Wikipedia talk:WikiProject Mathematics

This is a discussion page for WikiProject Mathematics

This page is devoted to discussions of issues relating to mathematics articles on Wikipedia. Related discussion pages include: Wikipedia talk:Manual of Style (mathematics) Portal talk:Mathematics Wikipedia talk:WikiProject Mathematics/Conventions Wikipedia talk:WikiProject Mathematics/Graphics Wikipedia talk:WikiProject Mathematics/PlanetMath Exchange Wikipedia talk:WikiProject Mathematics/Proofs Wikipedia talk:WikiProject Mathematics/Typography Wikipedia talk:WikiProject Mathematics/Wikipedia 1.0

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FFD: File:Sine Cos Proofs.pdf

The file File:Sine Cos Proofs.pdf has recently come up at WP:FFD. There may well not be a place for this file on WP; but it does seem rather a more useful self-contained take-away than the section of our current omnibus article Proofs_of_trigonometric_identities#Angle_sum_identities, which there might be a case for breaking into smaller self-contained chunks. Jheald (talk) 21:57, 8 June 2011 (UTC)

We've had many long discussions here on how an whether proofs should be included on WP, the results are given in Wikipedia:WikiProject Mathematics/Proofs. Keeping that in mind, "Proofs of trigonometric identities" is not exactly an example of the what proofs should be in WP and how they should be presented. It might be split up and incorporated into a wikibook on trigonometry, but to me it's not an encyclopedia article.--RDBury (talk) 07:30, 9 June 2011 (UTC)

I have to say I utterly disagree.

In my view "trignometric angle sum identity" is an appropriate topic for an encyclopedia; and in the context of treating such a topic in an encyclopedic way we should be trying to convey not just that there is an identity that exists, but also an instinctive understanding of why the identity exists -- including how it can be related to a geometric construction; how it follows directly using Euler's formula and considering real and imaginary parts; and how it follows directly from matrix multiplication (the last two of course being very closely related, but that is an additional bit of understanding). Proofs for the sake of proofs are not appropriate; but that sort of instictive understanding of why is something we should be aspiring to in a potential topic like this; and, indeed, for any mathematical topic for which we can provide it. Jheald (talk) 08:38, 9 June 2011 (UTC)

Compare for example the Wolfram article. Jheald (talk) 09:09, 9 June 2011 (UTC)

We have Angle sum identity which is, at the moment, a redirect. Perhaps it is a topic which should be expanded to an actual article, assuming that the material isn't already somewhere else that I missed. Proofs are good if they are sourced and have encyclopedic value. Unfortunately many proofs we have here unsourced exercises in algrebra/calculus/geometry and much of what I see in "Proofs of trigonometric identities" falls under the latter category. In many cases, if a reason "why" should be added for an identity/theorem, it can be incorporated into the exposition rather than separated out as a formal proof.

We probably shouldn't be using MathWorld as an example either. Overall it's a good resource but it also has a lot of material that isn't encyclopedic by WP standards.--RDBury (talk) 11:46, 9 June 2011 (UTC)

I agree that the exposition is the important thing, and that most of the time setting things out in the shape of a formal proof is probably not appropriate for us, unless that really is the most effective way to get the "why" background across.

I'm curious about your comment about Mathworld. That article on Trig addition formulas seemed entirely in keeping with how we might give an article here. I'm not particularly familiar with Mathworld more widely, but is there anything in that particular article you would view as non-encyclopedic? (And why?) Jheald (talk) 12:10, 9 June 2011 (UTC)

What I meant was that in general we shouldn't be using a MathWorld article as a example of what a WP article should look like. There have been many discussion here on MathWorld, just do a search in the archives. One that comes to mind for me is Wikipedia talk:WikiProject Mathematics/Archive 65#Missing science topics, the issue was basically there are many MathWorld articles where the subject does not meet WP:GNG criteria.--RDBury (talk) 15:19, 9 June 2011 (UTC)

It isn't just notability, unless that word is stretched pretty far. My biggest issue with MathWorld is actually neologisms. My impression is that it more or less makes up words, or repeats terminology used in a nonce sense as though it were accepted and standard.

Now, there's nothing wrong with making up words — mathematicians do it all the time. But they do it in research papers, and the new term is either picked up by others, or it isn't. Encyclopedias are in a different position and really should not make up words. Since MathWorld claims to be an encyclopedia, this is a very serious flaw. --Trovatore (talk) 23:20, 19 June 2011 (UTC)

Nothingness and the empty set discussion

There is a nothingness and the empty set discussion at the Nothingness article. That article can use a lot of improvement as to both content and sources. PPdd (talk)

The potential for Mathematics featured lists

On a tangent to the recognized content section above, which focuses on Featured Articles, I was wondering if members of this project had considered the potential for Featured Lists? At the moment there are three FLs under this project's banner, but all of them are people and/or event oriented. To my knowledge, there are no Featured Lists that focus on mathematics. Looking through Category:List-Class mathematics articles, I believe that there is the potential for some fantastic ones that do focus on the subject itself. I also feel that some topics actually lend themselves better to a list format than an article one. For instance, a merger of Prime knot and List of prime knots (renamed Prime knots) might improve our overall coverage of the subject, as well as setting the ground work for a future push towards featured status.

Now that Today's Featured List is up and running, there would also be the potential to get a maths list on the main page, exposing the work to the millions that visit the page every day. As someone heavily involved with TFL, I can say with certainty that a list based on a mathematical concept would be looked upon very favourably there.

It's undeniable that Featured Lists do place a degree of emphasis on presentation. The main thing to worry about is writing a well-sourced lead that introduces the topic. Beyond that, I would be very happy to take responsibility for all the minutiae of reference/table/image formatting. I wouldn't be seeking a co-nomination for the work: I'm simply determined to play my part in diversifying our selection of FLs. Feel free to drop me a note on my talk page if you might be interested in taking up the offer.

I hope to see some of you at WP:FLC in the future. Warm regards, —WFC— 15:22, 14 June 2011 (UTC)

Lists of mathematics topics is a former Featured List, as you will find if you look at Talk:Lists of mathematics topics.

It is definitely one of the best things ever done on Wikipedia. I think of it as not primarily for navigation, but for browsing, i.e. looking around to see what's out there that you hadn't thought of. It lost its featured status because of a lack of references. The references are in the articles ultimately linked to, two clicks away. I'm not sure how to compile references for a thing like this. It fits no genre; it is unique in the whole history of the printed word. It differs from things like the AMS subject classification system in including things like the list of factorial and binomial topics, the list of circle topics (each of those is fascinating in itself!), and there's lots of stuff like that. Michael Hardy (talk) 18:34, 14 June 2011 (UTC)

Lists of mathematics topics is indeed a fantastic resource. I've sought extra opinions on what would need to be done to restore it to featured status. Although I couldn't help but notice that List of mathematics topics redirects to a different article, which is a bit confusing. —WFC— 23:11, 14 June 2011 (UTC)

Addressing a more important point than what I addressed above: Lists within the scope of this particular WikiProject are among the best on Wikipedia, or for that matter within all of history. (Yeah—I know—you're going to say that's a hyperbolic exaggeration. But really. Wikipedia is truly unprecedented, and I don't think there's actually any exaggeration in this instance. 'nother words, I agree with the original sentiment here. Michael Hardy (talk) 03:31, 17 June 2011 (UTC)

Bplus-class

Hey there! I'm from WP Elements, and we want to start using Bplus-class for our articles, but without any idea how to introduce it. I noticed you use it, so could you help us to do it? Help is surely appreciated--R8R Gtrs (talk) 09:36, 16 June 2011 (UTC)

Imo we should be phasing B+ out in this project. Math guidelines are a bit less stringent than most projects, so a B+ here corresponds roughly to a B elsewhere. The fact that we have our own guidelines when nearly every other project uses standard WP 1.0 guidelines causes confusion for people for other projects who want to add our banner to an article. So unless you have a really compelling reason that your project needs to be a maverick and have different standards then everyone else, I'd say you're better off forgetting about the idea. I think the reason we're different is we were one of the first projects created, before there was much of a standard to go by, and since then inertia set in.--RDBury (talk) 10:51, 16 June 2011 (UTC)

Delisted FA

The Monty Hall problem article, one of our longest standing featured articles, has been delisted. From what I gather this was due to long-standing and apparently unresolvable editing disputes, see Wikipedia:Featured article review/Monty Hall problem/archive3 for the full discussion. I'm also a bit surprised that until now this hasn't appeared either here or on the article alerts page. (Correct me if I'm wrong, though I do try to keep an eye on both.) Any ideas on getting the article relisted?--RDBury (talk) 20:00, 16 June 2011 (UTC)

Redirection of equivalent norms

Currently, Equivalent norms redirects to norm (mathematics), which doesn't describe norm equivalence. Is there a better article for it to redirect to? — Kallikanzarid^talk 23:00, 16 June 2011 (UTC)

Aren't they described in Norm (mathematics)#Properties, or did you mean something more specific? Thenub314 (talk) 23:05, 16 June 2011 (UTC)

OK, now Equivalent norms redirects to Norm (mathematics)#Properties. Does that solve the problem? Jowa fan (talk) 02:49, 17 June 2011 (UTC)

Yeah, thanks. Looks like it was my poor eyesight :( — Kallikanzarid^talk 04:22, 17 June 2011 (UTC)

Pickands–Balkema–de Haan theorem

Pickands–Balkema–de Haan theorem is a complete orphan: No other articles link to it. Work on it! Michael Hardy (talk) 03:27, 17 June 2011 (UTC)

Um, well, OK, if you say so. It was trivial to create three useful links, I'm not sure why you couldn't have done it yourself. But perhaps people who actually know something about statistics will be able to contribute more here. Jowa fan (talk) —Preceding undated comment added 04:51, 17 June 2011 (UTC).

Just that there are only 24 hours in a day...... Michael Hardy (talk) 16:59, 17 June 2011 (UTC)

Constructive ordinal

I found constructive ordinal to be a red link, so I've redirected it to ordinal notation and labeled it a "redirect with possibilities". Should we have an article with this title? Michael Hardy (talk) 04:47, 19 June 2011 (UTC)

The redirect seems like the best choice; a constructive ordinal is just going to be an ordinal notation in the end. I don't think it's worth starting a separate article. — Carl (CBM · talk) 12:04, 19 June 2011 (UTC)

LivingBot

LivingBot is adding a number of dubious tags to some article talk pages, such as this [1]. Does anyone know about this? I'm inclined to revert... Jakob.scholbach (talk) 19:33, 20 June 2011 (UTC)

I've come across this "Betascript Publishing" before, I think they are people who take wikipedia articles package them as a book and sell them on amazon. I think the bot might be tagging articles that have been so packaged to indicate that these articles are not copyright violations, rather a published book copied their content. But this is all guessing. I do find the tag annoying though. RobHar (talk) 20:01, 20 June 2011 (UTC)

There is a recent long discussion on this and related issues: Wikipedia:Village pump (policy)/Archive 87#Wikipedia articles being sold by book companies. This is a growing trend to and somewhat unscrupulous since these publishers sell the books to unsuspecting people. Apparently it's legal as long as you put a link to WP somewhere in the book, even if you don't put it anywhere that's accessible on Amazon of Google Books. It's going make detecting things like circular referencing and copyright violations more and more difficult in the future. Tagging talk pages is supposed to help but I'm not sure what good it will do since if the trend continues (both profitable and legal so I expect it will) a large number articles will end up being published this way. The good news is that most of us will be "published authors" pretty soon.--RDBury (talk) 21:47, 20 June 2011 (UTC)

It strikes me as a reasonable way of handling an unpleasant situation. I don't see any problems with the tags remaining there. Jowa fan (talk) 01:11, 21 June 2011 (UTC) (revised opinion below)

Ah, I get it. That wasn't quite clear to me from the tag itself. Anyway, the only way to turn this into a less pleasant situation in the long run might be to have WP articles that are good enough so that respectable publishers publish them in a reasonable way. Jakob.scholbach (talk) 06:41, 21 June 2011 (UTC)

I take it back. Given the number of such books appearing (see table at VDM Publishing, currently about half a million titles), it won't take long to tag every single Wikipedia page. So we should probably try and stop the tagging before it gets out of hand. Jowa fan (talk) 07:18, 21 June 2011 (UTC)

There's some discussion at Wikipedia:Bots/Requests_for_approval/LivingBot_17#Review Jowa fan (talk) 07:35, 21 June 2011 (UTC)

This kind of spam seems to have finally reached the level where Amazon can no longer ignore it. [2] So hopefully we will soon see an end of this nonsense. Hans Adler 08:41, 21 June 2011 (UTC)

These things tend to be like whack-a-mole; if Amazon stops it then they'll pop up on Nook and Google Books. E.g. our Fibonacci number article was copied into books on sale at Google books here ($15.63) and here ($9.99). But people don't stop using e-mail because of e-mail spam and I expect it will be similar with this kind of spam; filters will be put in place and spammers will find ways around them, but people will put up with it because downloading a book at home is a lot easier than schlepping to the local bookstore. For WP editors I think it will mean more going to the library instead of looking stuff up on Google, in other words we need to add spam filters of our own. In the first example, the book has an ISBN number, has a 2005 copyright (before the content appeared on WP) and has links to buy at Barnes&Noble and Borders. The give-aways are that the content has little to do with the title, it's written WP's trademark summary style, and the sections begin with the Math Project's "In...". Obvious to a WP editor but it's hard to see how an automated filter would pick up on it.--RDBury (talk) 15:10, 21 June 2011 (UTC)

Google recently changed their ranking algorithm to penalize "content farms", sites with very low quality content that are mostly filled with ads. It seems to have worked, because one big content farm just had to lay off 10% of their staff [3]. Now content farmers seem to be moving into ebooks [4]. If Amazon and Barnes and Noble penalize farmed ebooks, then they won't be profitable, either. The people who publish these "books" only do it because it's profitable, and if it isn't, it won't be long before they vanish. (When was the last time you saw a Wikipedia mirror at the top of a Google search?) Ozob (talk) 00:08, 22 June 2011 (UTC)

To avoid fractured discussion, please continue at Wikipedia:Bots/Requests_for_approval/LivingBot_17#Review rather than here. Thank you LeadSongDog come howl! 04:32, 23 June 2011 (UTC)

New essay on Wikipedia editing for research scientists

I was prompted by some recent off-wiki email (asking me for advice on getting started with Wikipedia editing) to write an essay on Wikipedia editing for research scientists. It's in my user space for now but it seems reasonable to move it to Wikipedia essay namespace at some point. Any feedback would be welcome. —David Eppstein (talk) 17:27, 21 June 2011 (UTC)

Are you aware of this paper? I know some of the people involved. Seems to be well thought through. Charles Matthews (talk) 21:02, 21 June 2011 (UTC)

I wasn't aware of it, no. Looks quite helpful — thanks for the pointer. —David Eppstein (talk) 21:08, 21 June 2011 (UTC)

Mention using your watchlist and, in particular, putting appropriate project talk pages on it. JRSpriggs (talk) 08:46, 22 June 2011 (UTC)

Done, thanks. I've now moved this into Wikipedia namespace: Wikipedia:Wikipedia editing for research scientists. —David Eppstein (talk) 00:36, 25 June 2011 (UTC)

Horn angle

The new article Horn angle, is basically a DICDEF with inaccuracies (see the talk page). There is an obsolete term translated as Cornicular angle, or horn-like angle and Heath gives more than 3 pages of material on it (in small print) in his commentary on Euclid Book III Prop. 16. Mathworld also has a "Horn angle" article which has more modern references. I'd like to either change the article to a summary of Heath or change it to a redirect if no one thinks it's worthwhile.--RDBury (talk) 14:37, 23 June 2011 (UTC)

Does seem important enough for an article, although I guess it is more of an obscure historical issue than anything else. There are slightly longer discussions at [5] and [6] but without doing more reading I couldn't really confirm or deny my first impression that various people asked questions about whether this kind of "angle" makes sense, and that noone really gave much of an answer. Kingdon (talk) 23:25, 23 June 2011 (UTC)

MathJax

I'd like to mention MathJax and it's implementation. I was introduced to it by Salix Alba via the maths reference desk. Has anyone used it before? It's absolutely amazing. You can use in-line LaTeX and it sorts out all the font size problems, the base line heigh problems; everything. It looks really slick. At the moment we need to include some code in our vector.js files and then change our preference so that all maths code in displayed in LaTeX. But after that MathJax does the rest. I've included a couple of screen shots. The first one is without MathJax and with default IP preferences and settings. The second one is with MathJax added to my vector.js and with "always display LaTeX" preference. I'm sure you'll agree that the difference is quite astounding.

Without MathJax; standard default IP settings

With MathJax; one small preference change

I was hoping that we might discuss it, and it's future use. How many people have used it? Would we recommend using it as default in future, i.e. getting the developers involved? Any other comments would be welcome. — Fly by Night (talk) 22:58, 24 June 2011 (UTC)

Are there any particular Wikipedia articles in which this is used? If so, we could see some examples of how it's done. I haven't the foggiest idea what vector.js files are. Must one set one's preferences appropriately in order for this to work? If so, every reader who looks at an article in which this software is used without their preferences suitably set will see something different from what is intended. If the use of this software is to be widespread, then some examples and guidelines on its use should be at Wikipedia:Manual of Style (mathematics) and at Help:Displaying a formula. Michael Hardy (talk) 00:07, 25 June 2011 (UTC)

I think the only requirement on a Wikipedia article is that it uses <math> formatting instead of HTML formatting, but indeed one must set one's own preferences to see this. I would very much like to see mathjax become standard for Wikipedia math formatting, so that no special user-preference tweaking is required; it works well on the other sites I've used that use it (e.g. mathoverflow and mathscinet) and looks a lot better a lot more consistently than the alternatives. —David Eppstein (talk) 00:34, 25 June 2011 (UTC)

If what David Eppstein suggests can be done, it will solve a problem that's been plaguing this, the most active of all WikiProjects, since about the beginning of 2003 (that being when we got TeX, IIRC). Michael Hardy (talk) 03:18, 25 June 2011 (UTC)

It can be done. That was my very reason for coming here. Hopefully the developers will write it in as the default maths mode. But at the moment not many people use the MathJax set-up and it's still in testing. We need to get the maths Wiki project behind it before it's even conceivable that the developers will do anything about it. There's no need to write the whole page in maths mode. The beauty of MathJax is that it can handle HTML and LaTeX side by side; in fact that's the reason for it's introduction onto Wikipedia. All it does is change the way the browser sees the maths output. Why not follow the instructions in my bulleted post below and give it a go. — Fly by Night (talk) 03:37, 25 June 2011 (UTC)

Michael, I have posted an example above. The use of MathJax is a preference setting. You add two lines of code you your vector.js page, and then change your preferences so that all maths code appears as LaTeX output. The vector.js page (assuming your using the vector skin) is some extra code that you add that changed the way your browser displays Wikipedia; the .js suffix means Java Script. Then you will see all pages in the new way. But it only works for those users that have performed those two steps. I mentioned it here because the first step is to get the maths Wiki project to endorse it. Take a look at User:Nageh/mathJax for a better explanation. — Fly by Night (talk) 01:03, 25 June 2011 (UTC)

• To use MathJax (I borrowed this from Salix); you need to add

mathJax={}; mathJax.fontDir="http://cdn.mathjax.org/mathjax/latest/fonts";
importScript('User:Nageh/mathJax.js');

to your Special:MyPage/vector.js. Then switch the option for Math to "Leave it as TeX" in your Preferences - Appearance tab. That's assuming you use the vector skin. If you use another skin then replace vector with the name of the skin. — Fly by Night (talk) 01:09, 25 June 2011 (UTC)

I think it's working! I didn't have a Special:MyPage/vector.js file; I created it by adding that bit of code. Now all we have to do is implement David Eppstein's suggestion above and all the problems of the Universe are solved. Michael Hardy (talk) 03:31, 25 June 2011 (UTC)

Excellent! Another feature I really like is if you enter a backslash command incorrectly, it compiles all the code except that command and then highlights the incorrect command in red; instead of giving a screen full of red error message. My LaTeX editor can't even do that! To see the difference it makes, log out and view the page as an IP. — Fly by Night (talk) 03:41, 25 June 2011 (UTC)

While its still a bit early to get this set as default for all users it might be an idea to see if this could be set as a Wikipedia:Gadget making it easier to people to install it and increase the user base. A MathJax userbox might also help its uptake.--Salix (talk): 07:48, 25 June 2011 (UTC)

I use MathJax mainly because it is scalable; I don't like the small size of the default TeX rendering. And if any of you use Firefox and have STIX fonts installed, you may want to choose MathML as the renderer, for it is faster and better looking.--Netheril96 (talk) 08:33, 25 June 2011 (UTC)

MathJax has been brought up before here, see Wikipedia talk:WikiProject Mathematics/Archive 68, among others.--RDBury (talk) 11:43, 25 June 2011 (UTC)

Serious software bug!

${\begin{aligned}2+3&=5\\[8pt]3\times 3&=6\end{aligned}}$

Spacing by the use of \\[8pt] and the like within the align environment in TeX, and within arrays and matrices set in TeX, occurs in MANY Wikipedia articles. If you see what I'm seeing on the screen in front of me, it's not working here, and even worse—far, far worse—the reader actually sees "[8pt]" at the beginning of the following line, and will wonder what it means in the mathematical notation. Michael Hardy (talk) 16:54, 25 June 2011 (UTC)

(I observed this when I looked at the article titled meridian arc.) Michael Hardy (talk) 16:55, 25 June 2011 (UTC)

I am aware of this. It's a current limitation, not a bug. You will find a few things not (yet) implemented, which is because MathJax does not rely on a full-featured TeX back-end. This is one of the reasons why the extension is still for testing and not production usage. FYI, I am already working on a (temporary) work-around for this issue. Future bug reports should go to the extension's discussion page. Thanks for testing! Nageh (talk) 17:03, 25 June 2011 (UTC)

At q-Gaussian I find this:

$x\in \left[\pm {1 \over {\sqrt {\beta (1-q)}}}\right]$

Using mathJax, the way it appears in the article sets the material within the brackets visibly closer to the bottom of the brackets than to the top. Michael Hardy (talk) 17:36, 25 June 2011 (UTC)

It's even worse without MathJax. Try logging out and looking at the same formula as an IP without MathJax. The square root sign sticks out of the bottom of the brackets. See Here — Fly by Night (talk) 18:16, 25 June 2011 (UTC)

This one is of course a minor issue. Then one I labeled "serious software bug" is a major issue; it makes it unthinkable to force mathJax on everyone. Michael Hardy (talk) 04:14, 26 June 2011 (UTC)

That's why it's currently in testing, and hasn't been forced on anyone. Nageh said that it's a not a bug, but a limitation, and that he's working to get around it. Besides that, I wouldn't think that many people use that command you gave. I never seen it or used it, and I've been using LaTeX for the best part of 10 years. I think you might be in the minority of users that uses that type of command. In which case, even in its present state, it would work perfectly for the majority of users. — Fly by Night (talk) 13:53, 26 June 2011 (UTC)

• There is a feedback page at User_talk:Nageh/mathJax. It might be an idea to list any problems there as a more permanent reference. This discussion will be archived in a few days.

Charles Paul Narcisse Moreau

A new article titled Charles Paul Narcisse Moreau, created by user:r.e.b., is one of the more unusual biographical articles, in that identification of the person seems to be a moderately intractable problem, and the intractability itself seems somewhat well-documented. These three people seem to be known to have existed:

• A French military officer who organized a course of instruction on artillery and did various other things;
• A mathematician who introduced Moreau's necklace-counting function and wrote various other papers;
• A Colonel Moreau who is renowned as one of the losingest players ever in tournament chess, who lost all of the 26 games he played at a tournament in Monte Carlo in 1903.

The question is: Are all three the same person? Considerable circumstantial evidence that these three are the same has been published.

In the unlikely event that somebody knows something, could they further edit the article accordingly? Michael Hardy (talk) 23:50, 24 June 2011 (UTC)

There's a bit more here; NB that the later items are presumably a different Charles Moreau. CPM Moreau is at Calais in one case. May need specialist research. Charles Matthews (talk) 08:50, 26 June 2011 (UTC)

List of winners of the Mathcounts competition

There is a new weekly section on the main page called "Today's featured list" and I have nominated List of winners of the Mathcounts competition to have a spot here. There has been some opposition to the nomination and it looks like the list could become a removal candidate very soon unless the quality of the list is improved. If you are interested in maintaining the list's featured status and seeing a summary of it up on the main page, your help in improving the article would be greatly appreciated. Neelix (talk) 03:37, 25 June 2011 (UTC)

Ricci Tensor

The introduction of the article seems to say that the Ricci tensor is symmetric for all pseudo-Riemannian manifolds. In a book I'm reading at the moment, it says that an affine connection ∇ with zero torsion has symmetric Ricci tensor if and only if ∇ is locally equi-affine. Where we call an affine connection locally equi-affine if around each point x of M there is a parallel volume form, i.e. a non-vanishing n-form ω such that ∇ω = 0. Which one is correct, the article or the book? It seems to me that there are some missing hypotheses in the article's statement. — Fly by Night (talk) 17:04, 25 June 2011 (UTC)

I think you are forgetting that for a pseudo-Riemannian manifold it is assumed that you use the Levi-Civita connection, which is always equi-affine. (The Levi-Civita tensor always is a parallel volume form for the Levi-Civita connection.)TR 20:10, 25 June 2011 (UTC)

But that's my point: it's not assumed; the Levi-Civita connection's not even mentioned until much later in the article. Reading the introduction, there's absolutely no reason to believe that ∇ is the Levi-Civita connection. Moreover, in general, it is not assumed that a connection on a pseudo-Riemannian manifold is the Levi-Civita connection. Take the book I linked to, for example. It would be a good idea to add this, and more detail to the article to avoid confusion. — Fly by Night (talk) 20:55, 25 June 2011 (UTC)

The Ricci tensor of pseudo-Riemannian manifold is by definition the Ricci tensor defined by the Levi-Civita tensor defined by the pseudo-Riemannian metric. It never is anything else, even when you calculate the Ricci curvature of some other connection on that manifold. As to the Ricci curvature article, it does (implicitly) say in the last line of the definition section that up till that point the Levi-Civita curvature had been assumed. Looking, at that article in general, not clarifying that earlier seems to be the least of its problems. As the article is currently written it is most likely useless to anybody that does not already no what the Ricci curvature is.TR 21:39, 25 June 2011 (UTC)

The Ricci curvature associated to a general affine connection is something that is only studied seriously by a very small group of people, whereas the Ricci curvature associated to a pseudo-Riemannian manifold is one of the most important objects in relativity theory and Riemannian geometry. I think it's appropriate to focus on these cases, and I have consolidated the discussion of the Ricci tensor associated to an affine connection to a short section at the end, since it doesn't seem appropriate to treat this in parallel with the classical Ricci tensor (the two have completely different properties, and are used for completely different things).

I agree that the article is not very good. I've tried in the past to improve it, but progress has been slow. There hasn't really been much wider input, and I've not really been willing to devote the time to get the article into satisfactory shape on my own. It seems from the discussion page that the article historically has been pulled in different directions by mathematicians of different stripes, and physicists. It might be helpful to have a constructive discussion at Talk:Ricci curvature. Sławomir Biały (talk) 22:03, 25 June 2011 (UTC)

TimothyRias: the definition of the Ricci tensor is relative to an affine connection; any affine connection. The Ricci tensor is defined as the trace of the curvature tensor, i.e. Ric(Y,Z) = trace{X → R(X,Y)Z}; and what is R well

$R(X,Y)Z=\nabla _{X}\nabla _{Y}Z-\nabla _{Y}\nabla _{X}Z-\nabla _{[X,Y]}Z\,.$

If you're only interested in the Levi-Civita then that's one thing; but it's wrong to say that "the definition" of the Ricci tensor is with respect to the Levi-Civita connection. Sławomir Biały: Thanks for you edits to the article. But there still needs to be some mention at the beginning that we assume the manifold to carry its Levi-Civita connection. The article on pseudo-Riemannian manifolds does not make a big deal Levi-Civita connections either. It mentions some parallel with the Riemannian case, but also some big contrasts. It seems to be a very unnecessary assumption that most people hold; probably because of the way they leaned the subject. I'm not sure only a small number of people are interested. There has been a large increase in research involving projective, affine, equi-affine and centro-affine differential geometry over the last 20 to 30 years. — Fly by Night (talk) 22:49, 25 June 2011 (UTC)

I don't really think the Levi-Civita connection needs to be overly emphasized, but it's probably appropriate to mention it in the Definition section. There's a potentially greater risk of fuss over the curvature conventions. (Our sign convention for the Riemann tensor is the opposite that of Besse, which is used as a reference for the article, but our sign convention for the Ricci tensor is such that spheres are positively curved.) I've added text to resolve both issues I hope. Sławomir Biały (talk) 23:25, 25 June 2011 (UTC)

I've added a little footnote, but it doesn't look quite right next to the Harvard citation style. My footnote is indicated by a superscript number in square brackets. Not sure if you want to change the style… — Fly by Night (talk) 23:41, 25 June 2011 (UTC)

decimal points, full stops, and commas

WP:MOSMATH doesn't seem to say anything about things like this. I think in much of Europe it is customary to use a comma as a decimal point and a period (or "full stop") in the way most English-speaking people in the present day are taught to use commas in numerals. I think the system used in much of continental Europe has been taught in England within the memory of persons still living today.

Should WP:MOSMATH say something about this? Michael Hardy (talk) 21:26, 25 June 2011 (UTC)

The use of period for a decimal point has been standard in England for at least a century. See, for example, page scans of the 1911 Encyclopedia Britanica which are available on WikiSource. I don't think the issue would come up except for people copying and pasting tables from foreign language sources or using machine translation without proof reading. To me it's not an issue for MOSMATH anyway since most math articles don't have many big numbers; you're more likely to get them in geography articles.--RDBury (talk) 22:43, 25 June 2011 (UTC)

Actually, it's already in the general MOS, see WP:MOS#Large numbers and WP:MOS#Decimal separator.--RDBury (talk) 12:09, 26 June 2011 (UTC)

On my talk page, User:Peter Mercator has said that the convention alleged above to have been standard in England for at least a century is "laziness", and the opposite convention has been traditionally taught in English schools. In particular, he says that the usage that is no longer standard in English preserves the distinction between decimal points and full stops. I responded that it fails to preserve the distinction between mid-level dots as decimal points and mid-level dots to indicate multiplication. Michael Hardy (talk) 23:51, 26 June 2011 (UTC)

The raised decimal point is mentioned in Interpunct. In tex it is supported by the 'decimal' package, wherein we read "The decimal point (decimal separator) is variously implemented as a comma (European), a full point (North American), or as a raised full point (English)." This variation is present amongst the text books in my library. So the dispute, if there is one, is between American and British usage. Peter Mercator (talk) 11:46, 27 June 2011 (UTC)

WP:MOS#Decimal separator says "Use a period character between the integral and the fractional parts of a decimal number, not a comma or a raised dot". That seems clear and unambiguous to me. If you want to lobby for a change to the MOS guideline, you could start a discussion at Wikipedia talk:Manual of Style. Gandalf61 (talk) 12:01, 27 June 2011 (UTC)

Even in British English, the raised dot is seldom used, so this isn't a British versus American usage issue. As long as we're quoting the documentation from the LaTeX "decimal" package, let's be sure not to quote it out of context [7]:

In Great Britain until about 1970 or so the decimal separator was typically implemented as a raised dot (middle dot)... While the raised dot does make occasional appearances in British newspapers, it is, unfortunately, seldom seen nowadays even in British scientific journals.

I think a "revival" of the middot would be quite inappropriate given the overwhelming predominance of the period to denote the decimal point in modern English typography. Sławomir Biały (talk) 12:25, 27 June 2011 (UTC)

Notability of books

Discussion on the notability guidelines for specialized books, such as math or programming is going on at Wikipedia talk:Notability (books)#Criterion out of context. Some editors maintain that book that have not been covered in-depth in venues for a general audience, such as the New York Times, should be deleted from Wikipedia. However, recent AfD discussion on math and programming books ended up with such books being kept if they pass the less restrictive WP:GNG. I'm aware that every book in the Springer Graduate Texts in Mathematics, for instance, has probably been reviewed in some math journals, so passes GNG, but whether it passes NBOOK is open to interpretation. Please voice your opinion in that discussion. FuFoFuEd (talk) 01:24, 27 June 2011 (UTC)

Discrete Green's Theorem: is it really notable? and who did it first?

I was surprised to come across an article for Discrete Green's theorem. This isn't exactly a deep result; I suspect that it wasn't published much earlier only because noone thought it worthwhile. The "history" section of the article claims that the theorem was introduced in 2007. A MathSciNet search turns up something from 2005 with a reference list suggesting that the same authors published on this subject in 2003. I wouldn't be surprised to find that others independently had the same idea earlier.

My main concern with the article as it stands is that it reads too much like promotion of Finkelstein's work. There's also some potential conflict of interest with User:Amiruchka (who identifies himself as Amir Shachar) editing the page. In particular, it's unusual to have a link to a YouTube video in the lead paragraph. Does anyone know enough about the topic to improve this article? Jowa fan (talk) 07:45, 27 June 2011 (UTC)

There is no way this is new. Manifolds with corners are a little obscure (they are what you get when you e.g. take products of manifolds with boundary), but nevertheless they are not a new topic, and Stokes's theorem for them is not a new topic, either. See [8] for this very subject; it provides references to several books. Ozob (talk) 10:29, 27 June 2011 (UTC)

It's not really Stokes' theorem (or Green's theorem for that matter). It's just the ordinary one-variable fundamental theorem of calculus applied to the double integral of a function on a rectangle. It seems like the sort of thing that could be given as an exercise is a calculus textbook. Also, I note from his homepage that Amir Sachar and Amir Finkelstein are the same person. Sławomir Biały (talk) 10:41, 27 June 2011 (UTC)

Well, on a rectangle, Green's theorem is the ordinary one-variable fundamental theorem of calculus. :-) Ozob (talk) 10:47, 27 June 2011 (UTC)

Yes, of course. But calling this result "Green's theorem" in that very special case is a bit disingenuous (e.g., like referring to the Fundamental theorem of calculus on the interval [a,b] as "Stokes's theorem for the oriented manifold [a,b]). There's certainly no need to invoke manifolds with corners. Sławomir Biały (talk) 10:56, 27 June 2011 (UTC)

There is a paper by Yang & Albregtsen which uses the term and seems to be used as a reference fairly often in the literature. The article doesn't seem to mention this at all though. As used in the paper the notability is arguable but I'd come down on not notable. The article claims it's using a different version based on Power Point presentations, not even arguable notability.--RDBury (talk) 11:30, 27 June 2011 (UTC)

Regarding the theorem's significance: The theorem was formulated as a key theoretical result in both and . The importance of the ICCV conference and the Springer journal are undisputed. Further, Wang et al.'s work from 2007 (where the theorem was first formulated, see Theorem 1 in ) was already cited 37 times (June 2011). Within four years from its publication, at least two generalizations of the theorem were published (see in the "extensions" part). Note that the theorem generalizes both the Fundamental theorem of Calculus (into two dimensions, in an intuitive manner), and the Integral Image algorithm (into continuous domains and finite unifications of rectangles). Thus, the theorem generalizes both a classical result in Calculus and a fundamental algorithm in computer vision. Regarding the "who did this first" discussion: I never saw this theorem before I saw Wang et al.'s work. Even the authors were surprised that it was not found in the literature:

“ To the best of our knowledge the integral computations have been used only when the region D is rectangular. ”

(see ). I was familiar with the works you have mentioned. Throughout the years, many discretizations were suggested to Green's theorem (such as Tang's work from the 1980's) - however, none of them introduces this specific theorem. Regarding the claim that "this theorem could have been given as an assignment in a Calculus course" - well, it wouldn't be the first simple and elegant mathematical result. Regarding the YouTube video: it forms an introduction to the theorem and to the article. It is highly relevant to the article. It helps researchers understand it and explains the motivation behind it; the video receives encouraging comments from Wikipedians weekly. Regarding your concern that this article stands for a promotion of my (Finkelstein's) work: Note that my own original work is barely stated there, apart from the 'extensions' part, where my colleagues' work, Pham et al.'s, is given the same amount of credit. My contributions to Wolfram that are cited in this article do not aim to promote my work, but rather to help researchers better understand the theorem. Last, regarding my name - it used to be Amir Finkelstein, and I recently changed it to Amir Shachar in the memory of my beloved mother, Sarit, who unfortunately passed away one year ago.--amiruchka (talk)

On the issue of "Why is it so difficult to learn mathematics from Wikipedia articles?"

“ Wikipedia is an encyclopedia, not a textbook. Wikipedia articles are not supposed to be pedagogic treatments of their topics. Readers who are interested in learning a subject should consult a textbook listed in the article's references. If the article does not have references, ask for some on the article's talk page or at Wikipedia:Reference desk/Mathematics. Wikipedia's sister projects Wikibooks which hosts textbooks, and Wikiversity which hosts collaborative learning projects, may be additional resources to consider. ”

The fact that this is case makes me question the utility of encyclopedias in general. What does an encyclopedia do that a textbook covering every academic subject could not? A lot of the higher mathematics articles would seem to be much ado about nothing, if it were not for its utility for those who are simply reviewing for higher level math exams. An encyclopedia that reads like a glossary in prose-form is not very effective as tool for learning; so it has a very narrow purpose, in my opinion.

The habit seems to be, "Never try to combine encyclopedias and textbooks." That might be reasonable advice prior to the internet, as such a volume set would be much larger than an encyclopedia. However, now that we do not have that physical constraint, I cannot not see how we are better off by limiting Wikipedia to an "encyclopedia".siNkarma86—Expert Sectioneer of Wikipedia
^{86' ' = 19+9+14 + karma = 19+9+14 + talk} 03:02, 28 June 2011 (UTC)

A couple of things. One is that didactic exposition makes the articles less useful for readers who come to look things up. It is expected that an encyclopedia is first and foremost a reference work, a place to look things up.

Another serious issue is that a textbook exposition inevitably involves choices on the part of the author on how to guide the student to an understanding of the material. It is pretty much impossible to do that neutrally. Encyclopedic "just the facts" exposition does not eliminate that problem entirely, but in my judgment at least, it ameliorates it somewhat. --Trovatore (talk) 07:11, 28 June 2011 (UTC)

A third issue is that didactic exposition needs to assume a certain base level of the reader. This is not (always) necessary for an encyclopedic article, which should be able the relate facts too (almost) any level of reader, since the reader does not need to be brought to understand why a statement is true, but only that the statement is true. (The trouble of mathematics articles is finding a way too convey the content of a mathematical statement to a lay audience.)TR 07:46, 28 June 2011 (UTC)

Plus isn't this supposed to be what Wikiversity was about? The materials there aren't wonderful but if we put in a few links perhaps it would encourage some people to try and develop them. Another alternative might be to put some effort into identifying the best resources on the web for teaching various things and put links to them in a special section in relevant articles, not just externals but say something titled 'Learning resources'. The OP talks about combining encyclopaedia and textbook because we're not constrained by size, but one of the basic things one should do on the web is try and cut down each page to the right size for its main purpose. So the learning resources should be on different pages and just linked to. And if they are linked to why do they need to be jumbled in with the encyclopaedia pages? Dmcq (talk) 08:08, 28 June 2011 (UTC)