Wikipedia talk:WikiProject Mathematics/Archive 4

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This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

1 Graph (mathematics) vs Graph theory
2 joy of tex
3 Bug in new version
4 A little note on using purple dotted boxes
5 Wikipedia:WikiProject Mathematics has this article lost focus?
6 Wikipedia:How to write a Wikipedia article on Mathematics
7 \pi image in Template:Math-stub
8 PlanetMath
9 Where to contribute math articles? Wikipedia or Planet Math?
10 MathWorld references
11 Wikipedia:WikiProject Mathematics/PlanetMath Exchange -- version 0.1 -- comments requested (on this page)
12 Begging the question
13 New Mathematics Wikiportal
14 Tex rendering -- help!
15 binomial expansion of (p_1 + ... + p_n)^c
16 \phi or \varphi
17 use of phi and theta in spherical coordinates
18 Relevant proposed naming convention: ambiguous adjectives
19 Soliciting input on Estimation theory
20 straight or italic d?
21 Reformat of Participants list
22 "monotonicity" merged with "monotonic function"
23 Algebraic solution
24 periods at the end of formulas -- request for comment
25 Period before or after </math> -- please comment on this as there are opinions on both sides.
26 Vanity references?
27 Structure of math articles
28 encouraging references for formulas

Graph (mathematics) vs Graph theory

I am currently working on graph (mathematics) and graph theory. It is not clear to me what sort of distinction to draw between those two articles. User:Oleg Alexandrov has similar problems on matrix (mathematics) and matrix theory. Other articles having the same problem are

My opinion is the basic article (e.g graph) should contain

brief motivation
definitions
examples
generalizations of definition

whereas the theory article should contain

history
detailed motivation
relation to other areas
important problems

Any comments ? MathMartin 12:35, 7 Jan 2005 (UTC)

I don't think there should be two pages at all. One of them should be a redirect to the other and all the material should be on the same page unless some subtopic (maybe "History of X theory") grows large enough to be its own article. --Zero 13:18, 7 Jan 2005 (UTC)

I think for all of these topics, there should be the two pages mentioned (and more, each should eventually have a "history of" article also, giving a detailed and comprehensive history), and I think that MathMartin's description of how they should differ seems reasonable to me. See also Set theory, Set, Naive set theory and Axiomatic set theory. Paul August ☎ 14:19, Jan 7, 2005 (UTC)

I think Zero has a point. Ideally, one article should be enough. However, the longer articles get, the harder is to keep a "global picture" of the article. This has many consequences, among them being that mistakes are easier to slip through, consitency is harder to keep, etc. This is especially true on such an anarchic place like Wikipedia, where ultimately nobody is in charge of anything. So I would suggest splitting articles, which clear motivation, like MathMartin suggests. To to a good job at that, is not so easy though. Oleg Alexandrov 19:18, 7 Jan 2005 (UTC)

Here is my current (changed) opinion on this topic. In general there should be only one article called X theory. If this article grows too large certain parts of the article should be put into separate articles (like history of X theory) so that we get a hierarchical structure of articles. The subarticles (like history of X theory) should have a name making it obvious what sort of content belongs to the article. The subarticles should have a link to the main article at the top.

I think this hierarchy of articles is preferable to my earlier suggestion of parallel articles because it provides a

clearer and more intuitive structure for the reader
allows for better editing as the article can grow gradually from one article to a tree of articles without the need for restructering several articles at once

Several articles like french language, france or category theory already use this structure. I will merge graph (mathematics) into graph theory to provide a concrete example. MathMartin 15:15, 9 Jan 2005 (UTC)

Please don't. There is a specific need for short articles that give a definition and some examples, versus longer articles that talk about the theory in general. -- Walt Pohl 08:19, 10 Jan 2005 (UTC)

I already merged them. Can you point to any discussion on this subject or give a more detailed explaination ? MathMartin 10:12, 10 Jan 2005 (UTC)

MathMartin: As I said above, I think it would be better if these articles were kept separate. I agree with Walt Pohl, that there is a need for a short article that, for example, defines "graph",and gives some examples, so that a user doesn't have to wade through a longer article for that information. I think your original idea was correct, and so did Oleg Alexandrov, who gave some excellent reasons for supporting your idea. I don't understand why you changed your mind? I think you should consider changing it again ;-) Paul August ☎ 22:10, Jan 10, 2005 (UTC)

I also agree. It's nice to be able to say "In graph theory, the 'Petersen graph is a graph that ...". The first link gives the broad theory, the second gives a particular definition. Dbenbenn 22:26, 10 Jan 2005 (UTC)

I've always assumed that was the rationale for the division between X and X theory, though I'm not sure I've ever seen it spelled out. The rationale, as I have perceived it, is: most of the time, an article that mentions X just needs the definition, and not the whole theory. For example, the integers form a ring; it's sufficient to be able to jump to the definition, rather than a topic on ring theory, which will talk about noncommutative rings, ideals, etc. It makes using convenient math terminology somewhat more intimidating to use.

It could be that the way you're suggesting really is better, but since it's something of a de facto standard on math pages, I think it's something we should hash out here. -- Walt Pohl 23:10, 10 Jan 2005 (UTC)

I think MathMartin's action was a little premature given the active discussion on the issue, but on the other hand I think the structure is better now than it was before. I have no problem with an article containing mostly definitions, but the problem with the 2-part structure is that the theory page either has to repeat the definitions or to leave them out. The first is clearly undesirable. The second is also undesirable since someone reading the theory page should not need to flick back and forth to another page in order to understand it. I think the structure MathMartin has established is actually pretty good; of course there is always room for tweaking. --Zero 00:22, 11 Jan 2005 (UTC)

There is no harm in repeating the definition — as long as they are the same! ;-) Paul August ☎ 02:51, Jan 11, 2005 (UTC)

Even if they start off the same, sooner or later they will diverge. It always happens that way. --Zero 06:43, 11 Jan 2005 (UTC)

Well they don't have to be identically worded, as long as they are mathematically equivalent. Different ways of presenting the same definition can be a good thing. Of course, a definition may be edited, so as to become incorrect. And, of course, this can happen, whether there is one version of the definition or not. However, such an error is less likely to occur, and is easier to fix, if there is another "repeated" definition to which to refer;-) Paul August ☎ 15:21, Jan 11, 2005 (UTC)

Please, keep them separate. From a purely mathematical point of view, graph theory is a different entity than graph, it is like set of all theorems about graphs. Also, graph theory evolved (among other things) from study of minimal weighted spanning trees - where the spanning tree was defined as a rigid body of rods connecting set of points in Euclidean space, and the weight was given by the length of rods (that's definition Jarnik and Boruvka used, I think). See Boruvka's algorithm,Prim's algorithm (now I am looking at it, and don't quite understand the difference among these algorithms - it seems that they only differ in clever use of data structures, but the greedy method is always used; they should be merged in one article probably). Anyway, such historical connections are inapropriate in article about graph. Samohyl Jan 16:48, 11 Jan 2005 (UTC)

I will try to separate the pages again while trying to keep the hierarchical structure. My main point is, if we have separate pages on topics which are very similar, the ordering/relationship between the pages should be sufficiently clear even to a novice reader/editor. MathMartin 17:01, 11 Jan 2005 (UTC)

There is no need, necessarily, to remove any current content from Graph theory. As long as what is there now is relevant to it, which presumably it is. All that needs to be done, really, is recreate the Graph (mathematics) article, more or less as it was before the merge. There can be considerable content overlap between the "theory" article and the "graph" article. In my view, the main difference between them should be functional. The "graph" article should be narrow and concise, just explaining what a graph is. The "graph theory" article should be broad and comprehensive, saying what a "graph" is, in detail, as well as what "graph theory" is, in as complete a way as possible.

The problem of article "structure" is an important one. Martin is right to be considering it. I am glad he has brought it up here for discussion, and I would like to thank him for doing so. (Martin: Thanks ;-) As he says, having separate but related articles, for which the relationships are unclear is problematic. For example there is a real danger (and this may have already happened, to some extent) of our "graph" article becoming, more and more, like an article about "graph theory", without its editors being aware of, or taking sufficient notice of, the fact that there was already an article on "graph theory". We need to be vigilant against this. Adding some italicized disambiguation text at the beginning of each article explaining what the article is about and the existence of the other article, might help, in this regard.

Figuring out the best way to organize our mathematical content is a difficult problem with no easy solution. It will behoove us to give lots of serious thought to this and devote more time discussing it. I will say though, that I don't think that the ideal structure for these articles in Wikipedia is a "hierarchical" top-down one. Wikipedia just isn't like that. Nor in reality are most of the topics it covers. Even in mathematics where one might in principle organize all of the subject in one great hierarchy — and mighty and heroic attempts have been made to do just that — this is not, in my opinion, the best way, really, to think about mathematics, nor to learn it, nor to present it in an encyclopedia. The "true" structure of mathematics, in my view, while involving many hierarchies, is much more complicated. And, as it happens, Wikipedia is well suited to reflect this ;-)

Paul August ☎ 19:10, Jan 11, 2005 (UTC)

I have separated the pages and fixed the links. I did not duplicate the definitions because I think duplicating basic definitions is confusing for the reader. I think graph theory is understandable even without a definition of what a graph really is, because of the informal discussion in the introduction. MathMartin 18:39, 11 Jan 2005 (UTC)

I'm new here, so I can give an outsider's view on the split structure -- it's terrible. Not least because graph leads to a disambiguation page which confusing in itself -- until you finally realise you want graph (mathematics)... and then that all the information is under graph theory. A hierarchical structure under graph theory would lead to much less confusion. It does not necessarily mean graph theory has to grow out of hand as it can lead to more subtopics. Also on subtopics, I'd like to start a discussion on better linking to graph theory applications (as I said, I'm new, I'll take a look round first). Particularly I notice that network analysis and social networks could be better brought together. --stochata 20:33, 30 Jan 2005 (UTC)

I just flagged all three articles (Graph theory, Graph (mathematics), Glossary of graph theory) for a merge, ignorant of this discussion. I do agree that more than one page is a Good Idea, but I don't think the way the material is now sorted out is any good at all. I'm a fairly smart guy, with plenty of background. (Not to put on airs, but my mother was a prominent graph theorist and I grew up with the material the way other kids grew up with Curious George.) And still, when I read the "introductory" material at Graph (mathematics), I about drowned -- I am a little out of practice.

I just finished reworking and expanding Seven Bridges of Königsberg; this was one of my bedtime stories and I know it by heart, but I wanted to be sure to use all the correct terms. I ended up researching the jargon on the net external to WP and building my own glossary, which I slipped into Graph theory -- the only place I expected to see any general article on the subject. I'm not sorry I did, either; I sure didn't duplicate the advanced article at Glossary of graph theory, which reads more like a syllabus or perhaps a sheaf of classnotes.

I am going to go way out on a limb here and say I may be the most qualified individual to work over this stuff. Most folks know nothing at all about the subject and could care less. Experts know the material so well that they have difficulty explaining it to the unwashed horde. This is not the place for a textbook. Yes, there's no harm in presenting some advanced material (what experts consider to be the absolute minimum basics) for the few who are willing to work through it. But the bulk of people who visit just need to get a quick handle on the topic. I am a long way from being an expert on graph theory, but I believe I at least know enough to know when I don't know what I'm doing, and I won't monkey with anything like that without discussing it. I would like an expert to work with me on this, to check my work as I go along, to make suggestions.

If you want to see how I go about things, then besides looking at the seven bridges, you can check out my one-day glossary at Graph theory#Glossary. I think that is the kind of introductory material that needs to be most accessible to the casual reader. I shouldn't throw out the advanced stuff, but it should be clearly so labeled and better organized.

I see that this area has already been the subject of one hasty restructuring. I plan to replicate the existing material on a few dummy pages and edit them there. When this group reaches some sort of concensus on the dummies, we can change the "real" pages to follow.

Again, if it's not clear, I'm here recruiting an expert buddy for this effort. — Xiong (talk) 02:41, 2005 Mar 21 (UTC)

I have also been struggling with these unstructuredly interrelated pages. I have to say that I think what happened to the set theories is extremely horrible in ways of structure and duplication and ease of finding what you're looking for. Also in this way it is extremely hard to add information, since it is quite unclear what the best place for it is. Thus I would also ague for a hierarchic approach. The fact that mathematics may not be hierarchical itself doesn't present a problem, because of all the wikilinks. Graph theory may be an ideal area to work on, since there are so many excellent examples (wikipedia itself!) and could thus have a great motivational sections. As an aside I really dislike the glossaries. Perhaps we should incorporate them into the main storyline. And while we're at it add some lemma's, which are the reason d'etre for all those defs after all. -MarSch 13:37, 7 Apr 2005 (UTC)

joy of tex

I am trying to put a few equations in Hull-White model, but, at least on my browser the equations seem to come out in different sizes. Any tips on how to make the page look a little neater? Thanks. Pcb21| Pete 23:03, 13 Jan 2005 (UTC)

The size problem is because some of the equations are images generated by Wikipedia, which doesn't know the browser's font size. You could fix the problem by forcing all the displayed equations to be images, but I think that solution would be worse than the problem. Dbenbenn 23:33, 13 Jan 2005 (UTC)

Not necessarily - at least the page looks consistent. I've done so. Try to also avoid inline <math> (use HTML), since that usually comes out as a PNG inline and doesn't look very nice. Dysprosia 23:51, 13 Jan 2005 (UTC)

Bug in new version

Has anyone noticed that putting math tags inside a link (like this: [[Lp space|<math>L^p</math> space]]) no longer works? (See Sobolev space for an example). When did that happen? Should we file a bug report? Where do you file bug reports so that they are actually noticed? Uffish 02:56, 14 Jan 2005 (UTC)

Bugzilla

A little note on using purple dotted boxes

Don't. JRM 19:02, 2005 Jan 16 (UTC)

Or less facetiously: at least use "class='theorem'" or similar in addition to the style comment. This will allow updated style sheets to render theorems in whatever fashion the user wants, and to override any style you put in.

Wikipedia:WikiProject Mathematics has this article lost focus?

Greetings from a fellow mathematician. I am happy there are so many of us hanging around on Wikipedia. And I like the Wikipedia:WikiProject Mathematics thing. However, it seems to me there is just too much stuff in there, which could be better organized.

For instance, the second half of it could be condensed in a usage and style manual for writing Wikipedia articles on Mathematics, and put on a separate page. It could also be merged with Wikipedia:Styles of Mathematics Articles which seems to have never got off the ground.

The list of participants is getting large. Maybe it could go in a separate article too.

Also, some of the stuff in the article could be safely moved to the talk page, after incorporating all the insights written there in the usage and style manual above.

These are just some thoughts. It just looks to me this page lost some focus. What do you think?

Oleg Alexandrov 05:15, 18 Jan 2005 (UTC)

Yes, we could use some subpages now. Charles Matthews 13:58, 18 Jan 2005 (UTC)

I wasn't ever aware of it having any focus. If the question is whether it lacks focus, I will agree. But it has never been clear to me what this page is for. -- Dominus 14:21, 18 Jan 2005 (UTC)

I agree with Dominus that this page never really had focus. We've just used it as a place to thrash out issues on math pages. -- Walt Pohl 20:18, 18 Jan 2005 (UTC)

I agree with all of the above. Oleg: If you want to try to improve the focus and organization of the page in some of the ways (or others) you mention, I think that would be fine with me. You could just go ahead and give it a go ;-) ( See: Wikipedia:Be bold). But be prepared for possible objections to any changes you make ;-) Or you could try to discuss changes here first, especially if they are significant. Paul August ☎ 20:59, Jan 18, 2005 (UTC)

To be specific, I want to make some of this stuff into a true usage guide for math articles, that is a Wikipedia: Manual of style for math articles. How's that? Oleg Alexandrov 21:31, 18 Jan 2005 (UTC)

And I do mean on a separate page.... Oleg Alexandrov 21:42, 18 Jan 2005 (UTC)

Wikipedia:How to write a Wikipedia article on Mathematics

Well, having heard several why`s, one be bold, and no no`s, I forked out an article with the title above. Such an article is obviously necessary, and while what is here at WikiProject Mathematics has good stuff, it looks too much like a talk page. This new article still needs lots of work. For now I did not do much, as I don't want to wake up tomorrow morning seeing in my watchlist things like "reverted", "redirected", or even "submitted for speedy deletion". :)

If nobody objects (if you do, say it now :), then in several days I will continue polishing the new thing. Of course, if you contribute things to it, or if you simply add it to your watchlist, it will help.

Oleg Alexandrov 02:55, 20 Jan 2005 (UTC)

Thanks Oleg. I have reorganised and updated the project page; now there is much common material, and you may want to cut out from the project page most of the issues covered in your 'manual'. Charles Matthews 10:19, 20 Jan 2005 (UTC)

\pi image in Template:Math-stub

There is some debate over the use of a \pi image in Template:Math-stub; there's small edit war going on. Please see Template talk:Math-stub#Pi_image if you care to voice an opinion. (Please do not discuss this here; discuss it there; thanks.) —msh210 04:47, 27 Jan 2005 (UTC)

PlanetMath

I've been talking with the guy that runs planetmath.org (we go back 6 years). I'm in the preliminary stages of setting up a project to move over the content from PM to WP. Uncreated articles can pretty much be copied directly over, but others can be merged in or if the WP article is better then nothing needs to be done. PM's under the GFDL. The major difference between WP and PM is that PM allows users to own articles. Anyway, I'm wondering what you all think of this, and whether it could be a subproject of this project or if it should go somewhere else. I haven't been able to find precedent on this sort of thing. If anyone wants more details/has questions, please let me know! CryptoDerk 05:06, Jan 27, 2005 (UTC)

Hi everybody, I run PlanetMath. I'm here to help out with this process as best I can. I also would like to go the other direction, porting some Wikipedia content to PM, but that is of course mostly my problem. I just need to figure out how to best get the math subset of articles from here. Though, I do have the same history preservation problem you've been discussing for the PM->WP port, so I am especially interested in that discussion. Please know that you have me as a resource to provide advice and possibly system enhancements that would make the porting job easier. --Aaron Krowne 05:40, 28 Jan 2005 (UTC)

That is a great idea. Just yesterday I copied the very nice Potential theory article from there, as here there was nothing. Their articles are more formal than what we have in here. So when copied over those articles (a) need some more introduction and motivation, (b) some sentences need to formulated to use less symbols and some formulas HTML-ized (e.g., make $x\in\mathbb{C}$ into x in C) (c) Links to other Wikipedia subjects need to be made, and this can be time-consuming. But doing all these is well-worth it.

Those people use an idea which I find extremely nice. Each article has an official maintainer who actually has a big picture of the article, and screens all the incoming changes.

Oleg Alexandrov | talk 05:37, 27 Jan 2005 (UTC)

Yes, formality is one reason why he doesn't just want to merge the two together -- he intends to keep running PM primarily for researchers and research-related interests. So... should an organizational page for this be a subpage of this WikiProject in mathematics, or should it go somewhere else? CryptoDerk 05:48, Jan 27, 2005 (UTC)

While that is the way the site has developed, we would actually like more introductory and, shall we say, more "pedagogically complete" articles. I think in terms of coverage it is probably more natural for PM to subsume Wikipedia's math section. However this is all academic... for now we should each just focus on how to copy over whatever portions of the other's content we want. --Aaron Krowne 05:40, 28 Jan 2005 (UTC)

There is of course room on Wikipedia for such a page. The big question is, what should be there and what is a good way of going about it. Oleg Alexandrov | talk 02:35, 28 Jan 2005 (UTC)

I can easily generate lists of pages of articles on PM as well as relevant redirects (PM entries a list of synonymous names at the end of the articles). The most important thing is coming up with a protocol for converting them (differences in style, including LaTeX, etc.) -- I'll come up with a draft page in my user space and post a link here within the next day or so. I think the most important decision that needs to be made is how to refer back to PM. It's my understanding that we need to provide a link to the history on PM, but do we do it like the EB 1911 notice "This article based in part on information from Encylopedia Britannica 1911" or do we put it in an "External link" section? CryptoDerk 03:12, Jan 28, 2005 (UTC)

I don't know that wholesale copying of PM articles to WP is appropriate, given the significant differences in purpose, organisation, presentation and form of PM -- but then I'm not sure that this is what you are proposing. The problem lies not only in identifying articles that don't yet exist on WP, but also in making sure that the topic isn't covered elsewhere (as is very common on WP). In a lot of cases, inclusion of a theorem or concept in a wider article is preferable in the context of WP, while it might reasonably be expected to have it's own entry on PM.

On other notes...

References back to PM might best be done (when content has been copied) using a new template for that purpose, if this becomes a common thing. That would make is trivial to append such a notice to the end of the relevant articles. Text to link back to the appropriate canonical name of the PM article can be included as an input into the template (IIRC).
A subproject of this one would probably be appropriate, I think. An excellent start (and this would go some way to addressing my reservations above) would be to compile a list of PM articles that don't appear to have WP equivalents, so that people can go there, take up the cause of a particular topic and work out what needs to be done with it. That would be a great place to track the status of such articles, too, as they will often need significant editing. This may be exactly what you are imaginging, in which case I'm all for it.

All in all: great idea, good luck with it, and I look forward to hearing more! Oh, and my kingdom for PM's TeX to HTML system, but I guess it wouldn't quite work on WP.

Ben Cairns 04:12, 28 Jan 2005 (UTC)

I agree with you that this shouldn't be a wholesale copying over of articles. In the draft page I'll be sure to set up some guidelines (that will undoubtedly be changed), but I'd say the majority of the encylopedia entries are probably useful. Some will need to be combined in some cases (they frequently have separate articles for proofs, for example).

A template is indeed what I had in mind, and yes it's possible to include a variable to link back to the appropriate PM article, even if it's named differently over here.

I imagine when all this is set up with just a raw listing of articles, some people can work on creating articles over here while others can work on categorization, perhaps with the following categories:

Article already exists on WP and PM content is already similar or less than what WP has, so no need to copy.
Article already exists on WP but PM content is different or better (stubs).
Article doesn't exist and should be converted.
Article has already been converted.
Unknown status, or unchecked (no category).

Once again, this is still preliminary, so don't yell at me if I'm leaving something obvious out :) CryptoDerk 04:34, Jan 28, 2005 (UTC)

Is there a list of PM article titles? One way to do all this would be to create a page like the mathematics Requested Articles page, but dedicated to PM articles. Since different articles will need to be treated different ways, we could see how much is accomplished by redirecting and sorting on such a page, and compiling a list of non-transfers, with reasons. In any case, it needs to be a case of involving the broad community, rather than having a rigid plan. Charles Matthews 10:45, 28 Jan 2005 (UTC)

I agree, with both the most recent posts above. Sounds almost like a (broad, community-based and certainly not rigid) plan... Ben Cairns 12:59, 28 Jan 2005 (UTC).

Now, I think what I understand from what Charles said is the following (I could be wrong, but this makes sense to me): We should make a list of PlanetMath articles, or maybe several lists, grouped by subject area, as there are many articles there. Each element in the list should have several things. First, very importantly, the title of the PlanetMath article, second, the title of the corresponding Wikipedia article(s) if any, third the status of the Wikipedia article as compared to the Planet math one (say, "WP article is just a copy of the PM article", "WP article is better than the PM one", "Some merger recommended (which way)", etc). This comment thing is very important, because people seeing this can decide what to do, and update the status line after they took action. This also implies that the status comment must be signed (four tildas) by the user who did the comparision, so that after a long enough time another comparison is made.

What do you think? Now, the first element on each list entry, the PM article title, can be easily auto-generated, and new elements in the list can be easily added automatically later as new articles show up on PM. The second and third elements for each entry will need to be community based, as will take a huge effort to comment on thousands of articles. Oleg Alexandrov | talk 16:06, 28 Jan 2005 (UTC)

This is what I was planning on doing. There will be a lot of grunt work by users that needs to be done. CryptoDerk 16:51, Jan 28, 2005 (UTC)

Something like this seems reasonable. Paul August ☎ 17:46, Jan 28, 2005 (UTC)

I'm not sure this is a good idea. Don't get me wrong, I love PlanetMath. But a world in which there is only one comprehensive open-content math reference is not as good as one in which there are two. -- Walt Pohl 16:37, 28 Jan 2005 (UTC)

User:akrowne (the PM creator) was receptive of the idea, and I think he may have even been the one to approach ME about it a few months age, although I'd have to dig through my IRC logs. Similarly, he plans on grabbing some WP content and using it in PM. I do think that even with content exchange the two will serve different audiences. You've got people who might prefer the author control, setup, and community of PM, and PM has growing sections on things that WP doesn't offer — such as papers, books, and expositions. CryptoDerk 16:51, Jan 28, 2005 (UTC)

I think PM and WP can share content and remain independent. Paul August ☎ 17:46, Jan 28, 2005 (UTC)

But what's the point? It's not like either Wikipedia or PlanetMath are hard to find. They both score high in Google searches. So it doesn't help readers any. Maybe someone would have come along and written a great new potential theory article. Now we just have the same text in two different places. What good did it do?

I think a better idea for a project would be one to make sure that Wikipedia has an article for each PlanetMath article, and that each Wikipedia article links to the appropriate PlanetMath article. Actually duplicating the content seems pointless to me. -- Walt Pohl 20:33, 28 Jan 2005 (UTC)

Well, I think for one it can help fill in some red links. Plus, getting content from other places is, at the very least, a good starting point for building our own. Also, in the case of articles we already do have, we can make them better. WP integrates other free content (PD images, 1911 EB), so why not this? CryptoDerk 20:53, Jan 28, 2005 (UTC)

PD images are obviously a good idea, but I think Wikipedia has been ill-served by including material from things like the 1911 EB. Most pages based on 1911 EB entries are either terrible, or have been so completely rewritten that you couldn't tell they ever used EB. A couple of the math pages has history copied from an old public domain source, and they just sit there, undigestible lumps of text that no one really understands and everyone is afraid to edit. I don't think that will be a problem with PlanetMath, but inclusion of 1911 EB material is not an inspiring example. -- Walt Pohl 01:59, 29 Jan 2005 (UTC)

OK. Draft up at User:CryptoDerk/planetmathproject. Feel free to comment and change it. CryptoDerk 18:03, Jan 28, 2005 (UTC)

See User talk:CryptoDerk/planetmathproject how an automatically generated list of articles from Planet Math looks. Does not look optimistic. Oleg Alexandrov | talk 02:59, 29 Jan 2005 (UTC)

Notice: Wikipedia:WikiProject Mathematics/PlanetMath Exchange is now the location for this project. Active discussion is also going on here: Wikipedia talk:WikiProject Mathematics/PlanetMath Exchange. Additionally, when it goes live we should include a link to it from the main WikiProject Mathematics page. CryptoDerk 16:51, Jan 30, 2005 (UTC)

(I took the liberty editing the above notice to add a link to the talk page. Paul August ☎ 17:27, Jan 30, 2005 (UTC))

Where to contribute math articles? Wikipedia or Planet Math?

Hi,

I'm a newcomer here.

User:Oleg Alexandrov has insinuated on multiple occasions that the math articles that I write are far too complex and complicated for Wikipedia, and most recently suggested that I contribute to PlanetMath instead. I would like to get a clear statement from the Wikipedia math community whether this is indeed the key difference between Wikipedia and PlanetMath, and whether it really is the Wikipedia policy that practicing scientists/academics are encouraged to work on PlanetMath, leaving lay topics for lay authors on Wikipedia.

I am rather discouraged and disappointed; I wish I'd been told this *before* I got involved in wikipedia, and not after, as I have already invested a good bit of time in the enterprise, and its seems that it may all have been for naught.

I am also confused by Oleg's stance on this issue, as almost every math article in wikipedia seems (to me) far more complex and advanced than those which I write. For example: the list of articles that I've started or made major revisions to is here: User:Linas#Misunderstanding things; essentially all of these deal with undergraduate mathematics topics that some typical undergrad math major might encounter in school. By contrast, wikipedia has massive and massively complex articles such as Artin conjecture and Jet bundle and Banach space and Lattice (order) and Sheaf and Scheme (mathematics) which are not only advanced graduate-level topics, but are areas of active academic research. So this simple math /complicated math division leaves me perplexed.

My goal in writing for wikipedia was to have something to replace my paper copy of Abramowitz & Stegun: simple, concise, informative, filled with facts that you never knew or had forgotten, the universe of math at your fingertips. Just plain-old straight-ahead stuff, nothing fancy.

I think a clear editorial policy for acceptable content for math articles for wikipedia should be spelled out up front; if complexity is really an issue, then I strongly encourage a mass migration of the advanced math articles out of wikipedia and into planetmath, where they can serve some actual, useful purpose, instead of splitting the community between two wikis.

linas 06:04, 29 Jan 2005 (UTC)

Now I am in hot water. What I had mentioned to Linas was about style, not content, see character group for style which I don't quite like. But oh, well, it is good this topic is raised. What is a good Wikipedia aricle? I would also need that for the Wikipedia:How to write a Wikipedia article on Mathematics with which I am struggling. Oleg Alexandrov | talk 06:13, 29 Jan 2005 (UTC)

Hi Linas, I agree with you; Wikipedia should have as much "notable" math as possible. Please don't move to PlanetMath. "The universe of math at your fingertips": exactly! Wikipedia is not paper. We can always organize a subject so it has an easier overview with more detail later or in a subarticle. dbenbenn | talk 07:34, 29 Jan 2005 (UTC)

On further thought, I realize that I am (perhaps like everyone) using Wikipedia (and the web in general) in two very different ways, and that this is the source of the problem. When I am reading about a topic about which I know very little e.g. Banach space, I find the "lots of words; few formulas" approach to be excellent, as it lets me learn the subject quickly and painlessly. However, once I know the topic very well, I find that the words get in the way of the formulas: they start hampering understanding, not helping. They mislead, they are inexact intellectually, they clutter the page visually. The articles that I am contributing to wikipedia are mostly on topics I feel comfortable with; ergo, I like them better when they are mostly formulas with few words ... that is, reference articles in the style of Abramowitz & Stegun ... or my recent Christoffel symbols. I see the need in the world for both styles: the introductory article, and the compendium/reference. Now, how to resolve that tension in an editorially pleasing way? linas 07:48, 29 Jan 2005 (UTC)

Thus, perhaps, I nominate a new article style (and article naming convention), the style being called "reference" and the naming convention being that if "XYZ model" is the article that provides intro and examples and generalities, then "XYZ model (reference)" would be the long, exhaust(-ive/-ing) list of theorems and formulas. That would resolve several ugly pages I've been struggling with. For example, Upper half-plane is a prime candidate for this kind of split.linas 08:00, 29 Jan 2005 (UTC)

Linas - I don't think there is any problem with the level of the articles that you have started - the ones I have seen are, as you say, at the level of standard undergraduate mathematics. As for style, this will always be a largely subjective matter. A mathematical article that starts out as a concise summary of defintions and main results may be seen as a skeleton by other contributors, who will add introductory material, history, motivation, examples, applications etc. Eventually the article may become so large that the original neat skeleton is lost to sight, and the article needs to be re-arranged or maybe even re-factored. This is all part of the dynamic, open and collaborative nature of Wikipedia.

As an aside, I notice that the "ownership models" in Wikipedia and PlanetMath seem to be rather different. In the Wikipedia ownership model, an article does not have a single owner, and all users have free access to all articles. I understand (from reading [1]) that the default ownership model at PlanetMath is that an article has a specific owner (usually the person who started the article), and the owner must review each proposed change to that article, and may reject changes that they disagree with. It would be interesting to see if this leads to differences in the style, level and coverage of articles at the two sites. Gandalf61 10:33, Jan 29, 2005 (UTC)

I don't see that there is any overall feeling about level of WP articles, on mathematics. There was once a consensus that we were speaking to undergraduates with a year or so of university work behind them. That was just an indication; textbook material, as such, should be in Wikibooks. All one can really say, is that additions to a given article should in some sense match the approach there: any sudden changes of level can be unnecessarily confusing to readers, and should be flagged in some way, such as 'from the point of view of complex analysis' if one is switching away from a real-variable calculus topic.

Linas, I think you shouldn't generalise too much about this. There is certainly room here for any contributions of almost any level, if they integrate properly.

Charles Matthews 16:44, 29 Jan 2005 (UTC)

Linas: Please don't leave. From what I see, your contributions have been valuable and appropriate. Wikipedia is meant to be comprehensive. It should contain all of "notable" mathematics, from the general and introductory to the technical and advanced. "The best way to organize and present all this is not as clear. As Gandalf61 says, Wikipedia should provide "introductory material, history, motivation, examples, applications etc", Wikipedia can accommodate several overlapping and interrelated articles dealing similar subjects, see for example, this constellation of set theory articles:, set, subset, set theory, Naive set theory, Axiomatic set theory, Algebra of sets and the as yet unwritten History of set theory, Motivations of set theory, Applications of set theory, Frontiers of set theory, etc. See also the above discussion "Graph (mathematics) vs Graph theory". So something like what you suggest might be appropriate, but should probably be discussed some more, with some examples. Paul August ☎ 17:03, Jan 29, 2005 (UTC)

MathWorld references

So many mathematical articles reference MathWorld that I decided there should be a reference template, similar to Template:Book reference or Template:imdb title.

produces

Eric W. Weisstein, Happy Number at MathWorld.

Feel free to edit the template if you feel strongly about the form of the citation. (I purposely decided not to follow Weisstein's referencing instructions. I think "A Wolfram Web Resource" is a bit much.) What do people think? Start using it in math articles? dbenbenn | talk 04:31, 29 Jan 2005 (UTC)

I like it. I'm actually surprised we didn't already have one :o CryptoDerk 04:52, Jan 29, 2005 (UTC)

Main problem is that not all the MathWorld articles are written by Weisstein. Tompw 15:48, 29 Jan 2005 (UTC)

Yeah, I've noticed that too. They still say that Weisstein should be credited as the author, though. It isn't clear to me what kind of license they use at MathWorld for submissions; I suspect it's something like you transfer your copyright to them.

Do you think, for example, that a reference to Petersen Graph should credit "Pegg" as the author? I'm inclined to not bother; but if it's an issue, feel free to make another template, say Template:MathWorld author that would take a third parameter. dbenbenn | talk 20:48, 29 Jan 2005 (UTC)

Wikipedia:WikiProject Mathematics/PlanetMath Exchange -- version 0.1 -- comments requested (on this page)

Introducing the new subproject of WikiProject Mathematics:Wikipedia:WikiProject Mathematics/PlanetMath Exchange. Before you jump there, let me describe what to expect.

We have a purpose section, an instructions section, and the list of subjects in mathematics (according to AMS Subjects classification). Each subject list will contain the titles of all PlanetMath articles on that subject (automatically generated). For now, all lists are red links, except for Functional analysis, scroll down the page for that.

This is done on purpose. There is enough stuff to give people an idea of what to expect, and we are in preliminary enough stage that everything can still be modified.

I would like to invite people to share their thoughts here. Some of us believe that this project, rather than making Wikipedia a clone of PlanetMath, or the other way around, will instead benefit both of them. Oleg Alexandrov | talk 06:11, 31 Jan 2005 (UTC)

By way of summary, some of the things which have been discussed on Wikipedia talk:WikiProject Mathematics/PlanetMath Exchange) and tentatively agreed upon there and/or accomplished are:

We should go forward with this project.
The project name should be: "PlanetMath Exchange".
It should be a subproject of this project with the project page at: Wikipedia:WikiProject Mathematics/PlanetMath Exchange. A first draft of that page now exists there,
There should be an auto-generated list of all PlanetMath articles. The first auto-generated list of PlanetMath articles has been created here: Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis.
There should be a template created to facilitate the creation of a link to the appropriate PlanetMath article in any newly created WP article based on a PM one. Such a template has been created: Template:planetmath. Additionally Template:planetmath reference has been created for a general reference.

Comments? Paul August ☎ 06:20, Jan 31, 2005 (UTC)

Note: I modified #5 to include the other template as well. CryptoDerk 06:29, Jan 31, 2005 (UTC)

Begging the question

I'd like to point people to the mathematical remark in the article Begging the question. See also my comment on the talk page which has thus far generated no responses. There's gotta be a better example than either of these two. - dcljr 06:01, 9 Feb 2005 (UTC)

New Mathematics Wikiportal

I know I've posted this on most of your user talkpages, but I felt it was important to add to the project page as well.

I wanted to point out to you the new Mathematics Wikiportal- more specifically, to the Mathematics Collaboration of the Week page. I'm looking for any math-related stubs or non-existant articles that you would like to see on Wikipedia. Additionally, I wondered if you'd be willing to help out on some of the Collaboration of the Week pages.

I encourage you to vote on the current Collaboration of the Week, because I'm very interested in which articles you think need to be written or added to, and because I understand that I cannot do the enormous amount of work required on some of the Math stubs alone. I'm asking for your help, and also your critiques on the way the portal is set up.

Please direct all comments to my user-talk page, the Math Wikiportal talk page, or the Math Collaboration of the Week talk page. Thanks a lot for your support! ral315 02:54, Feb 11, 2005 (UTC)

ral315: This is a better way to communicate to the Wikipedian mathematics community, rather than posting on everybody's talk pages — some people consider that to be spamming. Your portal looks interesting. I'll put in on my watchlist and lend a hand as time and interest permits. As for mathematics articles needing attention check out Wikipedia:Pages needing attention/Mathematics. Paul August ☎ 06:27, Feb 11, 2005 (UTC)

As I said on User talk:Ral315#Wikiportal, personally, I really appreciated the note you left on my talk page. It might have been months before I'd have found the portal without it, as I'm much more active in other areas right now. And over the years, whenever I've taken the trouble to identify the people I thought would be interested in something and give them each a personal heads-up on it, I've only ever had thanks. But within Wikipedia there are many sub-communities, and this one seems not to like it. I've noted that now, and I'm sure you have too. I'm not convinced it's representative of the whole of Wikipedia, or even the Maths community, but certainly take it as applying to the more active members of this Wikiproject. Andrewa 13:05, 11 Feb 2005 (UTC)

Tex rendering -- help!

Can someone sort out my TeX rendering at effective population size please? I have most of it, but I'm not sure how to group subscripts/superscripts together e.g. p [sub] 1 + q [/sub] sort of idea. Dunc|☺ 15:03, 25 Feb 2005 (UTC)

Oh, I sorted that one myself. But I'm still stuck on having a fhat [sub]foo[/sub] because they won't go together, which leaves a gap and {} don't seem to work ?!? Dunc|☺ 15:26, 25 Feb 2005 (UTC)

Fixed. dbenbenn | talk 20:38, 25 Feb 2005 (UTC)

binomial expansion of (p_1 + ... + p_n)^c

I've asked this on Wikipedia:Reference_desk#.5B.5Bbinomial_expansion.5D.5D too, but, what is the binomial expansion of $(p 1 + ... + p n) c$ ? I don't think this is covered in the articles that are there at the moment. (I want to derive the fully general Hardy-Weinberg law). Dunc|☺ 19:22, 2 Mar 2005 (UTC)

Assuming c is an integer > 2, refer to the multinomial theorem. Charles Matthews 20:52, 2 Mar 2005 (UTC)

\phi or \varphi

It seems to be the norm on wikipedia to use $φ$ for writing one of the angle coordinates in spherical coordinates. I think that it is usually the norm to use $\varphi$ in mathematics and physics. I'd be willing to go through and change a bunch of the pages that use \phi to use \varphi instead. But I don't want to go against established policy. It just seems to me that the 'pedia should use the conventions that are common in mathematics. Has there been discussion about this issue before?

--Jacobolus 06:01, 6 Mar 2005 (UTC)

I believe the Wikipedia norm is the correct one. Dysprosia 06:19, 6 Mar 2005 (UTC)

As do I. Surely, it's a case of using one letter followed by another: theta (

θ

) then phi (

φ

). If varphi ( $\varphi$ ) were correct, surely we'd use vartheta ( $\vartheta$ ) for the first angle we designate? --stochata 13:32, 6 Mar 2005 (UTC)

I think that the "var" in "\varphi" just means "variant phi symbol", and doensn't necessarily imply that "\vartheta" should be used for theta. In all of the math books I just looked at (many of which are layed out in TeX), spherical and cylindrical coordinates were laid out using varphi. In the two physics books I looked at, the phi symbol was used. So I'll stick with phi I guess, as it appears (see discussion below this one) that the physicists' notation is winning out for other coordinate systems. --Jacobolus 18:19, 6 Mar 2005 (UTC)

I use \varphi when I write mathematics in TeX (In fact, I \let\phi\varphi), but I prefer \phi here. The wiki software is able to display \phi as an actual character, whereas it generates an image for \varphi. dbenbenn | talk 17:59, 6 Mar 2005 (UTC)

One pesky problem is that in many html fonts, phi displays inline as the varphi symbol, which means that there is visual inconsistency between rendered formulae and inline variable names. --Jacobolus 18:19, 6 Mar 2005 (UTC)

Note that in my comment below on the notation used by mathematics tutors for my undergrad -- I link to their book. They use phi rather than varphi. (Indeed, Jacobolus, the inline phi appears as varphi on my browser) --stochata 11:58, 8 Mar 2005 (UTC)

use of phi and theta in spherical coordinates

Hi all. I noticed recently that the articles on Vector fields in cylindrical and spherical coordinates and on Nabla in cylindrical and spherical coordinates have theta as the polar angle, phi as the longitude angle, r as the length of the vector, and rho as the length of the vector projected into the plane. In the article about Coordinates however, these uses of phi and theta, and respectively rho and r, are switched. This seems unnecessary conflict. I realize that physicists don't agree with mathematicians on the correct order of these terms, but at least some explanation should be given for the unwitting visitor, who might otherwise be very confused to see rho's and r's swapped so casually.

And then, some consistent drawings of coordinate systems and vector operations, etc. in these coordinate systems should be made. Here's my drawing of spherical coordinates: Image:Spherical_Coordinates.png. I'd be willing to make more drawings. But first some decision should be made about which convention to follow. That used in math or that used in physics.

Tied to this issue is my previous question about varphi and phi. Is one preferred as a coordinate name?

--Jacobolus 08:16, 6 Mar 2005 (UTC)

It should be only a matter of picking one standard and sticking to it. Dysprosia 09:49, 6 Mar 2005 (UTC)

I have never noticed a difference! I was taught to use theta, phi, r in my mathematics lessons at school, and later simply continued to use it through a physics degree. Which do we suppose is used by which category of people? (And maybe country of origin also affects the system used!) --stochata 13:38, 6 Mar 2005 (UTC)

I would agree with stochata that r is the prefered notation for the length of the vector, and so then ρ is the projection. And I agree with Dysprosia that consistency is what matters above all. So since you raised this issue, could you go through the pages using spherical coordinates, (like start at spherical coordinates, see what links there, etc), and change the notation in those places to keep things consistent? That would be much appreciated.

About the picture, I like it. Just one small remark. You will need to of course use a scaled version of it. In the scaled version you will need to make sure the fonts are the right size, and that aliasing is not too bad (pictures which have thin lines and thin curves tend to look ugly unless antialiasing is employed in some way). Oleg Alexandrov 16:24, 6 Mar 2005 (UTC)

I would argue in favor of the usage in Vector fields in cylindrical and spherical coordinates. Where

(r, θ, φ) are spherical coordinates with θ being the colatitude (angle with the positive z-axis) and φ the azimuthal angle.
(ρ, φ, z) are cylindrical coordinates with φ the azimuthal angle

The reason is that this usage is almost universally used by physicists. I think the reason stems from the fact that this is the notation used in Jackson's Classical Electrodynamics — the de facto textbook on electodynamics, where these coordinate systems are heavily utilized. Mathematicians may differ in their usage, but at least this way we include many mathematicians and nearly all physicists. -- Fropuff 17:34, 2005 Mar 6 (UTC)

Ok. So the notation used in Jackson and Griffiths and elsewhere in physics will be the norm. I'll make a prominent note at the top of the Coordinates (elementary mathematics) page (Aside: why is this called "elementary" mathematics... maybe just Coordinates (mathematics) would be better??), and then go with the physics notation. One last question. For inline text, is using the <math> and </math> tags frownned on? I've seen conflicting reports, and the usage seems to vary greatly between articles. I would generally be inclined to use them, but I'll try to stick to whatever the accepted standard is. --Jacobolus 18:12, 6 Mar 2005 (UTC)

One could argue that coordinates (mathematics) should discuss coordinates on arbitrary manifolds (or even more general spaces, i.e. with singularities). As far as inline TeX goes: the reason we try to avoid it is that the inline PNG's are too large and look bad with the surronding text. There has been lengthy arguments about this (see /Archive4(TeX)) and not everyone agrees. -- Fropuff 19:04, 2005 Mar 6 (UTC)

I've just checked the book by my undergrad tutors [2], and they certainly use theta, phi, r for spherical polars (and phi, rho, z for cylindricals as Fropuff suggests). Note that Riley was originally from a mathematics background. --stochata 11:55, 8 Mar 2005 (UTC)

My 2 cents: I am a mathematician, and I prefer the physics/engineering convention for several reasons.

Foremost is that, despite the beliefs of many ignorant American mathematicians and the usage of almost every American calculus textbook, the physics/engineering convention is simply by far the most widely-used convention of the two, throughout the world. It is the convention for virtually all (American and non-American) scientists, and for many, if not most, non-American mathematicians. American mathematicians are really the only group of users who enjoy a majority POV on this issue; it is only because of calculus textbooks that the whole world does not agree.

My second reason for favoring the physics/math convention is that it has far deeper historical origins in physics and science than the American usage does in math. The effort required for Americans to change would be far less than the effort required to re-write classical physics texts.

But, my most important reason is that the American convention is fundamentally flawed from a mathematical viewpoint. If this were simply a matter of two symbols getting interchanged, that would be one matter. But the American convention produces a left-handed coordinate system, and I don't think I need to explain why that poses a tremendous problem.

I taught a vector calculus class a couple years ago, doing something perhaps against better judgment -- teaching the non-American convention while the text used the American one. Of course, I also freely used differentials and the type of informal arguments physicists use for deriving tangent vectors, and so forth. I just made sure that I never assigned any problem using the textbook convention, and I told them not to read that part of the text. There wasn't too much confusion resulting, I mean, at least among those who weren't already confused by the time we reached general coordinate systems. Revolver 07:17, 12 Apr 2005 (UTC)

Relevant proposed naming convention: ambiguous adjectives

There is a proposal at Wikipedia talk:Naming conventions (ambiguous adjectives) that could affect several mathematics articles. -- Toby Bartels 08:40, 2005 Mar 7 (UTC)

Soliciting input on Estimation theory

Just seeking input on a new article: estimation theory. (Estimation didn't take a purely statistical explanation and I better know it as estimation theory.) Please leave article specific commentary on it's talk page instead of here. Thanks. Cburnett 06:56, 8 Mar 2005 (UTC)

straight or italic d?

What are your opinions about the use of upright d versus italic d in integration and for the exterior derivative? Currently, probably because it is less LaTeX, italic d seems predominant. Personally I prefer upright d as this more clearly contrasts with possible use of d as a function or number(distance). Examples

$\int f\,d\mu$	$\int f\,\mathrm{d}\mu$
$\frac{dy}{dx}$	$\frac{\mathrm{d}y}{\mathrm{d}x}$
$\int d(vx, z/x^2) \ln(x+1) \,d (x \mapsto \cos(x)d(x, w))$	$\int d(vx, z/x^2) \ln(x+1) \,\mathrm{d} (x \mapsto \cos(x)d(x, w))$
$\int fdt\wedge dx\wedge dy\wedge dz = \int f\,dt\,dx\,dy\,dz$	$\int f\mathrm{d}t\wedge \mathrm{d}x\wedge \mathrm{d}y\wedge \mathrm{d}z = \int f\,\mathrm{d}t\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$
$d\det\left({}^a_c {}^b_d\right) = d(ad-bc) = add + dda - bdc - cdb$	$\mathrm{d}\det\left({}^a_c {}^b_d\right) = \mathrm{d}(ad-bc) = a\mathrm{d}d + d\mathrm{d}a - b\mathrm{d}c - c\mathrm{d}b$
$d\det\left({}^a_c {}^b_d\right) = d(ad-bc) = a\,dd + d\,da - b\,dc - c\,db$	$\mathrm{d}\det\left({}^a_c {}^b_d\right) = \mathrm{d}(ad-bc) = a\,\mathrm{d}d + d\,\mathrm{d}a - b\,\mathrm{d}c - c\,\mathrm{d}b$
$\int f(x_1, \ldots, x_d) \,d_dx$	$\int f(x_1, \ldots, x_d) \,\mathrm{d}_dx$
$df(V) = V(f) = \left.\frac{d}{dt}\right\|_{t=0}f(\gamma_t)$	$\mathrm{d}f(V) = V(f) = \left.\frac{\mathrm{d}}{\mathrm{d}t}\right\|_{t=0}f(\gamma_t)$
$Δ: = (d + d ) 2 = d d + d * d$	$Δ: = (d + d ) 2 = dd + d * d$
$\Delta := (d+d^)^2 = dd^+d^*d\,$	$\Delta := (\mathrm{d}+\mathrm{d}^)^2 = \mathrm{d}\mathrm{d}^+\mathrm{d}^*\mathrm{d}\,$

Also, when defining something, do you use := instead of = and why? MarSch 17:30, 11 Mar 2005 (UTC)

It is standard to use italics for differentials such as dx (e.g., see Wolfram: [3]). The spacing ought to give you a clue to the nature of the symbol, note that you should add a little space to distinguish the variable (see Lamport p.50). e.g., $\int d\, x \, dx$ . --stochata 23:35, 11 Mar 2005 (UTC)

I like the idea of using a vertical "d", but it is not common. I think that in Wikipedia we are not supposed to be trend-setters but should follow common practice, so we have to use the italic ''d". --Zero 02:22, 12 Mar 2005 (UTC)

It's my estimate that this is largely a US/UK thing (with Americans using italics and the Brits using an upright shape). Personally, I prefer to use both a thin space and an upright shape -- why be coy? (I've added a row to the determinant example, so that we can all see what all four possibilities amount to there.) As usual, I oppose any sort of policy decision for all articles; we should follow the usual rule of tolerance for variation that applies to US/UK spelling differences. -- Toby Bartels 23:56, 2005 Mar 12 (UTC)

Toby, I am British (and currently in Britain) and I prefer the italic version (although I have seen the upright 'd', it doesn't strike me as that common -- although my area doesn't tend to use derivatives that much). I look forward to articles with phrases such as "dx, or dx in American mathematics" :-) --stochata 12:18, 13 Mar 2005 (UTC)

The Brits have spoken. :) I would say we need to restrict transatlantic differences to spelling (and politics) only. Italic dx has been the style on Wikipedia, and I think it should stay this way. Oleg Alexandrov 19:45, 14 Mar 2005 (UTC)

Shades of varphi! I think its a terrible idea to go out and try to retroactively edit hundreds of pages to use a different font in the math typsettings. Authors of new pages get to pick thier symbols, but they should make at least token attempts to be consistent with nearby articles. For the record, I have no love for := I sometimes use $\equiv$ in the privacy of my own room, but I would not subject the public to such degradations. One man's definition is another man's theorem. linas 16:21, 14 May 2005 (UTC)

My vote goes to "thin space (/,) and upright d", for better semantics and for all the other reasons mentioned here PizzaMargherita 07:06, 1 December 2005 (UTC)

Reformat of Participants list

I'm thinking about changing the format of Wikipedia:WikiProject Mathematics/Participants, making it into a table like so:

User (T¹ C²)	Areas of interest	Comments
Andrewa (T C)
AxelBoldt (T C)
Charles Matthews (T C)		I've added about 300 mathematics pages, many biographies, and lists of mathematical topics. I now also work on other areas of WP, but a well-organised and credible collection of mathematical articles is very much what is needed. We now pretty much have the house style and topic classification in place; there are some missing areas, and a great need to explain current research areas, as well as good history. I'm a sysop - one of not too many on this list.
Chas_zzz_brown (T C)	abstract algebra, group theory	My knowledge of topics outside of group theory is a monotonically decreasing function of their relationship to abstract algebra.
Mark Dominus (T C)
FunnyMan3595 (T C)	abstract algebra	I'm a freshman majoring in mathematics, but I already have quite a few courses under my belt. My specialty is abstract algebra.
irrªtiºnal (T C)		Let ε < 0 (hehe...) I am a highly unsuccessful mathematician. I am a man. I am single. I am free. I am an existentialist, therefore I am not.
Jeff (T C)	dynamical systems, complex systems, real analysis	I love to edit.
Kevin Baas (T C)		I started the fractional calculus section. Though it is still embryonic, it is very much 'my style', which is still under development. -Also started Information geometry section. I am just learning about this, though.
Ling Kah Jai (T C)		I have contributed an interesting article called last stone game.
LittleDan (T C)	geometry, group theory, vector spaces	I know up through geometry, and a fair amount of group theory and vector spaces. I can usually pick things up from wikipedia articles, if not from mathworld, then I can edit wiki articles for clarity.
Markus Krötzsch (T C)		I think many math articles still lack: general intros/motivation, links to relevant literature, objective account of alternative definitions (even if one definition is prefered in Wikipedia).
MarSch (T C)	geometry, category theory, physics
Miguel (T C)		How come Toby didn't tell me about this?
Pierre Abbat (T C)
Ram-Man (T C)
Revolver (T C)		Hi, I'm back.
Taku (T C)
Toby Bartels (T C)
Tomo (T C)

Notes: ¹ User's talk page; ² User's contributions

Any comments? Paul August ☎ 22:40, Mar 11, 2005 (UTC)

Much better, go for it -- so long as people aren't scared off to add their own entry. --stochata 14:36, 13 Mar 2005 (UTC)

Yes I had wondered about that. Figuring out the table syntax might discourage some. Although, perhaps we could consider a kind of IQ test, sort of like figure out the next term in this sequence … ;-) I'd be willing to write some instruction and/or provide a template. What do others think? It is a bit of work, so I don't want to undertake it if it is not deemed useful, or if we think it will put people off unnecessarily. Paul August ☎ 14:49, Mar 13, 2005 (UTC)

Well, trying to overcome the apathy...

I am against the table. I never learned the syntax of the Wiki table (all those absolute value signs everywhere :) and never plan to. And I don't see the gain of the table, ~~besides the obvious rosy background.~~ :)

Other thoughts? Oleg Alexandrov 16:21, 13 Mar 2005 (UTC)

PS And the background ain't even rosy! :) Oleg Alexandrov 16:21, 13 Mar 2005 (UTC)

Well I guess the main advantage of the table, in my mind, is that it encourages participants to enter fields of interest, plus it is eaisier to read, and I think the links to the user's talk page and contributions is helpful, for me at least. I'd be glad to help anyone with the syntax — or add a "rosy background" if that would help ;-) (Oleg: tables are fun! :) Paul August ☎ 16:56, Mar 13, 2005 (UTC)

I like it. Tomo 23:21, 13 Mar 2005 (UTC)

OK, although the response has been somewhat limited, I've decided to go ahead with the new format. Three users have expressed support, stochata, Tomo and MarSch (on my tak page). Oleg's was the only dissenting voice, but he has since warmed up enough to the idea to create a script to generate the table from the existing list ;-) So he is hoist on his own Perl petard, so to speak ;-) I would have preferred to have heard from some of the more senior participants (Charles Matthews, are you listening? ). Hopefully people are at worst indifferent. If anyone doesn't like it we can always revert it ;-) Paul August ☎ 21:41, Mar 18, 2005 (UTC)

"monotonicity" merged with "monotonic function"

After some discussion on talk:montonicity involving me, Toby Bartels, Michael Hardy, and Markus Krötzsch, it was agreed that monotonicity should be merged with monotonic function, which I have now done (monotonicity now redirects to monotonic function).

However there was a bit on a generalized notion of convergence for function between posets, which Toby thinks is worth keeping, but which I don't think necessarily belongs in the monotonic function article. Toby has suggested that perhaps it should be moved to its own article titled "order convergence". I made a stab at converting the orphaned text into a first draft for such an article (see: talk:montonicity) but I'm unfamiliar with this concept and am reluctant to actually create the new article myself. So If anyone knows anything about this, and would like to salvage this now orphaned content please do so.

Here is the text under discussion:

(Beginning of quoted text)

The notion of monotonicity allows one to express the principal instances of convergence (to a limit):

Given that a commensurate difference relation is defined between the members of S; that is, such that for any four (not necessarily distinct) members g, h, j, and k of S, either g − h ≤ j − k, or g − h ≥ j − k, and given that M from T to S is a map of equal monotonicity, then the values M(s) are called converging (to an upper limit), as the argument s increases, if either:

the set T has a last and largest member (which M maps explicitly to the corresponding limit value l in set S); or
for each member m of T, there exists a member <n > m such that for any two further members x > y with y > n, M(n) − M(m) ≥ M(x) − M(y).

As far as the set of all values M(s) does therefore have an upper bound (either within set S, or besides), and as far as every set which is bounded (from above) does have a least upper bound l, the values M(s) are called converging to the upper limit l as the argument s increases.

Similarly one may consider convergence of the values M(s) to a lower limit, as the argument s decreases; as well as convergence involving maps of opposite monotonicity.

(End of quoted text)

Paul August ☎ 21:13, Mar 14, 2005 (UTC)

Algebraic solution

Could someone here confirm that this new one sentence article is correct? An algebraic solution is a solution that is either a number or can be computed. That strikes me as so general as to be essentially meaningless, but google's been no help & I'm not competent in this area. Thanks. Michael Ward 03:06, 18 Mar 2005 (UTC)

It seems the definion does not make sense unless the term computation is explained. Maybe one should add a reference to or redirect to algebraic number or algebraic equation. Tomo 06:54, 18 Mar 2005 (UTC)

I've redirected this to closed-form solution. Charles Matthews 08:34, 18 Mar 2005 (UTC)

periods at the end of formulas -- request for comment

This is an edited version of my conversation with Omegatron, about periods at the end of sentence. I just wonder, what are your opinions about this? Thanks!

Is there a consensus that [period] is needed? looks bad to me. - Omegatron 00:19, Mar 19, 2005 (UTC)

I wonder if the reason it looks bad has to do with a peculiarity of using TeX on Wikipedia, as opposed to using TeX in the usual way. That is that if you put the period or comma outside the math tags, it gets mis-aligned. If you put it inside, however, it looks good. Michael Hardy 23:45, 19 Mar 2005 (UTC)

Period at the end of formula is the universal style in math. I am aware that in engineering for example, people do not do that. Did it happen that I modified something outside math (I try to stick to math, but sometimes the links from the list of mathematics topics lead into related subjects). If you would like, we can have a wider discussion about this. Oleg Alexandrov 00:24, 19 Mar 2005 (UTC)

Yeah it was an electronics article common drain, and they weren't sentences, either. I think even in mathematics articles it doesn't look good. I don't remember seeing it in my math books. It looks like a symbol, which could certainly confuse me; I don't know about other people. $Q \cdot Q .$ $\dot Q .$

...,1,2,3,....

Perhaps it's something from typesetting that doesn't carry over perfectly to the web? - Omegatron 00:30, Mar 19, 2005 (UTC)

I just pulled two math books off my shelf (math math, not engineering math) :-) and they are different. One has no punctuation next to formulas unless they are inline with the sentence. The other has periods the way you are using. - Omegatron 00:35, Mar 19, 2005 (UTC)

I just randomly pulled 5 applied math and probably books off my shelf. They all use period at the end. Would you like us to discuss this at Wikipedia talk:WikiProject Mathematics. Or would you take my promise that I will not mess up with any articles which are not either linked from list of mathematics topics, or in some math category, or listed as a math stub? Either way is very fine with me. Oleg Alexandrov 00:41, 19 Mar 2005 (UTC)

The encyclopedia of physics uses periods, too. :-) You are winning my bookshelf 2 to 1 so far. The engineering books don't, as you said. - Omegatron 00:42, Mar 19, 2005 (UTC)

If it's standard mathematics practice I guess go for it, and leave the engineering articles without. Of course, there are some articles that exist on the intersection between these two worlds. Has there been any discussion about it before you started adding them? - Omegatron 00:44, Mar 19, 2005 (UTC)

No, I did not consult anybody [about this]. But, I am already at letter "C", and at at least 5 Wikipedians I know had one or more of those on their watchlist (well, I assume so, as they contributed to those). I can certainly stop until we talk this over at Wikipedia talk:WikiProject Mathematics. All up to you. Oleg Alexandrov 00:47, 19 Mar 2005 (UTC)

Let's just move this conversation there and see what other people have to add, and you can keep going with the math articles. - Omegatron 00:49, Mar 19, 2005 (UTC)

I don't care for them when the formula is on its one line (I see a lot of "cleanup" on my equations). Inline with sentences is fine like this $\sum_{x=0}^{N-1}f(x)^2$ . But the period *not* inside the math tags. Cramér-Rao inequality is mixed with and without periods: Cramér-Rao inequality#Single-parameter proof doesn't but Cramér-Rao inequality#Multivariate normal distribution does.

In the end, I don't see you can really justify either no more than if why it should be Jones' or Jones's. Entirely style. Cburnett 02:13, 19 Mar 2005 (UTC)

I did not get to Cramér-Rao inequality yet. I think one needs to be consistent at least on a per-page basis. Oleg Alexandrov 02:33, 19 Mar 2005 (UTC)

That's primarily from one section having already been there. Might as well wait and see what results from this discussion. :) Cburnett 04:33, 19 Mar 2005 (UTC)

Yes, this is standard style in mathematics textbooks. But on screen I think it looks clumsy, is potentially confusing, and is unnecessary - I think the effect on continued fraction, for example, has not improved the article. My vote would be not to do this - and certainly to stop until you have a consensus. Gandalf61 13:46, Mar 19, 2005 (UTC)

I am reluctant to comment on this rather trivial matter, but I think the convention to treat formulas as part of the text for the sake of punctuation rules is useful and logical, and widespread in maths style guides. So I support Oleg's efforts. I don't see Gandalf's point that there is a distinction between maths in books and maths on the screen in this matter. -- Jitse Niesen 15:36, 19 Mar 2005 (UTC)

Agree. Charles Matthews 17:20, 19 Mar 2005 (UTC)

Also agree. Now may I get a pardon from Oleg for being one the worst offenders against this commandment? CSTAR 18:56, 19 Mar 2005 (UTC)

Penance required - start the Weil representation article ... Charles Matthews

OK, OK I suppose that's better than saying 500 padre nuestros.--CSTAR 18:00, 11 Apr 2005 (UTC)

From User talk:CesarB

I am now doing myself a bad service, but there is discussion going on at Wikipedia talk:WikiProject Mathematics about period at the end of formula if formula is at the end of sentence. So, you can go there and put your vote (which will be against me). I would like to ask you to specify there your background. It seems that mathematicians are mostly for period at the end of formula, while engineers (and now I see, computer scientists) are against.

In the future, I will avoid modifying non-math articles, like bra-ket notation, which is physics. I try to stick to math, but sometimes non-math articles (again, like bra-ket notation) are put in a math category, and then this kind of disagreements arise. Cheers, Oleg Alexandrov 19:42, 19 Mar 2005 (UTC)

I don't care either way, as long as it's obviously separate from the formula (like a big fat period). You not only added a period which looked like part of the formula, but you added it inside the <math> tags, which made it even more like part of the formula. cesarb 19:45, 19 Mar 2005 (UTC)

Often all it takes is to precede the period by a little bit of space and it no longer intrudes on the formula. --Zero 12:07, 20 Mar 2005 (UTC)

Agreed. Of course, how much space is needed depends on the formula (a formula full of whitespace would need more space than a formula with no whitespace at all). cesarb 13:42, 20 Mar 2005 (UTC)

I am for proper punctuation of formulae. BTW the bra-ket article is a really bad example IMHO, since it has lots and lots of miniscule formulae, which would probably benefit from inlining.MarSch 15:27, 20 Mar 2005 (UTC)

Period before or after </math> -- please comment on this as there are opinions on both sides.

It seems that the opinion leans (I would say overwhelmingly) towards putting period at the end of formula. There are situations in which there needs to be some space between formula and period, and in some situations one could be better off without a period if that would confuse things, but these are rather special cases, when careful and individual judgement needs to be made.

There is another quite dividing issue which needs to be settled. Shoud the period before or after </math>?

I would agree with Michael Hardy that the period should be before </math> so that it becomes part of the PNG image. Otherwise, if the period is separate, if the formula is at the edge of browser window, the period moves to the next line. Also, this introduces a big space between formula and period (and comma) which can look quite unnatural (I don't mean one quarter space, like \, in LaTeX, rather a full space).

On the other hand, Cburnett believes that (taken from his talk page):

I'm vehemently opposed to having to make an article work around bugs or unexpected behavior (see discussion above to see what I mean [there Cburnett argues that one should put one category and language link per line, even if that causes some extra space at the bottom]). I did get my browser to wrap periods to the next line with equations (images really). However, I don't readily see this as a WP issue but rather a browser issue. Either way, whatever is decided on the wikiproject page I'll go with. Just can't promise I'll always remember. :) Cburnett 04:04, 19 Mar 2005 (UTC)

I wonder what everybody else thinks. Comments would really be much appreciated. Thank you. Oleg Alexandrov 17:21, 20 Mar 2005 (UTC)

Another point to go for after </math> is like with the new grammar bot. Rending the period in the tags means a bot might see the period if HTML rendered or might not if PNG rendered. It makes for an inconsistency even if the period is placed consistently. If placed external to the tags then it will always be there. And, no intention of insulting here, you have to be ****extremely**** pedantic to worry about a browser wrapping a period. :) Cburnett 18:32, 20 Mar 2005 (UTC)

About the bot thing. The bot does the queries based on the wiki source, not the final html, so will have no problems sticking its nose in math formulas. Oleg Alexandrov 02:48, 21 Mar 2005 (UTC)

The grammar bot (I forget the exact user name, perhaps User:GrammarBot) ignores math tags because of the commas. If you're going to require a bot to parse math tags then you've just added more complexity to it......to keep a period from wrapping. Cburnett 03:26, 21 Mar 2005 (UTC)

I think so far GrammarBot was very sucessfully messing inside of formulas. Maybe it will be a new feature that it will not do that anymore. Now, about your concern. Let me tell you that the bot I wrote to put periods at the end of formulas semiautomatically had to deal with issues similar but worse than that (there is lots of variabitity to how people type formulas). Besides, the GrammarBot has nothing to do in or around a math formula anyway, since after the period (or comma) in an aligned formula one goes to a new line. Either way, I think our concern for bots should probably be the last thing to worry about. Oleg Alexandrov 03:59, 21 Mar 2005 (UTC)

If the bot is to detect sentences without a period then it'll have to parse inside and around formulas. Really, though, if you want to worry about wrapping periods then I'll worry about bots. Both are equally pedantic and both are concerned about a mundane detail instead of actually writing or editting articles. Cburnett 04:05, 21 Mar 2005 (UTC)

If you are not pedantic yourself, and if you don't care if there is a period at the end of formula to start with, why are you so pedantic about where the period is? :) I think you are right. We are wasting time here. You can do what you love most, editing articles, and I will continue with the issue which has been concerning me me for at least one month, that is, proper punctuation of math articles. How's that? :) Oleg Alexandrov 04:18, 21 Mar 2005 (UTC)

Try rereading what I wrote. Notably, the second sentence. Cburnett 04:27, 21 Mar 2005 (UTC)

You are right again. I focused on your very provocative third sentence. So let us not imply that what the other is doing is irrelevant, because then you should not take part in this discussion to start with.

On your second sentence, I do not buy the bot argument. We will probably not agree on this. Let us see what others have to say. Oleg Alexandrov 04:32, 21 Mar 2005 (UTC)

When did I call it irrelevant? Cburnett 05:06, 21 Mar 2005 (UTC)

My fault. I overreacted. I read it (the third sentence) to mean that some people spend their time in an useful way writing good articles, and some other people have nothing better to do than argue about pedantic issues ultimately of little importance. But I had time to think about it, and agree that what you said can be interpreted as saying that there are two kind of issues, one of writing articles and the other one of taking care of the fine details. So, sorry!

Either way, I think better arguments can be found than the bot thing, and it seems that ultimately nobody really cares about this issue except us two and cesarb. Let us see if more developments happen. Oleg Alexandrov 05:12, 21 Mar 2005 (UTC)

I would put it after </math>, because it's not part of the formula. Only things that are part of the formula should be inside the tags. As a bonus, it gives some extra spacing before the period.

I found an easy way to prevent breaking: the <nobr> element. Since it's not supported by mediawiki (and in fact not part of the HTML standard), I created a template nobr using the standard way of doing a <nobr> (and in fact, the way used by Mozilla's default HTML stylesheet).

Here's how to use it:

$1+1=2\;$ .

I disagree with Cburnett about it being pedantic; with some large formulas (I've seen formulas that take more than half of my screen, and I use a huge resolution), it's quite easy when using lower resolutions to end up with a period by itself in the next line.

A more extreme example (you can comment it out after the discussion is over, it will cause scrollbars to appear):

$a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z+a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z+\;$ .

cesarb 19:40, 20 Mar 2005 (UTC)

Oh, and by the way, if this is too verbose, it would be easy to create a template to simplify it, containing something like:

{{subst:nobr|<math>{{{1}}}</math>.}}

cesarb 19:57, 20 Mar 2005 (UTC)

Vote for after. We should not compromise logic. There should be better workarounds. Isn't there a Unicode character specifically to glue parts together? – Sebastian 05:33, 2005 Mar 21 (UTC)

If you are thinking of the non-breaking space, it won't work (it would only work if it was replacing a space character; there is no space character). The nobr template I made works. --cesarb 10:01, 21 Mar 2005 (UTC)

The template cesarb suggests would work. However, I don't see it getting widely adopted (it is hard enough to convince people to care about putting that period to start with).

I agree with Sebastian about the logic thing. When I type LaTeX papers I don't like the period to be inside of the formula. However, on Wikipedia we have just three options (a) put the period after /math and not worry about misalignment, as this is a browser bug — this is what Cburnett says (b) put the period after, but do some kind of quick fix like a template, which cesarb suggests and (c) put the period inside, which is kind of a hack too.

Dealing with numbered formulas, like

$\int_a^b f(x)\, dx = F(b)-F(a) \quad\quad\quad\quad (1)$

does not make things easier. Here, probably the period should go before (1) rather than after (with some spacing between the formula and the period in some situations — if necessary — but probably not in this case).

So, no perfect solutions, but I would still think the third option is better than the first two. Oleg Alexandrov 12:50, 21 Mar 2005 (UTC)

I don't see the problem with the numbered formulas. The number is not part of the formula. In fact, it usually is written in the same font as the text. Sometimes you even find a name for the equation before the number - so it should really be outside of the . Moreover, it is not uncommon to put the punctuation after the the number, which I also regard as more logical. Example: Eddington, The Constants of Nature in The World of Mathematics, Vol. 2. — Sebastian 09:45, 2005 Mar 22 (UTC)

Well, it is not standard to put the period after the equation number. (Actually, LaTeX does not even give you a choice.)

It seems that people are pretty split about this (2 for period inside, 3 for period outside), and there were not as many people involved in this as could have been.

So, I guess a solution would need to wait until the browser and display technology will advance — do you hear that Cburnett? — like switching to MathML where hopefully this will not be an issue.

However, there was broad agreement that sentences with formulas at the end must have a period. Unless I hear any objections, in several days I will resume putting the periods. I will put them inside the math tags, as again, it seems to me that this is the least problematic way. But, I will not attempt to convert the formulas where the period is there, but outside the math tag, as I had originally planned.

If, again, I hear no objections, I am aware that there could be disagreements about individual instances, where one might feel there needs to be some spacing between the period and the formula, or that a period does more harm than good in that instance. Since my work will be semi-automatic anyway, just feel free to revert or change those cases. In most situations however, I do not expect these to be an issue.

Anyway, let us see how it goes. Oleg Alexandrov 21:18, 23 Mar 2005 (UTC)

Objection. The (admittedly narrow) majority voted for outside, and it's technically feasible with the stub mentioned above; so there's no reason to put them inside. I also disagree with using LaTeX's inability as an argument. Our criterium should be what we deem most straightforward logically. — Sebastian 22:09, 2005 Mar 23 (UTC)

Vanity references?

I wanted to alert everyone to some edits I've just noticed. Take a look at IP 84.94.98.49's contribution list: [4]. Notice that all of the edits were adding links to abstracts or papers by someone named " J.Foukzon". They were not, as far as I could tell, particularly relevant to the articles (I could be wrong). I'm wondering if someone might be engaging in something which could be called "vanity references". This could be a particularly insidious form of vandalism. One that could be difficult to deal with, since it can be hard to verify that a reference is really relevant. Paul August ☎ 20:37, Mar 20, 2005 (UTC)

Certainly references like both the ones on Path integral formulation (now only visible in the history) are unnecessary and, while broadly 'relevant' to the subject at hand, at best add nothing to the article and at worst distract from more suitable references. The Foukzon references in that article are in fact conference papers that have not yet been presented (appearing July 2005); sheesh! Well spotted, Paul. Ben Cairns 22:06, 20 Mar 2005 (UTC).

I would say, delete without further fuss. Oleg Alexandrov 22:16, 20 Mar 2005 (UTC)

Structure of math articles

I have seen some mathematics articles that suffer from too narrow a perspective, like laplace operator, which completely ignored generalization to forms and still ignores a discription in terms of covariant derivatives so it would apply to all tensors. The laplace article is still very far from decent since it does not say anything usefull about the (general) Laplace operator, but that's another issue.

Also I have seen some mathematics articles which are now physicist territory, like Noether's theorem and Lagrangian. I think that a good article should start at it's highest level and then explain how lower levels are special cases of it. These lower levels may then also have their own page if necessary. And if something has application to physics or anything else, these should then be treated. Sometimes people say that this is an encyclopedia as a reason for excluding certain information that is considered too specialised/difficult. I don't see their point. Any comments? MarSch 16:07, 26 Mar 2005 (UTC)

I agree that we should discuss generalizations. However, I strongly disagree with your statement that "a good article should start at its highest level". Instead, we should "start simple, then move toward more abstract and general statements as the article proceeds" (quote from Wikipedia:WikiProject Mathematics). This has the advantage that we don't scare away people that are not interested in the generalizations; people that do want to read about the most general case will understand (and skip) the lower levels. For instance, I think the article on the Laplace operator should start with the definition

$\Delta f = \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2}.$

But by all means, proceed to treat the definition

Δ = d d * + d * d

The split mathematics/physics should be handled on a case-by-case basis. I definitely agree with you for Noether's theorem and I would be very happy if somebody will tackle this article. For another view, read Wikipedia:Village pump (miscellaneous)#where are the chemists?, from which I quote: "Turning to physics, I often find articles which appear to have been hijacked by mathematicians, causing them to loose insight into _physics_ principles." -- Jitse Niesen 22:31, 26 Mar 2005 (UTC)

Ugh. I completely disagree with the form of the recent edits to Laplace operator by User:MarSch. As a geometer, I like the fact that the full abstract definition has been added, but it should appear later in the article, after a simpler high-school/college-level definition.

Please keep in mind why people come to Wikipedia in the first place: to learn something new, to refresh thier memory, to look up a forgotten formula. There is nothing worse that one can do to a reader than to overwhelm them with abstractions they don't understand. For example, any chemist, who may have had a few semesters of quantum, would be lost in this article as it currently stands. Ditto for any structural engineer, or electronics engineer. These are people who would use wikipedia, and frankly, they outnumber the geometers by a hundred to one. The article should cater to that level of understanding first, and then, only later, turn to the more abstract definitions. As an example of where this works, see the definition of the discrete laplace operator, which appears at the end of the article, not at the beginining. linas 02:02, 27 Mar 2005 (UTC)

Agree with Jitse and Linas. Most people will not appreciate seeing things in their higher perspective upfront. Besides, bottom-up, from particular to general, is the natural way of learning things. Oleg Alexandrov 02:44, 27 Mar 2005 (UTC)

Thanks for your comments. My above viewpoints reflect my feeling of a lack of modern math content. I agree that by making the article more difficult I have, hopefully temporarily, made Laplace operator worse, because there wasn't and still isn't any informal stuff. I have been reading the project pages on structure of mathematics articles and searching for a good example article, and I have not been able to find what a good article should look like. I have given it some thought and I think what is most lacking from, as far as have seen, all articles is a good motivation at the beginning of the article (everything before the TOC) of why that article is interesting to read. After that should come a good informal treatment with few or no formulas and still after that should come the formal treatment. After this section should come some applications. What i was trying to say earlier was about the formal section, it should be as general as the article title warrants and then reduce to some special cases. At the moment Laplace operator has only a formal section, which is why it is very difficult to understand right now. Writing good motivational and informal stuff is probably one of the most difficult things one can do, because they require a very clear understanding of a subject. MarSch 11:34, 28 Mar 2005 (UTC)

I think we will all agree that math articles here need more motivation, more applications, more connections with other articles and relevant real world examples. This is mentioned at Wikipedia:How to write a Wikipedia article on Mathematics (maybe not in such uncertain terms as MarSch would like). However, I think no amount of motivation or explanation is going to make Laplace operator a good article, if instead of starting with the Laplacian as a sum of partial derivatives one goes right to the Laplacian on manifolds, a huge number of formulas, and a very general abstract treatment. I think that some kind of consensus was reached that going from most general to the particular is not the way to go. Oleg Alexandrov 18:29, 28 Mar 2005 (UTC)

The ideal on Wikipedia is to give a 'concentric' treatment: brief lead paragraph, then more details, then further details for the reader who needs them ... and even link to other pages when the extra details become very long. This is actually the opposite of the Bourbaki idea that you start with the supposedly 'correct' general definition. Now, we as mathematicians have some problems doing it that way; but in the end it is better to give an accessible treatment. Charles Matthews 15:00, 1 Apr 2005 (UTC)

This discussion and the one on Laplace operator have changed my mind. All parts of the article should start simple and end very very hard ;) -MarSch 14:34, 4 Apr 2005 (UTC)

encouraging references for formulas

formulas and constants are especially vulnerable to malicious vandalism. adding a square root, changing a single digit, etc. how do we fight it? two possible treatments:

encourage references for every formula
encourage people who know the formulas and numbers well to watch the pages

see Fourier_transform#Continuous_Fourier_transform for an example where I included an image from another site as a reference in comments after an anon removed an erroneous sqrt sign.

- Omegatron 16:01, Mar 28, 2005 (UTC)

the square root probably went over the 2pi? This is just a problem of definition. Do you want the Fourier transform and it's inverse to "look the same". It is a convention. You should probably mention that two versions exist.

In general I guess we gotta watch our formulas. If we use them to derive a few simple properties or prove something then mistakes will be spotted sooner.-MarSch 17:26, 28 Mar 2005 (UTC)

You're right. It was just over the 2pi. But I've seen other small changes here and there that were incorrect. - Omegatron 17:35, Mar 28, 2005 (UTC)

It's tricky to reference formulae as we often want to fit in with the style of related articles within Wikipedia, meaning we might use a "paraphrased" formula rather than one directly from a paper or book. (As a trivial example, we might write "sum nx" rather than "n sum x".) Just as for any other topic, that means those that know the subject need to watch the pages and check for subtle changes. --stochata 21:27, 28 Mar 2005 (UTC)

I agree in principle with Omegatron. I've added a section to Wikipedia:WikiProject_Mathematics/Proofs specifically deal with this type of issue. linas 03:58, 3 Apr 2005 (UTC)

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