Wikipedia talk:WikiProject Mathematics/Archive/2017/Mar

Merge Proposal


I created a merge proposal for Three-dimensional graph and Three-dimensional space.

Posted on talk page here: Talk:Three-dimensional_space, but I think this may be a better place to reach more people and hear opinions. I could see this going either way, but I wanted to see other thoughts =)

Popcrate (talk) 06:31, 1 March 2017 (UTC)


 * "" The merge must be done (and I'll do it) into Graph of a function. However as the title of the article is confusing I'll transform Three-dimensional_graph into a disambiguation page. D.Lazard (talk) 09:42, 1 March 2017 (UTC) ""

Just saw this ^ posted in the discussion: Talk:Three-dimensional_space. At the moment, Three-dimensional graph is now a disambiguous page Popcrate (talk) 10:30, 1 March 2017 (UTC)

Bickley–Naylor functions
The new article titled Bickley–Naylor functions has two obvious deficiencies: Probably it could be improved in other ways too. Michael Hardy (talk) 20:10, 1 March 2017 (UTC)
 * No other articles link to it; and
 * It doesn't say who Bickley and Naylor are.

Polyhedra
Would appreciate some more contributors to Talk:Polyhedron, especially Talk:Polyhedron. I am asking questions and getting evasive answers. There is so much animosity coming at me that I cannot tell what is ad hominem bile and what is a genuine content issue, but whichever it is, I am unable to have a sensible discussion. &mdash; Cheers, Steelpillow (Talk) 18:04, 21 February 2017 (UTC)
 * Some context, as the discussion is long and rambling: this concerns the definition of (non-convex) polyhedra, most recently significantly modified here, and whether we should say that all non-convex polyhedra have duals or qualify that statement somehow, most recently significantly modified here (but with several reverts and reinstatements after). As for the supposed animosity of the discussion, see here and here. —David Eppstein (talk) 18:32, 21 February 2017 (UTC)
 * If we are into the historical context we should add User talk:Steelpillow and Talk:Dual polyhedron. But the current content debate is what matters now. &mdash; Cheers, Steelpillow (Talk) 20:58, 21 February 2017 (UTC)
 * I am not acquainted with (non-convex) polyhedra, but, as far as I understand, different definitions coexist in their theory. If so, then we should honestly inform the reader that this is so. I did such things sometimes, both here (Baire set) and on EoM (Measurable space#On terminology). Why not? Boris Tsirelson (talk) 21:38, 21 February 2017 (UTC)
 * "I am unable to have a sensible discussion." This is sad but does seem to be an accurate description of the situation. --JBL (talk) 23:41, 21 February 2017 (UTC)

FYI, David Eppstein and Joel B. Lewis are the two editors I have been trying to engage with. &mdash; Cheers, Steelpillow (Talk) 19:44, 22 February 2017 (UTC)
 * For idiosyncratic definitions of "trying to engage" that I will not attempt to describe, because Steelpillow's uniform answer to any attempt to understand or describe his point of view is "that's not it". —David Eppstein (talk) 19:46, 22 February 2017 (UTC)
 * Which rather graphically illustrates the problem. Can some kind folks please take an independent look at it all? &mdash; Cheers, Steelpillow (Talk) 19:03, 23 February 2017 (UTC)
 * I tried (above), but no one cares... It seems to me, no one thinks "what to do?", all think "who wins this fight?" Thus, I am of no help. Boris Tsirelson (talk) 21:17, 23 February 2017 (UTC)
 * Your very reasonable comments above are in agreement with David Eppstein's edits, which have amounted to a substantial improvement in the article. --JBL (talk) 21:28, 23 February 2017 (UTC)
 * For what it's worth, despite this disagreement, I happen to think that Steelpillow has been a valuable contributor to the polyhedron articles, especially in his work making the articles more mathematically rigorous and better sourced, qualities that have been sadly lacking in some polyhedron contributions by other editors. But we appear to have a disagreement over whether we should settle on a single definition that is usable, rigorous, and general (my interpretation of Steelpillow's approach, which he will tell me is not what he actually means) or whether we should try to represent more equally the multiplicity of different definitions that are still used in this area (my preference in agreement with what Boris posted above). —David Eppstein (talk) 21:49, 23 February 2017 (UTC)
 * Nice: both participants understand the relevant math, thus, agree in what is REALLY true; the only content dispute is, in which terms to represent THE truth in the article. We know that sometimes different (nonequivalent) definitions coexist even in most professional mathematics (examples were given), just because mathematical truth is constant in time but its treatment by mortals is not. In addition, polyhedra are treated in sources of different academic levels; no wonder if terminology varies a little, and default assumptions differ. As far I understand the policies of wikipedia, in such situation we have to represent coexisting approaches with due weights. Of course, it is somewhat subjective, what are "due weights", and which versions to ignore as marginal or obsolete. Is this the only matter of dispute? Boris Tsirelson (talk) 06:48, 24 February 2017 (UTC)
 * Steelpillow's actual position in the dispute is difficult to discern from his or her comments. They tend to be oppositional but not in a constructive way. --JBL (talk) 13:13, 24 February 2017 (UTC)
 * Hmmm... @User:Steelpillow: Would you care to speak? I wonder, to what extent you (dis)agree with my description of the content dispute. Or do you prefer to wait for another "kind folks"? Boris Tsirelson (talk) 17:45, 24 February 2017 (UTC)
 * Hi all, just back online. Thank you. I think that a fair summary, although Wikipedia requires us to pay more attention to what reliable sources have actually said than to the ultimate truth of what they said (WP:RS, WP:NOTTRUTH, etc). I have suggested that, since this is an introductory article with only very basic mathematics, we should be guided by reliable secondary and tertiary sources on the subject, only supported by primary sources where necessary to fill in some of the detail, per WP:PSTS. Such sources typically confine themselves to Euclidean geometry and introduce the convex, star (non-convex) and dual polyhedra; they consider few if any of the many more specialist definitions in use. My attempts to describe and cite such sources have been summarily reverted, but I have not been able to get any sensible discussion of what they actually say and support, and how we should reflect that. Hence the link in my opening post here to the duality and citation discussion. &mdash; Cheers, Steelpillow (Talk) 11:25, 25 February 2017 (UTC)
 * Can you point to diffs where you added a source but that source was removed again and is no longer cited in the article? Because additional sources sounds like a useful thing to have. I don't recall seeing such sources added and removed but I suppose something like that could have been collateral damage of the other changes. And ironically, the best source I ended up finding for your preferred abstract-based definition is a highly specialist primary source (the Burgiel paper). —David Eppstein (talk) 16:54, 25 February 2017 (UTC)
 * Here is a sequence of edits where I cited three RS, new to the article, and here the revert. With respect to the reverter's edit comment, the only cite I deleted was a duplicate of an existing cite in the same section, which was used to justify an embellishment I was removing, and I subsequently tried to restore a modified copy with the text duplication removed, but this was not accepted either and was reverted by your good self. I posted them again when I started the discussion at Talk:Polyhedron, explaining that they had been reverted and asking why, so it is something of a surprise to me that they have yet to be noticed. &mdash; Cheers, Steelpillow (Talk) 18:19, 25 February 2017 (UTC)
 * In the edit in question, you removed an excellent secondary source (the survey article of Grunbaum and Shepard) and replaced it with a different one. Obviously, it is not possible to defend this by vague hand-waving in the direction of Wikipedia policies about sourcing.  (Incidentally, Cundy and Rollett is still being used as a source in the article; Wenninger is not, but since its history as a source in this article involves it being introduced to support a statement that it does not actually contain, I have trouble being upset by this.)  --JBL (talk) 19:01, 25 February 2017 (UTC)
 * Cundy and Rollett is a fine work, but the claim it is being used to source (the count of ten convex polyhedra with equal regular faces) is not actually in it, and the other statement supposedly sourced to it that Steelpillow is complaining about being removed ("A polyhedron created in this way is dual to the original.") is completely content-free. So if we are to continue using it as a source, it would be helpful to find some other statement that it is actually useful to source... —David Eppstein (talk) 20:48, 25 February 2017 (UTC)
 * JBL is wrong to say that I removed any source. I removed one citation instance because the factoid it supported was of no great significance: as I just said, I left another instance for that source in place. What matters with Wenninger is whether it supports the current version, and in this diff I was using it to support the claims that "The dual of a uniform polyhedron can also be obtained by the process of polar reciprocation in a concentric sphere. However, using this construction, in some cases the reciprocal figure is not a proper polyhedron." which is exactly what Wenninger's book addresses. Similarly with David Eppstein, I was citing Cundy and Rollett to verify the basic nature of polyhedral duality and not any headcount. In effect I was replacing the primary citation instance which JBL wants to keep with a tertiary source, which is good. If the sentence "a polyhedron created this way is dual to the original" is content-free then it can be removed, but the citation covered also the immediately preceding text as well, so cannot be summarily deleted. Furthermore I cited C&R a second time for another aspect and that reversion remains to be explained. So, as anybody who actually cares to check the diffs properly can see, these criticisms here are not merely shallow but actually false. &mdash; Cheers, Steelpillow (Talk) 12:50, 26 February 2017 (UTC)
 * Finally, something substantive to work with! The convex case is not a "factoid" -- convex prototypes are by far the best defined, most studied and most applied of all families of polyhedra. Essentially any discussion of any interesting feature of polyhedra (or polytopes in any dimension) should begin with a discussion of the convex case. Duality is a particularly good setting to do the convex case first, because convex polytopes all have duals and they can be produced by a standard technique -- thus, they exhibit in a broad family the desirable properties that one wants from a "good" notion.  --JBL (talk) 15:51, 26 February 2017 (UTC)
 * Later addition: Steelpillow has made clear below that it was a mistake to believe this comment involved substantive or constructive engagement. --JBL (talk) 21:18, 26 February 2017 (UTC)
 * Cundy and Rollett talk about duality only in terms of polar reciprocation, and they don't give a definition of polyhedra at all. So it is a mistake to use them to support material on abstract duality, as SteelPillow was trying to do. —David Eppstein (talk) 17:31, 26 February 2017 (UTC)
 * Again, these criticisms are simply not borne out - even downright contradicted - by the diffs which Eppstein asked for and which I provided. The "factoid" in question is the observation that a dual has the same number of edges as the original, it has nothing to do with convexity. Nowhere does my diff show a C&R cite "trying to support material on abstract duality" - they were supporting observations on the most basic of geometrical properties. I do hope that other editors are beginning to see a pattern in these criticisms. &mdash; Cheers, Steelpillow (Talk) 19:18, 26 February 2017 (UTC)
 * Your diff is about polyhedra in general, not the special ones for which C&R's approach works. (They are very sloppy about what they mean by a polyhedron, but as the same part of their book states that a midsphere always exists, they are certainly not talking about polyhedra in full generality.) And the diff doesn't talk about edges at all. This incident raises to me a broader issue, which is the usefulness of popular-audience books as sources on matters where some delicacy and rigor are required to avoid misstatements. Popular books are generally less WP:TECHNICAL, and that's a good thing for our readers, but they're also generally sloppier, as this one is. And there can be an echo-chamber effect, much like the one that occurs from one Wikipedia article to another, where one popular book says something dubious (like in this case that all polyhedra have midspheres, despite having previously mentioned some deltahedra that don't) and other sources just repeat it without checking it or verifying the conditions under which it might be true. Using such sources requires extra care on the part of Wikipedia editors, to make sure that the definitions of the source and the Wikipedia article actually match and that the source is not making mistakes, not merely looking to see that it sort of looks like a statement about the same general topic.
 * Similarly, another of SteelPillow's preferred sources, Cromwell's Polyhedra, came under what for MathSciNet counts as highly unusual and vicious criticism for its sloppiness — see Talk:Polyhedron — and SteelPillow basically laughed it off as not applying to his edits. —David Eppstein (talk) 20:05, 26 February 2017 (UTC)
 * I am pleased at last to see achnowledgement that popular books are a good thing for readers but that their errors need careful clarification. In the present case Grûnbaum's papers offer several such clarifications and the one which I cited was also reverted without explanation. Then again, my diff includes deletion of the content: "the same number of edges." To claim as Eppstein does that it does not talk about edges is at best misdirection, I have only ever said that I deleted that bit and the diff is the proof of that, so I am not sure what point Eppstein is trying to make here. &mdash; Cheers, Steelpillow (Talk) 11:18, 27 February 2017 (UTC)
 * The fundamental property of duality is that it exchanges k-dimensional faces for (n-k-1)-dimensional faces. In the case of 3-D polytopes, this means edges for edges as well as faces for vertices.  Moreover, this sentence has been part of the article for long before the current dispute.  If there is anything in your edit that you feel is worth doing still then a productive way to proceed would be to post a short comment proposing the edit on the talk page, together with a short, substantive rationale, and try to build consensus for it -- the way everyone else on WP does. --JBL (talk) 13:36, 27 February 2017 (UTC)
 * I did, and this was your response. &mdash; Cheers, Steelpillow (Talk) 20:34, 27 February 2017 (UTC)
 * Your belief that you have proposed an edit together with a substantive rationale for it is mistaken. --JBL (talk) 21:08, 27 February 2017 (UTC)
 * Being not acquainted with these sources, I can only ask some questions...
 * Question 1: is there a single definition of a polyhedron that is accepted by all secondary sources?


 * Some reservations: (a) I treat equivalent definitions as the same definition; (b) well, not quite "all" secondary sources, but somehow the mainstream of them; some may be excluded as marginal or obsolete. Boris Tsirelson (talk) 19:14, 25 February 2017 (UTC)
 * See Talk:Polyhedron for my attempt to survey the secondary sources I had at hand. Short answer: No. I didn't have Cromwell available, and his book should be included too, but it won't change the short answer. —David Eppstein (talk) 19:27, 25 February 2017 (UTC)
 * Aha! I see. A nice survey. And a convincing negative answer. Do you agree with this negative answer? Boris Tsirelson (talk) 20:06, 25 February 2017 (UTC)
 * The negative answer is correct, although I have a slightly different selection of sources to hand. It is common to define convex (or otherwise non-intersecting) polyhedra first and then to generalize to star polyhedra (for example both Coxeter and Cromwell do this). The many other kinds (such as abstract) are more advanced topics. &mdash; Cheers, Steelpillow (Talk) 12:50, 26 February 2017 (UTC)
 * Sо, тhe negative answer is correct. Therefore, do we restrict ourselves to secondary sources or not, anyway, we combine sources that interpret differently the term "polyhedron". Thus, according to such essays as "WP:Combining sources" and "WP:These are not original research", we should specify the context, when citing a claim from a source. Otherwise "it would be a misuse of the source material to fail to clarify the quotation" (says the latter essay). Boris Tsirelson (talk) 13:41, 26 February 2017 (UTC)
 * On the other hand, it is of course a legitimate option, to first consider convex polyhedrons (unproblematic, I hope), and afterwards turn to more problematic cases. Boris Tsirelson (talk) 13:47, 26 February 2017 (UTC)
 * Agreed. I would add that if a general principle is the subject of a section, it can be better to enunciate the principle before turning to the convex and any other cases to discover how universal the principle is or is not. One does not want to introduce subtle complexities into the opening sentences. &mdash; Cheers, Steelpillow (Talk) 19:18, 26 February 2017 (UTC)

The discussion shows that, here, there is no universally accepted general principle (general definition of a polyhedron). Even, when a general principle exists, this is rarely a good thing to present it before the special cases from which it has been generalized, unless one want to be understood only by experts of the subject. In fact, one can understand the need of a generalization, and the reasons of the choices which are done for it, only if one is accustomed to the special cases. For example, understanding Lebesgue integration requires to understand why Riemann integration is not sufficient. Thus, the last post of shows clearly that his aim is not an encyclopaedia that is understandable by as many people as possible. It is to push his own point of view on the role of generalizations and abstractions. IMO, too much time has been spent to discuss with. It is time to close this discussion (IMO, by a consensus against claims). D.Lazard (talk) 15:34, 27 February 2017 (UTC)

Do you really push generalizations and abstractions? I ask, since I see your phrase "It is common to define convex (or otherwise non-intersecting) polyhedra first and then to generalize to star polyhedra" (above). Boris Tsirelson (talk) 16:11, 27 February 2017 (UTC)
 * No I don't, I think D.Lazard may have been paying more attention to others' commentaries on me instead of what I have actually been writing. I try to push the kind of treatment seen in basic texts. The origins of polyhedra and of their duality lie in Euclidean solid geometry and this is neither a generalization nor an abstraction, but it is where most basic texts begin. While there is no universally accepted definition, there is a universally accepted starting point. As D.Lazard rightly points out, the generalizations and abstractions naturally follow on from that. If he feels that the section on duality should follow the same pattern and discuss the particular cases first before describing the well-known principle of duality and its less well-known limitations, that is a discussion we can have - note that I said it "can" be better to state it first, not that it necessarily is better. My key point in this is simply that statement of the underlying principle is well enough verifiable from multiple secondary and tertiary sources that it cannot be summarily airbrushed out (but it can and should be qualified). What is so unencyclopedic about that? &mdash; Cheers, Steelpillow (Talk) 20:29, 27 February 2017 (UTC)
 * To give an actual example of my approach to abstraction and generalizations, here I discuss demoting the abstract aspect in order to focus on the more traditional. It is part of a discussion at Talk:Polyhedra. &mdash; Cheers, Steelpillow (Talk) 20:50, 27 February 2017 (UTC)
 * Now I am rather puzzled. It seems, all participants like the same: simple first, hard afterwards. Or not? I fail to understand, what is the REAL disagreement. Is the meaning lost in long and boring quarrel about "this diff, that diff"?.. Boris Tsirelson (talk) 20:44, 27 February 2017 (UTC)
 * Make love math, not war diffs. Boris Tsirelson (talk) 21:04, 27 February 2017 (UTC)
 * Don't say I didn't warn you. --JBL (talk) 21:14, 27 February 2017 (UTC)
 * Yes you did; and still, I prefer to observe it myself. Boris Tsirelson (talk) 06:08, 28 February 2017 (UTC)

, after soliciting input in several different venues, you have yet to find a single person to agree with you that there is anything substantively wrong with any of the edits others have made recently to polyhedron. At some point you should learn something from this. --JBL (talk) 21:20, 27 February 2017 (UTC)


 * I too am puzzled. I think the best I can do is to post my proposed content here and see what folks make of it this time round:


 * Perhaps folks can give their critiques here? &mdash; Cheers, Steelpillow (Talk) 21:45, 27 February 2017 (UTC)
 * My critique is that you seem to be (verbosely) proposing "let's go back to the old way we did it, before all the recent changes" without in any way addressing the criticisms that have been raised on the Polyhedron talk page about why the old way was problematic, nor in any way describing any problems with the new version of that content that warrants wholesale undoing. —David Eppstein (talk) 21:53, 27 February 2017 (UTC)
 * I endorse this whole-heartedly. --JBL (talk) 21:55, 27 February 2017 (UTC)
 * Steelpillow, I am astonished. Before, you agreed with "Otherwise it would be a misuse of the source material to fail to clarify the quotation". And now you write, basically, "no problem with polyhedra" without restricting the class of the polyhedra. Why? Isn't this a misinformation? Did you mean something like "no problem with convex polyhedra"? Boris Tsirelson (talk) 06:04, 28 February 2017 (UTC)
 * I have said before, there is a distinction between stating a principle and claiming that it is true in all circumstances. Not all the circumstances treated by introductory texts - high symmetry (regular and uniform) in both the convex and star cases - are currently mentioned, so this proposal fills that gap - the issue with polarizing the uniform set is included in that. Some other classes - including the "new" way espoused by Eppstein - are mentioned further on in the article but it is not sensible to discuss their duality before even introducing them. In particular I would suggest that the abstract discussion is too advanced for this section and I would prefer to see it relegated to the appropriate subsection, but include it in this discussion draft because others may wish to keep it. I hope these criticisms answer some of the questions that Eppstein has raised. The principle of duality for polyhedra is given in popular published works, the content I give is cited and I repeat does NOT endorse it as always true. If a clearer form of words is desirable, then fine, let's talk about that. If further citation is desirable, then fine I'll dig up some more. For example one might add something along the lines of "The principle does not hold in all contexts" and cite say Gailiunas & Sharp and/or Grünbaum & Shephard. The reason I came to this page is to try and get such issues with it sensibly discussed, not to grind on about how right I am. I hope this reduces your astonishment a little. &mdash; Cheers, Steelpillow (Talk) 10:34, 28 February 2017 (UTC) [Updated 10:53, 28 February 2017 (UTC)]
 * P.S. On the "misuse of source material" issue, Grünbaum has written several papers which touch on the wider context of the polyhedral principle of duality, making it clear that it is not confined to the narrower focus of Cundy & Rollett and Wenninger. I can add some more citations for that if needed. &mdash; Cheers, Steelpillow (Talk) 11:14, 28 February 2017 (UTC)
 * The phrase "the sum does not depend on how the additions are grouped" (taken from "Summation") means, of course, that this is true always (in that context). Similarly, the phrase "Dual polyhedra exist in pairs" means, of course, that this is true always (in the given context). You try to weaken this principle, universally accepted in mathematics. I guess, you cannot find any mathematician in support of such innovation. Yes, "a clearer form of words is desirable", moreover, absolutely necessary. Otherwise you just disturb all mathematicians with patently wrong claims. Either add something like "convex", or say explicitly that "the following is an informal introduction; for the context and exact formulations see section ..." or something like that. Boris Tsirelson (talk) 18:30, 28 February 2017 (UTC)
 * You seem to be saying that the phrase "Dual polyhedra exist in pairs" is universally accepted in mathematics, is this correct? David Eppstein and JBL have been criticising me heavily because they thought I was saying just that and pushing the principle too strongly. I have been concerned to answer their criticisms. Now you say I am weakening it too much. Are you now coming in from the opposite direction? &mdash; Cheers, Steelpillow (Talk) 19:46, 28 February 2017 (UTC)
 * Oops, no, sorry for being not clear enough. I mean that it is universally accepted in mathematics that a statement containing free variables (the summands in my first example, the polyhedra in my second example) is interpreted as true for all values of these variables (permitted by the given context). That is, "always" is implicitly added. (See for instance ; there should be much better sources, but for now I have this one). And of course I agree with David and Joel that the phrase "Dual polyhedra exist in pairs" is a false claim, since it is interpreted (by default) as "Dual polyhedra exist in pairs, always". Boris Tsirelson (talk) 20:15, 28 February 2017 (UTC)
 * OK, thanks, I understand what you mean now. The remark is not central to the discussion but was intended only as an informal clarification. I have no problem if it is simply left out. &mdash; Cheers, Steelpillow (Talk) 21:02, 28 February 2017 (UTC)
 * Nice. But please check all other claims contained in your text; I took this one just for example. Probably, there are more problems of the same kind. Boris Tsirelson (talk) 21:14, 28 February 2017 (UTC)
 * I have updated my proposal above here by striking out the offending sentence and adding back a bullet point about edges, whose removal was objected to. I really am not aware of any other deficiencies, which of course is not to say there aren't any. Are there? &mdash; Cheers, Steelpillow (Talk) 19:57, 1 March 2017 (UTC)
 * Yes: as has been mentioned several times on the Polyhedron talk page (and possibly alluded to by Boris Tsirelson), the first sentence is still totally misleading, a lie wrapped in obfuscation by the undefined word "figure." Moreover, you continue to simply ignore the current version (which suffers from none of these deficiencies) and the work others have put into it -- this essentially non-collaborative approach is incompatible with the basic principles of Wikipedia.  --JBL (talk) 20:48, 1 March 2017 (UTC)
 * Indeed. Now I observe that Steelpillow pushes very insistently the idea of presentation of mathematical truth in everyday language, full of inaccuracies. Quite a pity. Yes, I was warned by Joel, but hope dies last... Boris Tsirelson (talk) 21:44, 1 March 2017 (UTC)

I am sorry, I am genuinely puzzled by this view. I have repeatedly answered the points raised by JBL: that the principle is stated in reliable sources and that the principle and the universality (or otherwise) of the principle are different things. Nobody has contradicted that. If "in context X, principle Y states Z" is given in RS, how does lying come into it? How does an editor's opinion of truth trump verification? I seem to be the only one here trying to focus on reliable sources. How does repeatedly advocating verification get mistaken for "pushing truth"? There has been some discussion of sources but not nearly enough to clarify that. It seems to me that the word "figure" is such a basic concept in geometry that it needs no explanation, but if people are unhappy with it I have suggested the alternative "construction", but nobody has replied to me on this. I am not ignoring the current version, I am proposing a couple of changes to it for reasons which I have given over and over (a statement of duality before turning to the convex case, and the inclusion of the uniform case) and which nobody has yet answered with any clarity. The draft which I give above is indeed modified from my earlier efforts in the light of the current version, and some of those updates are discussed in this very thread. Where a problem has been clearly identified, I have been glad to modify my proposed change accordingly. Is that not a collaborative approach? So I simply cannot see where JBL's criticism is coming from, nor why Tsirel finds it so convincing. Can somebody please answer my replies here to the points still being raised against my proposal and not simply ignore my replies or dismiss them out of hand? For example, something along the lines of "you are pushing lie A as truth when you say B and your defence C is wrong because D", or, "in geometry, a general object is nowadays usually referred to as an 'E' and not a "figure" or a "construction", or whatever, would be very helpful. &mdash; Cheers, Steelpillow (Talk) 11:47, 2 March 2017 (UTC)
 * "the principle and the universality (or otherwise) of the principle are different things"? I am not acquainted with such terminology. I just never faced it (in mathematics). We have statements; they are true or false; etc. But what do you call "principle"? Having a generally wrong statement, can we always call it a "principle"? Or only under some conditions? Which conditions, and why? For instance, may I say "Principle: functions have derivatives", or not? Boris Tsirelson (talk) 11:59, 2 March 2017 (UTC)
 * Well, not quite never; we have "Littlewood's three principles of real analysis". That article says they are heuristics, so that nobody should confuse them with theorems. They are intentionally vague. But this is an exception, very rare in mathematics (and, I guess, permitted only to such great minds as Littlewood). I think so, and I wonder, what other thinks. If indeed we state a "principle", we must say very clearly that this a heuristic. Boris Tsirelson (talk) 12:09, 2 March 2017 (UTC)
 * Of course in that case there actually is sourcing to support the name and the phrasing -- unlike the SP approach of making a false statement unsupported by sources, writing it to include made-up unsourced terms, then declaring it a "general principle" without sources, then complaining about a version in which the corresponding statement is sourced. (Can we all tell how fed up I am with this?)  I for one accept D. Lazard's suggestion to call this discussion over, with a consensus rejection of Steelpillow's position and arguments. --JBL (talk) 13:20, 2 March 2017 (UTC)
 * In reply to Tsirel: To me, a "principle" is whatever some RS says it is. For example Lines; Soild Geometry, Macmillan 1935, p.159 (which I have to hand at this moment) decribes an ability to interchange certain statements about vertices, faces and suchlike to yield dual pairs of statements and these are examples of "the principle of duality". He then gives some examples of dual polyhedra. Wenninger, Dual Models, CUP 1983, p.1 uses the phrase "duality relationship". It arises in projective geometry as a formal theorem, where the process of reciprocation about some quadric surface (usually a sphere in the present case) yields a dual construction. Its application to polyhedra in Euclidean space causes some problems because projective duality is not a theorem of Euclidean geometry. Duality appears in different geometrical guise in the division of any compact, unbounded manifold into polygons, for example on a topological sphere a polyhedron and its dual are equivalent to a dual pair of planar graphs. This kind of property can be further abstracted to yield certain characteristics which may be used to define a polyhedron. But solid geometry and topology do not always agree on whether a given construction is a "polyhedron" or not. It is possible to take a figure which is a polyhedron under both approaches but its dual, when also constructed, breaks one or the other definition. Thus, the "principle of duality" (or whatever one chooses to call it), when applied to some arbitrary class of polyhedra, may or may not be valid. There are many complexities to these arguments, some highlighted for example by B. Grünbaum and G. C. Shepard; "Duality of Polyhedra", Shaping Space: A Polyhedral Approach, (eds. Senechal & Fleck) Birkhäuser, 1988, p.205 ff, For example they make the point that the principle (which they describe as a "statement" from "folklore") implies a unique dual, which is valid in topology or combinatorics but not in geometry. My approach mirrors theirs, to make the statement first and then to give examples of its applicability (or otherwise). If I am wrong in borrowning Lines' old terminology, is there a more suitable term? &mdash; Cheers, Steelpillow (Talk) 13:30, 2 March 2017 (UTC)
 * So, according to Steelpillow, there are secondary sources that consider not quite defined notions and their not quite proved properties. I do not know whether these sources exist and are notable; if they do, let them be mentioned with due weight, in a separate section, with a clear indication that this is "not quite math". Boris Tsirelson (talk) 18:26, 2 March 2017 (UTC)

Vertical Plane / Horizontal Plane / Vertical and Horizontal
The state of the first of these three articles is atrocious: The other two are not great either.
 * Vertical plane
 * Horizontal plane
 * Horizontal and vertical

I came to these because Horizontal and vertical was listed in the category "flat earth theory", which made no sense to me. I realize what they were referring to is the flat earth approximation. I think it should be removed from that category, but I'm asking for more thoughts on that on the talk page here: Category_talk:Flat_Earth_theory.

Welcome your feedback on what to do on any of these issues. I am open to collaborating to fix Vertical plane. I'd like to see these articles looking more like Horizontal coordinate system. --David Tornheim (talk) 08:05, 4 March 2017 (UTC)


 * Flat Earth aside, "vertical" is sometimes used in advanced mathematics in the context of foliations; "vertical plane" could be treated as an elementary case of it, see Foliation. Boris Tsirelson (talk) 08:42, 4 March 2017 (UTC)


 * Interesting. Sorry, I don't have an B.A., M.A. or PhD in math, just a Masters Degree in Electrical Engineering.  LOL.  I don't think our readers will have the first clue about something as advanced as linear algebra.  I don't object to having a formal definition in the article somewhere if WP:RS secondary sources support the definition, but I wouldn't make that the focus of the article for lay readers.  --David Tornheim (talk) 08:49, 4 March 2017 (UTC)


 * Sure. Really, my intention was to seek some help from other mathematicians, since I myself have too slight idea of foliations. On the other hand, electrical engineering is closer to math than other engineering; does it avoid linear algebra? Note also a nice elementary phrase from the linked article: " the 2-dimensional leaves of a book are enumerated by a (1-dimensional) page number"; something like that could be used...Boris Tsirelson (talk) 08:57, 4 March 2017 (UTC)


 * Yes. Engineering is very mathematical, but I wouldn't say electrical is more mathematical than the other fields.  Aerospace I believe uses incredibly complex differential equations to describe airflow, and I know Mechanical's use of fluid flow and Fourier transforms to model physical structures is hardly any simpler than the modelling dynamic electrical networks and integrated circuit devices.  I didn't take Linear Algebra until years after my M.S.E.E., when I thought about getting an M.A. math, but changed my mind about that.  I get  "the 2-dimensional leaves of a book are enumerated by a (1-dimensional) page number".  Might not be the best example since a page number is a discrete number and is abstract, whereas the page is a physical object in continuous 2-D space.  I would use the edge of the page instead.  --David Tornheim (talk) 09:14, 4 March 2017 (UTC)

Critical mathematics pedagogy
I'm unhappy with the Critical mathematics pedagogy article, but I don't know enough about mathematics education to put it in its proper context. It looks as if it has been written without a broad view of the topic. --Slashme (talk) 08:15, 6 March 2017 (UTC)
 * I suspect the article and the subject of "critical mathematics pedagogy" are entirely dishonest and their real purpose is the pursuit of political power by some of those who lust after power. Michael Hardy (talk) 21:52, 6 March 2017 (UTC)
 * "Mathematics colonizes part of reality"! I could not imagine such a mystery thriller... Boris Tsirelson (talk) 22:00, 6 March 2017 (UTC)

Three mathematical related WP:AfD
Additional opinions at Articles for deletion/Rational numerals, Articles for deletion/Delta numerals and Articles for deletion/Armands Strazds‎ (3rd nomination) would be welcome. D.Lazard (talk) 12:33, 6 March 2017 (UTC)
 * Thanks for the note. Interesting stuff even if it does not survive. Maybe he is to something. This clock def. got my attention. --David Tornheim (talk) 22:41, 6 March 2017 (UTC)
 * If you found the clock interesting, take a look at this: suranadira.com

A linguist would be shocked
I'd like to start a collection that hopefully will be both amusing and useful. But I do not know, the collection of what is it. Could it be a list article? Of which title? Do you like the idea? The (current) collection follows. Boris Tsirelson (talk) 08:00, 4 March 2017 (UTC)

For now I put it on my userpage: "Oddities of mathematical terminology". Boris Tsirelson (talk) 21:42, 6 March 2017 (UTC)

A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".

A set, however, is not a door: it can be neither open or closed, and it can be both open and closed. (Examples?)

Like the alligator pear that is neither an alligator nor a pear and the biologist’s white ant that is neither white nor an ant, the probabilist’s random variable is neither random nor a variable. (Alligator pear = avocado; white ant = termite.)

"Finite measure" is a measure, but "signed measure", "vector measure" and "finitely additive measure" are (generally) not measures. On the other hand, every measure is both a signed measure and a finitely additive measure. That is, "signed" means here "not necessarily unsigned", "vector" means "not necessarily scalar", and "finitely additive" means "not necessarily countably additive". See also Measure (mathematics).

Unbounded operator on X means "not necessarily bounded operator, not necessarily defined on the whole X".

In mathematics, a “red herring” need not, in general, be either red or a herring.


 * And then there's the "constant random variable". Barryriedsmith (talk) 12:49, 4 March 2017 (UTC)
 * Aha, the list is growing! Boris Tsirelson (talk) 14:36, 4 March 2017 (UTC)

And every differential equation is a stochastic differential equation but most stochastic differential equations are not differential equations. But I seriously doubt that any linguist would be shocked by all this. Michael Hardy (talk) 03:50, 5 March 2017 (UTC)


 * And Dirac delta function is not a function.
 * This case provoked a dispute in July 2016. This list could be instrumental in such disputes.
 * About linguist, you gave me an idea to ask on WikiProject Linguistics. Boris Tsirelson (talk) 05:40, 5 March 2017 (UTC)

I wrote a blog article about this a few years ago. It has some examples. —Mark Dominus (talk) 03:41, 7 March 2017 (UTC)


 * Yes, I see! Who is Ranjit Bhatnagar? I guess, the lead programmer mentioned in "Sissyfight 2000". I fail to get any response from wikipedian linguists. "Adjectives in mathematics are rarely nonstandard"? Not so rarely, I'd say. The adjective "generalized" is (usually) nonstandard, and many others are sometimes nonstandard.
 * Taking into account that you came to Wikipedia already in 2002, I would be glad to know your opinion: can this staff be a list article? Boris Tsirelson (talk) 19:58, 7 March 2017 (UTC)


 * I would guess that less than one in a fifty uses of mathematical adjectives is nonstandard.  The standard examples are extremely numerous.  Consider, for example, compact spaces, separable spaces, normal spaces, regular spaces, connected spaces, first countable spaces, second countable spaces, Polish spaces, Hausdorff spaces, contractible spaces, metric spaces,  T₀ spaces and six other kinds of Tₓ space, locally compact spaces, path-connected spaces, and so forth, all of which are kinds of spaces. In contrast, nonstandard examples are few and far between.  Repeat the previous exercise for sets or groups: for every odd counterexample (a hom-set is not in general a set) there are dozens of non-counterexamples (finite sets, partially ordered sets, recursive sets, etc.)


 * In my opinion, I don't think this should be a list article, for two reasons. You would need a reliable source attesting that your examples are “oddities”.  Also, although I find the topic interesting, it is not clear to me that it is of encyclopedic value.


 * There might be more value in an article on the use of mathematical pejoratives, if a source could be found. Mathematicians have a great variety of pejorative adjectives such as trivial, irregular, nonstandard, degenerate, inadmissible, which may have different connotations.  There is also the mathematical use of words like trivial, obvious, easy, clear, straightforward, routine, and so forth that may connote different kinds of simplicity.  For example one term may connote a long but uninteresting calculation and another may describe a claim that follows immediately from something already known. —Mark Dominus (talk) 16:49, 8 March 2017 (UTC)


 * I see, thank you. Boris Tsirelson (talk) 22:31, 8 March 2017 (UTC)


 * I like the idea, and I am reminded of "List of chemical compounds with unusual names".
 * —Wavelength (talk) 20:20, 7 March 2017 (UTC)


 * Thank you for this precedent case! Boris Tsirelson (talk) 20:46, 7 March 2017 (UTC)
 * Some mathematicians may also be shocked by this kind of things. I have recently inserted in the lead of Quadric the assertion that "a degenerated quadric is generally not considered to be a quadric." In fact, a pair of planes is rarely considered as a quadric, although it is an algebraic set of degree 2. This has been the subject of thread in the talk page. By the way, I am not sure whether cones and cylinders were considered (in classical geometry) as quadrics or, only as degenerated quadrics. D.Lazard (talk) 21:10, 7 March 2017 (UTC)

Arnold Ross
I wrote an article on Arnold Ross (mathematician from Ohio State) several years ago. It focuses more on the educational program he founded as (1) he's best known for it, and (2) that's what the sources covered. I don't want his academic career to be a blind spot, though, so I'm looking for suggestions on secondary sources that I might have missed. If you can help, probably best to follow up on the article's talk page. Thanks! czar 06:13, 9 March 2017 (UTC)

formatting

 * $$\left|y[n]\right| = \left|\sum_{k=-\infty}^\infty h[n-k] x[k]\right|$$


 * $$\le \sum_{k=-\infty}^\infty \left|h[n-k]\right| \left|x[k]\right|$$ (by the triangle inequality)



\begin{align} & \le \sum_{k=-\infty}^\infty \left|h[n-k]\right| \| x \|_\infty \\ & = \| x \|_{\infty} \sum_{k=-\infty}^\infty \left|h[n-k]\right| \\ & = \| x \|_{\infty} \sum_{k=-\infty}^\infty \left|h[k]\right| \end{align} $$ I copied the above from BIBO stability. It appears that the reason why "align" is not used throughout, but only in the last three lines, is the need for the link to Triangle inequality. Otherwise one would write something like this:

\begin{align} \left|y[n]\right| & = \left|\sum_{k=-\infty}^\infty h[n-k] x[k]\right| \\ & \le \sum_{k=-\infty}^\infty \left|h[n-k]\right| \left|x[k]\right| \quad \text{(by the triangle inequality)} \\ & \le \sum_{k=-\infty}^\infty \left|h[n-k]\right| \| x \|_\infty \\ & = \| x \|_{\infty} \sum_{k=-\infty}^\infty \left|h[n-k]\right| \\ & = \| x \|_{\infty} \sum_{k=-\infty}^\infty \left|h[k]\right| \end{align} $$ Is it too much to hope that we can have some sane way of formatting properly while including links? Michael Hardy (talk) 21:48, 6 March 2017 (UTC)
 * I can see why it’s happening but don’t have suggestion as to how to fix it. TeX align works only within a single block of formulae. So to align the lines they need to be in the same block, but they cannot then contain a wikilink. If you were writing a paper you might write the whole thing in TeX, but WP articles are not like that. I can’t see an easy way around this, other than a fundamental rewrite of how formulae work.-- JohnBlackburne wordsdeeds 21:59, 6 March 2017 (UTC)
 * If I were writing a paper I might also use \intertext{}. Michael Hardy (talk) 00:04, 11 March 2017 (UTC)
 * I might suggest assigning an equation number to the equation which needs explanation and then adding at the bottom "(1) by the triangle equality" or similar. --Izno (talk) 22:33, 6 March 2017 (UTC)
 * Yes, or in this case just say something in a sentence afterwards like "The triangle inequality justifies moving the absolute values into the sum in the second line". Another thing to keep in mind is that many of our viewers see these equations on narrow-width mobile devices, and it is helpful for them to keep the line lengths down (because that translates into keeping the font size in the formula large enough to read). So pulling the text explanation out of the equations helps in that respect. —David Eppstein (talk) 23:02, 6 March 2017 (UTC)

Francis Buekenhout
The new article titled Francis Buekenhout needs some proper inline citations.

(I rearranged it to put the occasion for notability at the beginning, and added a few links. I also added some links to the article from other articles.) Michael Hardy (talk) 22:03, 17 March 2017 (UTC)

Multiple integral
"Multiple integral" is a mess. Look at Sect.3.3.3 called (recently, by User:Onmaditque) "very difficult example". Also, the notion "domain normal w.r.t. axis" is used intensively but never defined. And more... Boris Tsirelson (talk) 07:15, 19 March 2017 (UTC)

And now I see that the whole (former) Section 3.3 (Normal domains...) is deleted by the user mentioned above. Boris Tsirelson (talk) 11:30, 19 March 2017 (UTC)


 * Mostly the edits there were disimprovements. I restored the section on normal domains, and got rid of the silly edits to the section titles.   Sławomir Biały  (talk) 12:45, 19 March 2017 (UTC)


 * The editor continues to disimprove the article. I have urged them to initiate discussion on the talk page before continuing.   Sławomir Biały  (talk) 15:46, 19 March 2017 (UTC)

Operator (mathematics)
This article was a mess. In particular, differential operators (among other important kinds of operators) are not even mentioned in the article. IMO, with the recent edits by an IP user, this article becomes worse. Other opinions are thus needed. D.Lazard (talk) 18:08, 19 March 2017 (UTC)


 * There is a problem that operator (mathematics) formerly discussed only linear operators, but linear operator already redirects to linear map. This was clearly not an ideal situation.  What is a better configuration of topics?   Sławomir Biały  (talk) 18:25, 19 March 2017 (UTC)
 * As this concerns only a single article, it is better to continue the discussion on this article's talk page. I'll thus copy the above posts on Talk:Operator (mathematics), and reply there. D.Lazard (talk) 18:48, 19 March 2017 (UTC)

Abel sum--
I found that Abel summation and Abel summation method redirected to two different pages, so I did this edit. Now those two and Abel sum all redirect to the same article. But perhaps the question of their most felicitous target page could bear discussion. Michael Hardy (talk) 18:06, 23 March 2017 (UTC)

Category:Category-theoretic categories
Please see the discussion on renaming Category:Category-theoretic categories at Categories for discussion/Log/2017 March 24. – Fayenatic  L ondon 16:05, 24 March 2017 (UTC)

Generating function transformation
The long new article titled Generating function transformation could use some work. Michael Hardy (talk) 05:23, 25 March 2017 (UTC)

Dispute over precision
There is an ongoing dispute at Pythagorean comma. Please could we have some help from someone mathematically inclined? Burninthruthesky (talk) 07:55, 28 March 2017 (UTC)


 * I did (try to help). Boris Tsirelson (talk) 09:05, 28 March 2017 (UTC)
 * Thanks for your input. I have replied. Burninthruthesky (talk) 09:23, 28 March 2017 (UTC)

Porter's constant
The new article titled Porter's constant could use more work, including some specificity about the constant's role in understanding the efficiency of Euclid's algorithm. Michael Hardy (talk) 04:14, 30 March 2017 (UTC)
 * Let's see if this link works . . . Michael Hardy (talk) 04:18, 30 March 2017 (UTC)

Using a Full-stop and Comma
In all articles, most of the equations are followed by a full stop (.) or a. Do we really need this? Sulthan90 (talk) 17:36, 29 March 2017 (UTC)


 * Sentences are expected to be properly punctuated, even if they end in an equation. See MOS:MATH.   Sławomir Biały  (talk) 17:49, 29 March 2017 (UTC)


 * The same applies when the formula is in the middle of a sentence. "Just as in mathematics publications", according to the policy cited above. Boris Tsirelson (talk) 17:54, 29 March 2017 (UTC)


 * Beyond our MOS, the Knuth, et. al., paper on Mathematical writing page 4, item 23, also recommends treating an equation as an ordinary part of a sentence. --Mark viking (talk) 18:40, 29 March 2017 (UTC)
 * I really really deeply dislike this convention, but we're probably not in a place to fix it. I think it's really confusing, because the punctuation is displayed at the same level as the math, which makes it look like it should be serving a mathematical function rather than a grammatical one.  It's a confusion of levels.
 * It's along the lines of the reason that right-thinking people have stopped moving punctuation inside quote marks, when the punctuation is not part of the text being quoted.
 * If the punctuation is really necessary (I think the terminal punctuation really isn't, particularly) then what really ought to happen is that it should go on a separate line. Naive TeX actually does this for you.  For example, you could write something like this:
 * If the punctuation is really necessary (I think the terminal punctuation really isn't, particularly) then what really ought to happen is that it should go on a separate line. Naive TeX actually does this for you.  For example, you could write something like this:

The Pythagoreans discovered that \[a^2+b^2=c^2\], where $a$, $b$, and $c$ are the two legs and the hypotenuse of a right triangle.
 * This renders thus:
 * The Pythagoreans discovered that
 * $$a^2+b^2=c^2$$
 * , where a, b, and c are the two legs and hypotenuse of a right triangle.
 * You'll find advice in various places as to how to avoid this "mistake", but in my view it is actually correct and the way the sentence ought to be rendered, because it puts the comma in the part of the text that it belongs in.
 * In practice, the bare comma starting the line is visually jarring, but my preferred solution is simply to leave it out, rather than put it where it "logically" doesn't belong. --Trovatore (talk) 19:00, 29 March 2017 (UTC)
 * I'd say, this happens just because articles are written in a natural (rather than formal) language. Natural language is a compromise between being logical and being convenient. Likewise I hate to see "$$a+b=b+a \; \forall a,b$$", but surely I cannot convince others not to treat the quantifier as just an abbreviation for the words "for all". And ultimately they are right; the translation to a formal language must anyway be done by a human that understands the natural language in spite of all that. Such is the life. As for me, this is lesser evil than that.  Boris Tsirelson (talk) 19:09, 29 March 2017 (UTC)
 * Yeah, but it can be actively confusing in this context. Sometimes a period actually means something at the end of a mathematical utterance.  For example, it's not unheard of to distinguish the real number 1. from the natural number 1.  See what I did there? --Trovatore (talk) 19:14, 29 March 2017 (UTC)
 * Every illogical feature can be confusing. A matter of habit. When in danger, the author should clarify somehow. A natural language prefers convenience in most cases and troubles in rare cases. Your example is rare case. Boris Tsirelson (talk) 19:20, 29 March 2017 (UTC)
 * Oh, of course. I still don't like the convention.  I would prefer to just drop these punctuation marks; I don't think they really add much.  The purpose of punctuation is to divide utterances up into semantic units, and when you have displayed equations, they're already pretty much divided. --Trovatore (talk) 19:23, 29 March 2017 (UTC)
 * I see. On the other hand, in this case I am a bit disturbed by the absence of punctuation marks, such as ",", ";" or nothing. These are (at least) three different cases... Well, you may say that I can implicitly insert them myself. True. A matter of habit. Also, for me the distinction between inline and displayed formulas is mostly typographical, and I would not like two different ways of using punctuation. Boris Tsirelson (talk) 19:39, 29 March 2017 (UTC)


 * Without any ambition for discussing the various manuals of rules for layout I feel pressed to emphasize that I see the reasons for confusion, the situations when perceiving danger, and the predicates natural, convenient, rare, or frequent all exposed -at high level- to confirmation bias. BTW, I'm inclined to prefer Trovatore's view. Purgy (talk) 06:34, 30 March 2017 (UTC)

Even I dislike the use of these punctuations in equations as pointed out it's confusing. Wikipedia is place of team and I would like to know what practice is good for Wikipedia and Visitors? -Sulthan90 (talk) 19:43, 29 March 2017 (UTC)
 * Regrettably, the convention that we have does seem to be the standard one in mathematical publications. If I could wave a magic wand, I'd change it, but Wikipedia is not the place for innovations. --Trovatore (talk) 06:25, 30 March 2017 (UTC)


 * I think it is good for WP if most editors do not mind which layout is preferred by the current gurus of the manuals, as long as the intended meaning of their contributions is upheld in the resulting edits of style. In my view a calmly growing WP appears more attractive to visitors (= good) compared to layout warring. Purgy (talk) 06:34, 30 March 2017 (UTC)

Many new Wikipedians?
I have the impression that many newbie Wikipedian mathematicians are among us lately, creating new articles without knowing standard Wikipedia conventions. Have others notice that? Michael Hardy (talk) 04:38, 30 March 2017 (UTC)
 * I do not observe systematically the new articles. However, I remarked that FGLM algorithm has recently been created by a red-linked user, which is newbie in mathematics, but edits other fields since around 3 years.
 * On the other hand, while IP and red-linked users require generally to be speedy reverted, I have remarked more cases where their edits deserve to be kept or improved. In at least one case, such an edit has been unduly reverted (see last thread of Talk:Natural number). Thus some more care in reverts could be useful. D.Lazard (talk) 07:30, 30 March 2017 (UTC)
 * I'm not sure whether that is meant to assess a potential problem or not and how "not knowing WP conventions" materializes in articles. Generally speaking the more mathematicians we have the better and if not knowing Wikipedia conventions simply meant writing without adhering to the Wikiformat in every detail I couldn't care less. If however it meant largely unsourced writing and violations of WP:OR, then it would be an issue.--Kmhkmh (talk) 08:12, 30 March 2017 (UTC)
 * We need a systematic way of informing them of certain basics. Maybe a template page. Among commonplace problems resulting from newbie's lack of awareness are these:
 * Creating articles to which no other articles link and then not adding any links to the new article.
 * Starting an article with something like this: "Let {Tn} be a sequence of bounded linear operators on a separable Hilbert space . .." One must tell the lay reader at the outset that mathematics is what the article is about, and the phrase "In linear operator theory" doesn't do that (whereas "In geometry" does, and similarly algebra, number theory, arithmetic, calculus, and some others). In some cases the title of the article makes all this unnecessary, but that's not the typical case.
 * Writing a biographical article chronologically, so that we find out the subject's father was a blacksmith and he attended St. Whoever's School and so forth before we find out what he's noted for, which should be in the first paragraph and not unusually in the first or second sentence.
 * Miscellaneous WP:MOS and WP:MOSMATH items. Using en-dashes in page ranges and year ranges, knowing that in non-TeX notation variables should be italicized and punctuation and digits should not, some routine things about TeX usage, not using too many capital letters in section headings.
 * maybe a few more items . ..

Michael Hardy (talk) 21:27, 30 March 2017 (UTC)
 * Personally I don't really agree on the "importance" of all those item and in the case of the biography not even on that item itself actually, but sure providing newcomers with needed information is always a good idea as long as it doesn't creates an overload of regulation that might drive them away before they've really started.
 * Maybe we could modify one of those welcome templates into a special one geared towards mathematicians or editors interested in math topics.
 * --Kmhkmh (talk) 12:39, 31 March 2017 (UTC)