understanding of the error in the previous proof (dependence on k) and looked as if they were shortening the argument. In those circumstances, adding comments here about "rampant incompetence and dickery of the people related with sock hunting" is inappropriate. Even the posting above is premature. When reverted by the SPI clerk Rschen774 for reverting an administrative close, Incnis Mrsi complained on the clerk's page. The clerk responded: "Well that's not a very good attitude to have.  As Mathsci stated, you are welcome to open a new report. However, you should not be reverting the actions of a clerk." Determining sockpuppetry requires patience and carefully reasoned arguments with diffs. Sometimes it takes days or weeks to find out whether an account is a sockpuppet. Even after they restored their 3rd edit, it's still too early to tell. Mathsci (talk) 07:31, 25 June 2013 (UTC)
 * If someone still has a doubt, I repeat: compare [ Endohiraku], a brand-new account, and Pirokiazuma, a recently blocked account with previous evidences of sockpuppetry. Not only an interest to the same article, but the same clumsy use of “this” and edit summaries ended with full stop (.), rather atypical syntax for Wikipedians. Incnis Mrsi (talk) 11:09, 25 June 2013 (UTC)
 * I had a look there and I think the proof that keeps getting messed up should really be phrased in much simpler terms, somebody seems to think they should refer to set difference and cardinality and stick in loads of tiny subscripts in something that should be perfectly easily accessible to high school children.. Dmcq (talk) 13:16, 25 June 2013 (UTC)
 * I tend to think that the subscript k makes sense. But I'm an expert in mathematics, not in readability.  — Arthur Rubin  (talk) 18:26, 25 June 2013 (UTC)
 * If you take k as a constant defined at the beginning there's no point repeating it throughout the proof. The only variable is x. Dmcq (talk) 18:46, 25 June 2013 (UTC)
 * For what it's worth, I agree. The number k is fixed throughout the portion of the proof where the bound is relevant.  I think the original $$M_x$$ should be restored, for clarity, but that also it should be emphasized that k is fixed.   Sławomir Biały  (talk) 19:01, 25 June 2013 (UTC)
 * I've implemented a change along these lines.  Sławomir Biały  (talk) 19:08, 25 June 2013 (UTC)
 * The addition of the subscript does make sense. Pirokiazuma missed the dependence on k, while Endohiroku drew attention to it. Can that really br the same person?


 * Independently of all this, the problem with the article being edited is that it is not properly sourced. It's easy enough to do. Not all the proofs given, e.g. that of Erdos, are in the unique source (I looked at the pages listed). I haven't checked what's in Hardy & Wright, but that's a classic source. It would be good to add a few inline citations. And yes, the article should be accessible to high school students.


 * Although Kww blocked the suspected sockpuppet, I cannot see any overwhelming reason for it to be a sockpuppet. In this case there were problems not only with the mathematics of the 3rd edit (identical to the 4th) but with the grammar. I reverted both these edits. English is not the native language of the editor: they are struggling. I have no idea why in that edit they changed a short and simple statement to a short and cryptic riddle. Indeed closer examination shows that what Endohiraku added is essentially the same as what Arthur Rubin spelled out in this subsequent edit. But in any event there was really too little data to infer anything. Mathsci (talk) 18:51, 25 June 2013 (UTC)
 * English is not the native language of the Randy and this, as Mathsci inferred, explains his/her attitude? Where (and when) my English was insufficient to edit an article boldly, I started from posting to the talk page. And I did not attempt to deride the people who started to discuss the matter. It is the (general) WP:competence problem, not a language problem. Just drop it and let’s revert any “cryptic riddle” until Randy realized that his/her changes have no chance without a preliminary discussion. Incnis Mrsi (talk) 02:56, 26 June 2013 (UTC)
 * Incnis Mrsi has been given advice by the SPI clerk Rschen and by the checkuser Deskana about how to report sockpuppets. Articles on primes attract all sorts of editors, including some with delusions. What might have prevented some of these problems and the recent set of edits (even by regulars here) is for the article to have been properly sourced with a smattering of inline citations. It is true that the subject is elementary pre-university mathematics that any Tom, Dick or Igor can do, but that's no reason not to have sources that cover all the content. Mathsci (talk) 04:29, 26 June 2013 (UTC)


 * A further obvious sockpuppet has edited the article, again with an incorrect "simplification" of the Erdos proof. An SPI report was filed with a request for CU. The underlying IP has now been blocked. Mathsci (talk) 06:31, 29 June 2013 (UTC)

Move proposal
I propose to rename


 * Real multivariable function → Functions of several real variables (many real variables to one real/complex etc.variable)
 * Several complex variables → Functions of several complex variables (many complex variables to any real/ one complex etc. variable)

since the titles are clearer and match. If needed, other articles which may split from them could have more refined names like "complex-valued functions of several real variables" etc. Any objections? Feel free to call me a hypocrite for bad naming of real multivariable function/several real variables if you must. M&and;Ŝc2ħεИτlk 08:27, 27 June 2013 (UTC)


 * "Several complex variables" is a branch of analysis, so a move of that article is not appropriate. As to the first, the proposed target is inconsistent with our naming conventions for articles, and should be "Function of several real variables" if anything.   Sławomir Biały  (talk) 11:54, 27 June 2013 (UTC)


 * I seemed to have over-copy/pasted, several complex variables is supposed to read in the brackets "many complex variables to one complex variable". Anyway, in which case I don't see why "several complex variables" couldn't be renamed to "function of several complex variables", but it's not essential and I'll leave it alone, and move Real multivariable function → Function of several real variables. M&and;Ŝc2ħεИτlk 18:42, 27 June 2013 (UTC)
 * There is an entire area of mathematics called "Several complex variables". This is what the article is about (or should be about).   Sławomir Biały  (talk) 18:55, 27 June 2013 (UTC)


 * OK, sorry, I've never actually come across that as a title, I've always read/been taught it as "complex analysis". M&and;Ŝc2ħεИτlk 19:10, 27 June 2013 (UTC)
 * Yep, it even has its own top-level Mathematics Subject Classification: MSC 32-XX "Several complex variables and analytic spaces".  Sławomir Biały  (talk) 19:30, 27 June 2013 (UTC)

Proposed contents for pages on Linear function, Linear equation and Line (geometry)
I invite you to look at these pages: Linear function, Linear equation and Line (geometry). I have translated them from wiki pages I was creating. (Please do not judge the folder name wikipedia. My host demanded a folder name before I was prepared for such a request and I already have a PMwiki called wiki on that domain so that was the first folder name that came to my brain. I was already in a long, long chat with the host about getting the math content to render. This site is just a sandbox where I can work on wikipedia type articles in peace. Gave up on clean urls.)

Please consider adding this content to the corresponding English wikipages.

Some notes (I know I am verbose). Thank-you for your consideration. Lfahlberg (talk) 09:12, 28 June 2013 (UTC)
 * 1) The contents of the pages in my sandbox contain information that my kids (pupils and students), their parents and professionals from other fields with whom I collaborate,... always seem to be confused about. So I think it important to include them on wikipedia pages. Also many of the international wikipedia pages are directly translated from the en.wikipedia pages. So the en.wikipedia pages rather "set the standard".
 * 2) I think that the equations for lines in the current article Linear equation should be moved to Line (geometry) (I did not include all of the formulas from there and added others from other dimensional spaces) and that perhaps some of the general information about geometry in Line (geometry)  could be moved to Geometry. That being said, I must confess to loving great circles and not only suggesting that they go on the Line (geometry) page but wanting to have them above the fold (visible when opened) to create some interest about lines not just among the little ones, but among adults. (I find great circle routes fascinatingly counter-intuitive.)
 * 3) I do not know how to make svg images (nor am I really interested in learning -I always hated Corel Draw). So I cannot do that at all. I make all my images in GeoGebra or Sage and I hope to create a youtube channel showing how to do this for images in the wikipedia pages (I am the voice of the youtube geogebra channel.) But within the png format I can change almost anything anybody thinks needs changing.
 * 4) The pages I am asking you to look at render well on a big monitor, a netbook monitor, an ipad and even on my droid phone (although there the images come out above the text...)
 * 5) Finally, even if we do not agree to change the en.wikipedia pages, any comments and suggestions on these pages would be greatly appreciated (ignore the mk interface and write in english on the talk pages.)
 * I’ll try comment all this sequentially:
 * (I do not understand the point)
 * Lfahlberg possibly does not understand the difference between an equation and a geometric shape, but it does not imply that there is no difference. First of all, interpretation of a shape as an equation assumes a coordinate system, whereas line (geometry) is a concept more fundamental than coordinates. An attempt to dump all these into one large heap will result in a great logical confusion and destructured exposition, a thing which I really detest. Second, Lfahlberg referred to a great circle not in vain, apparently in a paradoxical insight. A line in general is not necessarily a line in an Euclidean or affine space. Geometric spaces without affine coordinates exits, aren’t they? Please, try to realize what does it mean before resuming the discussion.
 * Any videos how to make drawings in a software which can’t export anything in a vector form will not be appreciated here. I even will insist on censoring of these “educational” stuff, if it appeared, both here and on Commons.
 * Accessibility of a general content (text and images) is not a problem topical to this Wikiproject. Accessibility of formulae is, indeed.
 * Finally, why user talk:Lfahlberg would be a place for a forum worse than mk.wikipedia? BTW, repeating new threads about the same thing from the same person are boring. When I posted several related threads, I made each of them with === === and combined under a single == == header. Incnis Mrsi (talk) 10:09, 28 June 2013 (UTC)


 * If Lfahlberg wishes, I could produce SVG images for what is needed. BTW, hope this section on planes and hyperplanes is not too painful. Regards. M&and;Ŝc2ħεИτlk 10:22, 28 June 2013 (UTC)


 * The current article Linear function (calculus) already has too much on linear equations or, well, whatever general form and parametric form are. The article should really focus on properties of functions, not properties of equations or parameterizations of lines. I am going to open a discussion about that on the article's talk page. &mdash; Carl (CBM · talk) 11:31, 28 June 2013 (UTC)

Ex nihilo
The article titled Ex nihilo contains this one-sentence paragraph:
 * In mathematics, ex nihilo can refer to an answer to a question provided with no working, thus appearing to have developed "out of nothing".

It seems to me that that falls short of infallibility. Michael Hardy (talk) 17:58, 22 June 2013 (UTC)


 * I removed it. — Quondum 12:56, 29 June 2013 (UTC)

Highly totient number?
Making use of the new random math article link, I happened upon Highly totient number. I have never heard of this and a base Google search turned up nothing unrelated to Wikipedia. Google scholar generated only one hit, ''Masser, D. W., and Peter Shiu. "On sparsely totient numbers" Pacific J. Math 121 (1986): 407-426.'' There is an OEIS sequence, but it again references the WP article. Right now the topic looks not too notable to me, but I could be missing something. The article content seems fine; if notability is lacking, perhaps it could be merged into Euler's totient function. Thoughts?

Thanks, --Mark viking (talk) 04:54, 27 June 2013 (UTC)


 * The only reference is to planetmath, which isn't good enough. A merge to Euler's totient function seems reasonable. M&and;Ŝc2ħεИτlk 06:02, 27 June 2013 (UTC)


 * There is probably something to add to Euler's totient function on totient numbers (ie values of the function) where this could be included. Spectral sequence (talk) 16:57, 28 June 2013 (UTC)


 * There appears to be a problem, in that the Masser & Shiu reference gives a different definition for highly totient number (and conjectures that in fact they are precisely the primes). The Planet Math link given does not work for me.  Although the definition in the article makes sense and actually seems quite interesting, I can find no reliable source that mentions this concept.  I has been going to transfer the test to Euler's totient function but will not do so unless I can find a reference for it.  Spectral sequence (talk) 20:41, 29 June 2013 (UTC)