Wikipedia talk:WikiProject Mathematics/Archive/2011/Feb

A concrete proposal to help the beginners

My suggestion is to adopt a guideline for math pages (particularly the more advanced ones) that they should include a specific pointer to the more elementary topics that need to be mastered in order to understand the more advanced page. The pointer should consist not merely in a mention of a page imbedded in a clause in a long sentence, but a specific mention that the linked page is more accessible. Here is an example. Riemannian manifolds and their curvature cannot even begin to be approached until the student has mastered the theorema egregium of Gauss and the idea that Gaussian curvature is an intrinsic invariant. Pages such as Riemannian manifold should make it clear that the reader has to understand surfaces first. A similar example: I believe the reason the contributor who expressed himself above cannot make any headway in exterior algebra is because the wedge product appears there in a completely "ex nihilo" fashion. By the time the article gets around to construct the exterior algebra in terms of the tensor algebra (!), we have already lost all beginners. The page exterior algebra is a great page, but it could be made more accessible to someone with basic background in linear algebra, but not much more. I tried to link it to more elementary pages in the spirit of my suggested guideline above, but encountered reverts on the grounds of being "unencyclopedic". We should adopt a guideline making it encyclopedic to try to help beginners. Tkuvho (talk) 22:09, 19 January 2011 (UTC)

I'm not completely opposed to this in principle (though the idea has never really gone over well in the past). But it seems to me that there are a lot of practical difficulties in getting it really right. Just to start with, I'm not sure I agree with your specific example — when I took a course in semi-Riemannian geometry, I had never studied the theorema egregium by that name, though I did know the concept more or less. I doubt that that theorem per se is a true prerequisite, though I'm not saying it wouldn't be helpful. I see this proposal as giving us new and exciting things to argue about in every article.

For difficult articles, the list of concepts to be mastered before a "beginner" can approach them is pretty intimidating. Is the idea to present, say, just a few immediately-more-general notions, with it being understood that you also need the sort of general familiarity with a whole range of concepts and techniques without which you wouldn't understand the immediate "prerequisites" either? --Trovatore (talk) 06:27, 20 January 2011 (UTC)

"The idea" is that a beginner who looks at, say, riemannian manifold, should not walk away baffled, intimidated, and non-plussed, having learned nothing. If we offer him some leads to lower-level articles, he will either look at those and learn something, or else say, OK, to understand Riemannian manifolds I need first to know what Gaussian curvature is. This is far less discouraging than walking away completely baffled, which seems to have been the experience of some of the beginners who expressed themselves above. Every college course has a list of prerequisites in the course catalog. I am not sure why some mild approximation in wiki should be viewed as such anathema. And I don't think this is "condescending" toward the beginner (see comment below), on the contrary, endless blather about "non-encyclopedic" is condescending. Tkuvho (talk) 14:00, 20 January 2011 (UTC)

Well, I agree with the reverts because I don't think your pointer was in quite the right place and expressed in quite the right way. At Chain rule#The chain rule in one dimension, there's a hatnote that says, For an explanation of notation used in this section, see Function composition. Placing the pointer separately from the main text warns the reader what he's getting into before he starts, and I think that's better style.

But I also wonder whether we should have that kind of message at all. I think a really good article wouldn't need a hatnote like that. I have some recollection that we've discussed this here before, but I can't remember what the outcome was. Ozob (talk) 00:14, 20 January 2011 (UTC)

If you go to the "Search Archives" box and enter "Prerequisites" (here, I've done it for you) some relevant discussions appear. --Trovatore (talk) 06:18, 20 January 2011 (UTC)

The hatnote may be a good idea. At any rate this sort of thing should be anchored in official guidelines because you will always have purists who come along and say this is unnecessary. A beginner's needs should be anchored in guidelines. As far as your remark concerning "really good articles", I agree in principle but we have very few of really great ones in the sense of being accessible to beginners. Certainly neither Riemannian manifold nor exterior algebra is at present, as I argued above. Should we wait for them magically to turn into "really great ones"? The users above were right to complain about them. Tkuvho (talk) 05:53, 20 January 2011 (UTC)

I think it is generally a bad idea to start of an article by saying: "you should know this, this, and that before attempting to read this." (Or any friendlier message with the same content.) It feels really condescending to me. Moreover, it encourages laziness on part of the editors, by just allowing them to put up some prerequisites and not push to obtain the uttermost accessibility that is possible for the subject. In particular, it encourages starting articles at a high entry level, instead of steadily increasing the difficulty level as the article proceeds. Another thing to keep in mind, is that there can exist vastly different roads to understanding a mathematical subject. A pattern I sometimes see in the thinking about accessibility of math pages on this project, is that it tends to focus on the path that a typical mathematics student would take in learning about the subject. This is not surprising since it is the path that many of contributors here followed/are following, but many users will actually have a different background, which often misses some of the mathematical foundations that a mathematics student would have, but might on the other hand might include a lot of hands experience of using similar structures. For example, students of theoretical physics will learn about Riemannian manifolds in a GR class without any solid knowledge Gaussian curvature or the theory of surfaces (that a mathematics student would have.) Similarly, when (even if) physics and engineering learn what a tensor of a vector bundle is, they usually have been working with examples of these structures for years. I think that a similar effect to providing a list of prerequisites, (without the possible condescending connotation) can be achieved by detailing in the lead what types of things a concept is generalizing and/or naming a few well-known (to people that do not already know about the subject) concrete examples. This typically are things that a reader should know about to understand the article. A reader that has never heard about any of these things, will generally get the clue that he has encountered an article for which he doesn't even properly understand the basic context. Although hopefully he will have a much better idea of the context then before.TimothyRias (talk) 13:29, 20 January 2011 (UTC)

As one of those reverting the change I should add my thoughts. Perhaps my overriding concern is that articles are about a particular topic, and so be written about that, in an encyclopaedic but accessible way. That means that comments about the article, even indirect ones such as "before reading this, read this", have no place in it. Far better to write the article in a clear, straightforward way to make it as accessible as possible to as wide an audience as possible.

That does not mean we don't help those who would be better off reading something else first. In fact we go to great lengths to support them. Through well-chosen wikilinks, through 'See also' links, through navigation boxes, templates and project pages we guide users to articles on related topics and more fundamental ones so they can find those most of use to them. We don't make assumptions about what they know, we show the connections between topics so readers can navigate to the ones they need. We also provide references that often are much more useful for learning from than a factual encyclopaedia article. Arguably we do more like this, and do it better, than any other encyclopaedia, in a way that doesn't interfere with writing the best encyclopaedia articles we can.--JohnBlackburne^words_deeds 13:52, 20 January 2011 (UTC)

This discussion should not be about specific reverts but rather about a mild "prerequisite" guideline. If you feel strongly about exterior algebra we should focus on a more neutral example such as riemannian manifold, see my comment above. There is no way of making this accessible without copying a large part of differential geometry of surfaces into it. Either we provide gentle hints to the beginner, or we don't, and merely leave him baffled. Tkuvho (talk) 14:05, 20 January 2011 (UTC)

I've added an introduction section to Riemannian manifold which I hope should help. I think many of the complaints about math articles on Wikipedia can be addressed by improving the lede or adding a less technical introduction. However that should not preclude other, perhaps interim, steps, that suggest an article to read first. If we can have a { { main } } tag, why not an { { intro ] } tag that says something like For an introduction to this subject see. I'm often bothered by the adjective "encyclopedic" as used on Wikipedia, which seems to mean "helpful, but not too helpful" rather than its dictionary meaning.--agr (talk) 16:52, 20 January 2011 (UTC)

It's a problem with technical articles that the people who know enough about a subject to write about it intelligently tend to be more used to writing for their colleagues than for the general public. So many articles are filled with jargon that only someone who would already be familiar with the subject out be able to get past. (I just ran across this in a psychology article so the problem isn't restricted to mathematics.) On the other hand it's impossible to start from first principles on every article so a certain level of prior knowledge must be assumed. I don't like the idea of adding a specific prerequisites section because the introduction should be telling the reader that implicitly already. For example in math we tend to start article with a phrase like "In topology ...", which should tell the reader that if their not familiar with topology then they'll probably find the article rough going. In the example above, the article on Riemannian manifolds should have a sentence to the effect that it arose from the study and/or is a generalization of the idea of Gaussian curvature and the reader should get the idea that it would be a good idea to be familiar with the latter before getting into the details of of the former. Also, WP is meant to be a reference and not a textbook, so the task isn't to teach the subject from a clearly defined starting point anyway. I do think the general level of the target audience should be identified somewhere though, probably on the talk page. It may be tricky to do this for longer articles since some have advanced level information even the introduction in written at an elementary level. I think it would be helpful for future editors, once the article has taken shape as to content, to know for example that the introduction and history sections should be kept accessible to a general audience, the derivation should be understandable to someone with freshman calculus, and the rest of the article is at grad school or higher level.--RDBury (talk) 16:59, 20 January 2011 (UTC)

@RDBury: I like your proposal a lot. Note however that what you are proposing is much more radical than my proposal. I am merely proposing a mild introduction hatnote guideline, which only involves minor adjustments to existing articles (that, in my opinion, go a long way in helping beginners). If I understand your proposal for the introduction correctly, it would involve rewriting a large percentage of our articles, and would certainly require an official guideline to succeed. Just check the current lede at exterior algebra and tell me if it is "accessible to a general audience", which seems to be evolving in the opposite direction. Thus, a discussion of determinants and rank has just been deleted. What seems to have taken its place is a discussion of equivalence of categories and universal constructions, with the justification being that "we are constrained by a need to summarize the article in the lead, and a large part of that is dedicated to these issues". Is the lede supposed to be a scientific abstract of the article?

Tkuvho — my sense is that (i) you read RDBury as saying that all introduction sections should be kept accessible to a general audience but that (ii) he was really saying that there should be a way of recording the decision that a particular article has an introduction section that can be kept that accessible. Certainly there are plenty of topics (actually, the ones I'm most interested in writing about are all in this category) where the best we can hope for a general audience to take away from the article is not much more than "that's some complicated math thing". However if an article has been written with an accessible introduction, then clearly it can be, and RDBury was proposing (I think) that there should be some way to remember that. --Trovatore (talk) 06:16, 21 January 2011 (UTC)

(Just to be clear, I was speaking in generalities and not really looking at a specific article. To answer your question, no, imo abstracts belong in a journal article but not an encyclopedia article. Off the top of my head I'd say the introduction for the article like "exterior algebra" should be written for a junior or senior college math major.)--RDBury (talk) 05:19, 21 January 2011 (UTC)

Consensus in the past has been that the lead of the article should conform to WP:LEAD, meaning that it should be an overview of the article that is accessible as possible, but it should not leave out the harder bits just because those are impossible to describe for the layman. The lead needs to be a summary of the article for everyone—beginners, experts, and everyone in between. There has also been consensus in the past that a separate introductory section can be helpful for beginners. There is obviously confusion in this thread whether by "introductory section" you mean "lead" or actually "introductory section" in the sense that our WP:MSM uses. Could you please clarify? Sławomir Biały (talk) 12:35, 21 January 2011 (UTC)

I do think of lead section and introduction as the same thing, sorry if that caused confusion.--RDBury (talk) 15:08, 21 January 2011 (UTC)

Note that this does not have to conflict with making the lead more accessible than the main text. Being a summary, the text in the lead does not have to have the same amount of rigor as the main text. In many cases it would be OK to have a statement in the lead that is (from the perspective of a mathematician) slightly ambivalent, which is clarified with more mathematical rigor in the main text.TR 12:46, 21 January 2011 (UTC)

Agreed. Sławomir Biały (talk) 13:22, 21 January 2011 (UTC)

@agr: Thanks for sharing your thoughts on the adjective "encyclopedic". I wholeheartedly agree. I like your suggestion for an { { intro } } tag. If we can get a guideline approved in this direction, we would have an official basis for fighting off some of the "encyclopedic" browbeating. As far as I see that makes the two of us supporting the idea, though, with an additional "maybe" from Trovatore. Any ideas, fellow editors? Tkuvho (talk) 19:13, 20 January 2011 (UTC)

I don't think that RDBury's proposal is radical. I think it's similar to the existing official guideline at Wikipedia:Manual of Style (mathematics). Most of the articles that people are complaining about are currently in violation of this guideline. WhatamIdoing (talk) 21:04, 20 January 2011 (UTC)

The lede is currently dominated by a Bourbakist formalist attitude that has seriously degraded the quality of the article. The vague expostulations border on error, as when the lede confides that the exterior algebra construction can be generalized to more general vector spaces such as spaces of vector fields or differential forms. This may lead the reader to conclude that one is calculating the exterior algebra of the said infinite-dimensional vector space, which would be complete nonsense. I can't fight this alone, though. Tkuvho (talk) 21:28, 20 January 2011 (UTC)

The lede of exterior algebra is not at all like Bourbaki. I disagree with your other claim as well, what exactly is your problem with saying the exterior algebra construction can be generalized to vector fields? RobHar (talk) 06:08, 21 January 2011 (UTC)

It can, it's just that these are not vector spaces, but sections of respective bundles, so construction is done pointwise, and then we take sections of the resulting bundle. — Kallikanzarid^talk 08:29, 21 January 2011 (UTC)

(@Tkuvho) The lead is supposed to summarize the most important points of the article. Since the article seems to be largely sourced to Bourbaki, naturally the lead is going to summarize some "Bourbakist" material. By and large, it's actually the more accessible content that tends to violate WP:LEAD, and there is always a tension between the demands of making a technical article accessible and conforming to WP:LEAD. In the case of the exterior algebra, two paragraphs of introductory material of the lead is wildly out of proportion to its representation in the text. Sławomir Biały (talk) 12:38, 21 January 2011 (UTC)

(ui)I'm not sure that appeals to WP:LEAD are valid since we are, in effect, discussing the possibility of changing it, at least for math articles. (There seems to a couple threads here at once, actually.) I think the rationale for WP:LEAD are: a) WP is a reference work so people from a wide range of backgrounds may come to an article. b) Many people reading an article will not read beyond the lead section, some won't go beyond the first sentence. c) An article should provide benefit to as wide a range of possible readers as possible, from those who just want a vague idea what the subject is to those who are already familiar with it and want to fill in some details in their understanding. My conclusion is that the lead section primarily serves the lower end of that spectrum. It the private sector it's called an "elevator speech", or "How would you describe the your job (or the subject of an article) to someone you met randomly in an elevator before they get off at the next stop?" The higher end of the spectrum are served by the latter parts of the article and will probably blow past the lead section anyway. This is a big reason WP writing is so different from textbook writing, in a textbook you can assume all readers are starting at the same point and are committed (with their tuition money) to see it though to the end. Yes, you do want to include the important aspects of the subject since even a casual reader may want to know why someone might be interested in this strange new idea they've come across. But this should be written with the casual reader in mind for the lead section. My favorite example of how this should be done (perhaps because I put a lot of work into the article) is W:Catenary. Everything above the "Mathematical description" section should be accessible to a high school student and there is even eye candy so no one falls asleep.--RDBury (talk) 16:21, 21 January 2011 (UTC)

Remark, changing WP:LEAD is pretty much out of the question. It is a wikipedia wide guideline, changing it would require consensus very much beyond this project. Since it is wikipedia wide guideline, it will apply to mathematics articles no matter what additional guidelines we would impose. The most we could do is provide a guideline, of how leads in maths article could best realize the requirements of WP:LEAD. Writing such a guideline, that collects various "best practices" of how to deal with the difficulties of satisfying the various aspects of WP:LEAD in articles about abstract mathematical subjects, might actually be a good idea.TR 16:41, 21 January 2011 (UTC)

There should not be any situation where text X is the best article on a given subject but WP:LEAD forces us to choose an inferior text Y. If there is in a rare instance, WP:LEAD can be ignored--it's just a guideline. If problems arise regularly and there is project consensus on what should be done differently, WP:LEAD can certainly be supplemented by a math specific style guide or altered itself if need be. The guidelines are there to help editors, not get in their way.--agr (talk) 22:33, 22 January 2011 (UTC)

A guide of best practices seems like a good start in any event. There is clearly a lot of confusion, not just about how WP:LEAD can help improve our articles, but indeed what WP:LEAD actually demands. I find our own WP:MSM not to be very helpful in clarifying what the ideal lead of a mathematics article should look like. In particular, it confuses an introductory section for the lead, whereas I think one of our current best practices is that these are generally different things. Since the time that was written, many of the other guidelines have changed to reflect the improving content of Wikipedia. I think that our own guideline should also be brought up to a higher standard as well. We have more good articles now then we did back then, and today's good articles are even "gooder" than yesterday's. Of course, given the confusion and disagreements here, bringing our guideline up to speed is likely still to be a long way off. But I think it should be a priority. Sławomir Biały (talk) 23:04, 22 January 2011 (UTC)

Some best practices

Here are some suggestions for the lead. I've itemized them for easier discussion.

1. The lead should conform to WP:LEAD: The purpose of the lead is to define the topic and summarize the article with appropriate weight. (The proposed guideline of best practices is in addition to the requirements of WP:LEAD, which editors are encouraged to consult before continuing.)
2. For a mathematics article, as a general rule, the lead should at a minimum include answers to the following questions: (1) What is it? (2) What is it useful for? (3) What field is it studied in?
3. The lead should be as accessible as possible to those without a specific mathematical background. This may include providing a concise intuitive description of the subject, even if it isn't fully rigorous.
4. Generally speaking, explaining things in words as opposed to mathematical symbols improves the accessibility. Likewise, if any specialized jargon appearing in the lead can be easily explained, it is a good idea to do so (even if in very informal terms).
5. In spite of the goal of making the lead accessible, the lead should avoid teaching the subject. (WP:NOT#TEXTBOOK)
6. Because of the constraints on the length of the lead, a separate "Introduction" or "Motivation" section may be warranted to allow a more complete intuitive description of the subject. However, like all content on Wikipedia, such a section is held to the same standards of sourcing (WP:V) and should be written in an encyclopedic and formal tone. These constraints may dictate the precise structure of such a section (it may take a historical perspective such as in Metric tensor, or the perspective of increasing generalization like Group (mathematics).)

--Sławomir Biały (talk) 23:40, 22 January 2011 (UTC)

Sounds good to me--Kmhkmh (talk) 15:49, 23 January 2011 (UTC)

There was an old change I was involved in that might be relevant. I set up a motivation and overview section in exponential function which was later changed to just "Overview". You might find the discussion at Talk:Exponential function#Slight muddle? and the next section. It seems there is a real desire in some editors to have article written in a purely logical fashion like some old textbooks where the final result only appears on the last page. I think there really is a need for explicit style guidelines in this area, though even here when I quoted the guidelines another editor responded very negatively to the ideas there. Dmcq (talk) 00:04, 23 January 2011 (UTC)

I agree with your thesis. I find that a good way to deal with people who say things like "I wipe my arse with the Mathematics manual of style!!" is to ignore them until they become interested in something else, and then to go ahead and whatever one was going to do anyway. This particular arse-wiping editor seems to have quit Wikipedia since the discussion you mentioned. —Mark Dominus (talk) 10:13, 23 January 2011 (UTC)

1) Should this discussion be moved to another location? Maybe the talk page of WP:MOSMATH, since I think it is a good idea to record the result of this discussion somewhere, for example as a section of WP:MOSMATH. 2) I generally agree with the points above. Something that could be add is that, if use of jargon is unavoidable, it is generally a good idea to avoid using more than one new piece jargon in a sentence. This way it is possible for readers with a vague acquaintance of the subject, but who are fuzzy on the jargon to get some idea of the meaning of the jargon from the context.TR 08:59, 31 January 2011 (UTC)

Perturbation problem beyond all orders

Perturbation problem beyond all orders could use some work. Michael Hardy (talk) 04:54, 30 January 2011 (UTC)

Accessibility of WP:Math (or "No, I don't have Dyscalculia but WP:Math is just facts and proofs.")

I know, I'm beating this horse over again going over the archives but there few issues and common themes that seem to repeat themselves. WP:NOTTEXTBOOK is often referenced (like in the FAQ above and essay reference) as the excuse for the difficulty of what it's hard to learn anything from WP:Math pages. I do not believe this fair that it's intended purpose. That was meant to leading questions followed by systematic problem solutions as examples. In that same section it states:

5. Scientific journals and research papers. A Wikipedia article should not be presented on the assumption that the reader is well versed in the topic's field. Introductory language in the lead and initial sections of the article should be written in plain terms and concepts that can be understood by any literate reader of Wikipedia without any knowledge in the given field before advancing to more detailed explanations of the topic. While wikilinks should be provided for advanced terms and concepts in that field, articles should be written on the assumption that the reader will not or cannot follow these links, instead attempting to infer their meaning from the text.

Also in right below that in that same section:

7. Academic language. Texts should be written for everyday readers, not for academics. Article titles should reflect common usage, not academic terminology, whenever possible.

This is the problem with the current state of WP:Math and it's infamous for this, both inside and out of the wikipedia community.

"Article titles should reflect common usage, not academic terminology, whenever possible." What is an example of an article title that follows "academic terminology" in preference to "common usage" that would say the same thing or something similarly adequate to the purpose? Michael Hardy (talk) 18:01, 30 January 2011 (UTC)

BTW, I agree with 5 and 7 above. And I've seen cases where they're violated, and tried to fix them. But far more often they are followed. Michael Hardy (talk) 18:06, 30 January 2011 (UTC)

I've done my part in the past few years to link jargon to appropriate pages, fix circular definitions across pages by providing an entrance for someone trying to find an in, and created a few images (all of which to been replaced by better ones it seems). I totally get that it's one it's one of the best resources for the intelligentsia and I don't want to diminish that but that isn't the goal of an encyclopedia. I recently was shocked when I popped in an old copy Encarta and compared the text of our math articles. The articles are brief but you can actual pick up the topic if you not an expert. I feel a little overwhelmed though and hope someone hears and understands the community's pain. --ZacBowling ^(user|talk) 11:05, 30 January 2011 (UTC)

Sigh. Sigh. Sigh. Yes, you're beating the same horse again. There are a few misconceptions on your side. First, if you think that every topic could be made accessible to laymen then why not start with the hardest topic of all ("rocket science" so to say) and after reading the article you'll be an expert. Is that what you have in mind? Second, we have just been discussing right on this very page the issue of accessibility (scroll up). If you have constructive suggestions on how to improve exterior algebra, which have been praised for the recent improvements, you are welcome. Third, pillar one states that "[Wikipedia] incorporates elements of general and specialized encyclopedias, almanacs, and gazetteers.", emphasis on "and specialized". Last but not least, the last two words of point 7 read "whenever possible". Nageh (talk) 11:17, 30 January 2011 (UTC)

Ad "WP:Math is just facts and proofs": Facts and proofs are inherent to abstract and formal sciences. As long as it's not Euclidean geometry it's hard to draw pretty pictures to visually demonstrate the problem. Nageh (talk) 11:20, 30 January 2011 (UTC)

"Texts should be written for everyday readers, not for academics. Article titles should reflect common usage, not academic terminology, whenever possible" - this is impossible. Math is about rigor, you cannot replace strictly defined terms with colorful metaphors - except for the lede, 'Introduction' and 'Motivation' sections, where it is permissible to some degree. If you think math can be done the way liberal arts are, you are sadly mistaken — Kallikanzarid^talk 11:41, 30 January 2011 (UTC)

I sympathize with user ZacBowling. The kind of Bourbakist rhetoric people get for voicing frustration over inaccessibility is discouraging. Tkuvho (talk) 11:45, 30 January 2011 (UTC)

The point where many mathematical articles (admittedly) can be improved are the lead and introductory sections, as Kallikanzarid has pointed out. However, it is impossible to dumb down the core of most articles without getting rid of advanced topics all together. Otherwise, as I suggested, why not skip all the basics, all the elementary and high school stuff and start right with the most advanced topics assuming it is all a matter of presentation? Nageh (talk) 11:51, 30 January 2011 (UTC)

You again? :D You're funny and all, but one more time and I'm reporting you for being a troll — Kallikanzarid^talk 12:04, 30 January 2011 (UTC)

Certainly more can and should be done to increase accessibility; but this has to be within a framework of reasonable expectations. It is somewhat misleading, for example, to make comparison with cutting-edge physics, where a one-hour documentary can make you feel that you have clue about the Higgs boson or strings; when in fact the content doesn't give you access to the simplest computations or basic intuitions in quantum theory at all. Reasonable here means that topics up to about first year graduate study, for which there are adequate and fairly stable textbook treatments, should be presented with some of the heuristic remarks that might well accompany lectures. Saying that Galois discovered that polynomials exhibit hidden symmetries is probably OK; that group theory and field theory help to express the idea conveniently is OK too. I have seen too many such "loose" remarks cut out of lead sections over the years. Have a look at back versions of spectral sequence to see what I mean: the current version really assumes you first know what an abelian category is, which would have been news to the users of spectral sequences in their great period 1945-1960. So some pushback is necessary. But on the other hand the trouble you can get in is illustrated by this, which I happened upon this morning. Trying to be overly heuristic about the Riemann Hypothesis tangles you up with describing the state of research on the primes, which is trouble we don't need in basic exposition (it is very much "facts and proofs" to describe the state-of-the-art in serious topics).

Therefore a "reasonable" way forward would seem to me to be to delineate "core" topics of advanced mathematics and to try to bring their exposition up to scratch, at least where all heuristics are probably out there in the literature and just need to be referenced. Vague remarks that contain elements of OR are also against key policies. Charles Matthews (talk) 12:05, 30 January 2011 (UTC)

One of the main problems is that individuals like Kallikanzarid who have shown their lack of understanding of some of the more advanced issues, continue to edit pages as well as expressing themselves in a virulent fashion throughout wiki. The problem with accessibility at exterior algebra has not yet been resolved, partly due to the lack of understanding of some of the participants. Tkuvho (talk) 12:11, 30 January 2011 (UTC)

I might say the same thing, although with a slightly different emphasis... Sławomir Biały (talk) 13:46, 30 January 2011 (UTC)

FWIW, I have always in interpreted the "academic language" section to be referring to articles like apple that are commonly discussed in non-academic settings. It would be possible to fancy up that article with a lot of terms from biology, for example by saying "endocarp" instead of "core". But the common term for the core of an apple is "core".

The intended audience for apple is much broader than the intended audience for Galois cohomology, and it would be silly to expect the latter to be accessible in the same way that the former should be. The common, everyday word for "homological algebra" is "homological algebra"; there is no other, more common, term to use.

The "research papers" section, which claims that readers should not need to follow wikilinks, has been at odds with actual practice for years, and should generally just be ignored. This is not just in math; see B flat major for another article that you couldn't read unless you knew many terms. The lede of that article is also full of specialized terminology, and is also perfectly appropriate. — Carl (CBM · talk) 12:27, 30 January 2011 (UTC)

I'm not sure what the end result of all this discussion is going to be. I like User:Sławomir Biały's best practices listed above and perhaps they should be added to MOSMATH before they disappear into the archives forever. Some, perhaps most math article could be improved in terms of accessibility, and there are several reasons that some articles have to be less accessible than others. But I don't see any specific changes to MOSMATH or anything else concrete that can be decided here being suggested. I'd like to add that, while WPMATH has a large number of articles, it has a relatively small number of editors working on them. So I think some recognition is due to this project for getting math articles into the shape they're in now, even if it's still a work in progress.--RDBury (talk) 14:20, 30 January 2011 (UTC)

This section's heading looks like someone didn't pay much attention before posting. "Just facts and proofs"? There aren't very many proofs in Wikipedia math articles. Proofs are something we have very little of here. Michael Hardy (talk) 17:57, 30 January 2011 (UTC)

I was quoting a CS professor I know from Berkeley. We had a long conversation about it since I'm fairly active in the community here. --ZacBowling ^(user|talk) 00:56, 31 January 2011 (UTC)

I'm a software engineer myself with a focus on user experience so that is where my brain goes. (coincidentally I used to work a TI developing the software for graphing calculators). Here are a couple of ideas:

• The <math></math> tags should be a little more accessible when used. It's more a technical challenge (my kind of thing), but I would be nice if math symbols could optionally link to topic articles in the syntax.
• A common info box that links to the areas of math the page is directly related too (set theory, elementary algebra, etc), sub categories with pages (eg: matrix calculus), and a field for an optional list of areas of math, physics, and other sciences that the topic can be applied too.
• If someone has stumbled into a page that requires knowledge of a general topic to even understand the current page, the page should within the first few sentences state that and give a link back to a topic. A bunch of pages simply say "In mathematics," and then a list of topic specific jargon. If you are lucky, you find a category tag or hit the talk page and see area of math the topic is trying to cover (like Schubert variety and Bender–Knuth involution)

It's sad that WP:Math is the only Wikipedia area that makes me feel like I should be using Simple English Wikipedia. --ZacBowling ^(user|talk) 01:56, 31 January 2011 (UTC)

Re "It's sad that WP:Math is the only Wikipedia area that makes me feel like I should be using Simple English Wikipedia." This is more a function of mathematics than Wikipedia's treatment of mathematics. Paul August ☎ 02:01, 31 January 2011 (UTC)

Hmm. I think it would be nice if our articles had more navboxes. For instance, take my own dear field of algebraic geometry. It has the generic "areas of mathematics" navbox at the bottom. Now, someone interested in browsing algebraic geometry articles could go to Category:Algebraic geometry, but that category has hundreds of entries plus subcategories. The algebraic geometry article spends most of its time on foundational issues like what varieties and schemes are, and nowhere does it give the reader a map of the subject. A much cleaner solution would be to have a navbox. I think that wider use of navboxes would to some extent address the second and third bullet points above. (I don't know what to do about the first, though.) Ozob (talk) 02:44, 31 January 2011 (UTC)

Since algebraic geometry makes no attempt to use summary style (WP:SUMMARY), something could certainly be done there by quite conventional means. The imposition of a section on "derived algebraic geometry" (no refs) makes it look pretty haphazard. Charles Matthews (talk) 08:20, 31 January 2011 (UTC)

Yes, I think the article is in sad shape. But writing a good survey article for an entire field of mathematics is very, very hard. As an entirely inadequate band-aid, I have created Template:Algebraic curves navbox. It is large and unwieldy, but I think it is a pretty accurate survey of the important topics in the theory of algebraic curves. At least, of those we have articles on. (E.g., I didn't find an article on Mori's bend and break or on rational connectedness, both of which I think would be nice additions. And I couldn't find a really appropriate article on the Riemann–Hilbert correspondence for curves and all of the wonderful stuff related to it (representations of fundamental groups, etc.).)

I am not too attached to the organization that I chose. Classifying everything in some way, let alone a good way, was plenty hard. It may be better to break this into several navboxes, but I'm not sure what would be better. Also I am sure I've made mistakes and left out important things. For the moment I've added the navbox to algebraic curve, elliptic curve, plane curve, and Riemann surface, but of course anyone should feel free to add it to appropriate articles. Ozob (talk) 04:10, 1 February 2011 (UTC)

I have to say that a navbox link is a poor substitute for a {{details}} link, when it comes to exposition and structure. Charles Matthews (talk) 08:03, 1 February 2011 (UTC)

Ozob's navibox is very helpful and well-designed. May there be more like it. Tkuvho (talk) 09:16, 1 February 2011 (UTC)

Well, I've thought about rewriting the algebraic geometry article into a good survey article, but I'm too intimidated by the scope to actually try. Even the algebraic curves navbox is much less than I had initially set out to do. I started out trying to do an algebraic geometry navbox, and I was entirely overwhelmed: Either it was going to be too huge for me to make or it was going to be too selective to do its job. Curves are a specific enough subject that making a navbox like this was actually feasible. And while I agree that navboxes may not be as useful as a survey article, they are a lot easier to do. Ozob (talk) 11:40, 1 February 2011 (UTC)

Some candid observations

I have some relevant thoughts on the original post of this thread. The fact is that there are a great many mathematics articles that are inaccessible, and I don't think anyone can credibly deny this. There are plenty of terrible mathematics articles, some of which no doubt I myself have inflicted on the world. I do think that improving the accessibility of mathematics articles is an important and worthy goal, and I think the best we can hope for in general discussions here is a systematic solution, such as bringing the MOSMATH in line with our current best practices. But project members often display a lack of concern for these issues, or at least a lack of sensitivity to them, and various often sinister reasons have been ascribed for this. But I would like to make some candid observations that I think help explain why things are this way.

Wikipedia's mathematics editors seem to be mostly academics of one stripe or another, and this also seems to be less true of other content areas. To some extent, this dictates how our coverage of mathematics topics develops. I have written articles for the following reasons, and I think that so have many other mathematics editors if I had to guess at their motives based on their behavior: (1) to understand the topic of a seminar I am involved with, (2) as a convenient reference for myself (and other researchers), (3) as a resource for my students (who may be undergraduate or graduate students), (4) to help learn a subject myself or out of sheer curiosity of a subject that I know little about. While I'm sure that the whole altruistic "free encyclopedia" thing may make us feel good about our contributions, it's much too rarefied to elicit any real work on the encyclopedia (for me, at any rate). Out of my own motivations (and I presume those of others), very little has to do with making the encyclopedia accessible to Joe on the street. The only time accessibility is a big personal concern is when I am writing for students, but in their case I assume a fairly specific background (especially when they are graduate students) that the wider population isn't likely to have.

Wikipedia's mathematics editors themselves are also products of the wider world of mathematics, which seems to lack expository source material aimed at Joe on the street. For us, articles published in the Notices of the American Mathematical Society are expository, although most of these articles are almost certainly not understandable to Joe. The rest of the sciences have serious expository outlets like Scientific American, the American Scientist, Nature, and Science, that attempt to explain cutting-edge developments in the sciences to laypeople. But mathematics has no such outlet: Journals in mathematics that specialize in exposition do not emphasize mathematics that is of substantial contemporary interest. One can attempt to rationalize this by saying that "It's the nature of the subject" and "It's much more difficult to make mathematics accessible than other content areas". Critics here dismiss these rationalizations as mere excuses, but I think it is significant that there are so few expository sources for most of mathematics. Sławomir Biały (talk) 13:06, 31 January 2011 (UTC)

It is quite true that mathematics generally is short of survey articles. Let's assume that this WikiProject really could solve three problems:

1. Writing surveys that would help mathematicians get into topics not in their specialist area;
2. Writing surveys that would help non-mathematicians get into topics; and
3. Writing material that would help anyone read the contemporary literature on the Web (and elsewhere).

Then the summary of a great deal of debate comes out that #1 and #3 are handled better than #2. Complaints that aim at #3 (NB what recent papers typically lack is definitions and basic facts), as a way of sorting out #2, are misguided. I think we saw this during a flurry of interest in E8 in the media not so long ago: the media reports were essentially without content, while we added some material on Kazhdan-Lusztig polynomials that meant the actual result could be stated clearly. What #2 would require in that context is exposition of exceptional Lie groups (for example for a chemist), not an attempt to say what the research had been. Charles Matthews (talk) 13:51, 31 January 2011 (UTC)

"there are so few expository sources for most of mathematics" - what about The Princeton Companion to Mathematics? --Boris Tsirelson (talk) 07:00, 1 February 2011 (UTC)

I concur with Boris. There are plenty of expository sources. The japanese encyclopedia is an excellent source. Most of their articles start with the simplest nontrivial example of a theory about to be developed, and works out the example before proceeding to generalisations. The idea that mathematics is somehow different from other scientific fields (and hence hard to explain) is a lame excuse for indulging in Bourbakism. Tkuvho (talk) 11:12, 1 February 2011 (UTC)

I clearly said that advanced mathematics generally lacks expository sources aimed at Joe on the street: that is, aimed at a completely non-mathematical audience. I wouldn't argue that there are expository sources aimed at mathematical audiences. The Princeton Mathematical Companion is pitched at about the same level as many of the "Notices" articles, and most of it is not accessible to Joe on the street. But I think this is a good example because it illustrates about the right level of expository style for several distinct groups of people in this discussion: those who wish to improve the accessibility of portions of our encyclopedia, those who feel that the compendious style of many of our articles is ok, and those that post here to complain that mathematics articles are inaccessible. There is obviously tension between these three groups, and getting them to agree on an acceptable style might be one way forward. Sławomir Biały (talk) 12:42, 1 February 2011 (UTC)

Also, what is the Japanese Encyclopedia? I'm familiar with Ito's Encyclopedic dictionary of mathematics, though I would emphatically disagree that the exposition in that text would be comfortable to non-mathematicians. Sławomir Biały (talk) 12:45, 1 February 2011 (UTC)

That's the one I had in mind. I see that you emphatically disagree about non-mathematicians. Let's leave them aside for a moment. The expository style of Ito's series is attractive because it is geared to explaining basic things rather than trying to cover as much ground as possible. That's a guideline that we should adopt as well. But first we need to get away from the idea that this is somehow "impossible" due to the inscrutable nature of mathematics. Only Bourbaki is inscrutable. I am a great fan of category theory, by the way, and its spectacular applications such such as synthetic differential geometry. But every thing has its place. Tkuvho (talk) 13:47, 1 February 2011 (UTC)

I agree that we should strive not to be Bourbakist. The expository style of either Ito or the Companion is definitely appropriate for a mathematically mature audience. However, I'd like you to please read again what I originally wrote, you will see that I am here talking exclusively about the problem of making things accessible to a non-mathematical audience. Sławomir Biały (talk) 13:53, 1 February 2011 (UTC)

We will never be able to make this accessible to Joe in the street. Your thread is a sub-thread of an earlier thread where useful ideas such as introductions and navboxes were discussed (and some created since). I think we should orient ourselves on people like the originator of the larger thread, who obviously have technical training in college mathematics. Generic discussions of whether "dumbing things down" for a scientific audience is possible or not possible are not going to get us anywhere. You can participate in the current improvement of the algebraic curve group of pages if you believe such improvement is possible. Tkuvho (talk) 14:11, 1 February 2011 (UTC)

But it does seem relevant in relation to the highlighted points from WP:NOTTEXTBOOK in the previous section, which refer to "any literate reader". If we can at least agree on an appropriate way to cover advanced mathematics, then this would indeed be progress. It would help if this were enshrined in some guideline, since the letter of WP:NOTTEXTBOOK would seem to (wrongfully) exclude most of our mathematical content. Sławomir Biały (talk) 14:22, 1 February 2011 (UTC)

Glad you are back. This is an important issue. Perhaps "literate" should be made more specific with reference to mathematics to mean "scientifically literate". This should be discussed in a separate thread. Tkuvho (talk) 14:29, 1 February 2011 (UTC)

List of mathematics journals

I have been working recently on List of mathematics journals. The list was pretty much unattended for a while, and recently some editors from the Academic Journals wikiproject asked us to clean it up. Journals aren't our core focus, but this list is certainly in the broad scope of the math project, as well as the scope of the journals project.

There is a notability "essay" WP:NJournals, which apparently has some weight at AFD discussions, which says that (as one possible criterion) if a journal has an impact factor and is indexed in Math Reviews and Zentralblatt MATH, then we can create an article on it. So I have pruned the redlinks on the list to journals that meet those criteria, and I am working on creating the articles. I made a journal article helper program that can help format the information about a journal into a reasonable stub. If you're interested, you can look up information on your favorite redlinked journal and make a stub article about it (this is easiest if you are at a computer with access to MathSciNet and Journal Citation Reports). — Carl (CBM · talk) 15:17, 1 February 2011 (UTC)

Math related FP nomination

Another pair of cellular automata animations have been nominated, see WP:Featured picture candidates/Non-intermediate phases of BML Traffic Model. See are related to the CA animations that were promoted to FP a week or so ago.--RDBury (talk) 16:01, 1 February 2011 (UTC)

Flat function

The article titled Flat function is somewhat orphaned, i.e. very few other articles link to it. This sort of function plays an important role in the theory of test functions, used in developing generalized functions. It also is used to show why complex differentiability is so much stronger than real differentiability. There must be other things that ought to link to it. Michael Hardy (talk) 20:06, 1 February 2011 (UTC)

I just added a link from the "See also" section of power series. Michael Hardy (talk) 20:08, 1 February 2011 (UTC)

Accelerated PSO

I declined a WP:PROD on this article but am sending it to AFD on request from the original PRODer. Some input from those familiar with computer science and mathmatics would be helpful. The discussion can be viewed here. --Ron Ritzman (talk) 01:40, 3 February 2011 (UTC)

Dehn plane

The Dehn plane article is up for deletion. While plausible searching the usual suspects Planet Math, Encyclopaedia of Mathematics don't yield and references.--Salix (talk): 05:28, 3 February 2011 (UTC)

Bourbakism or provocation?

User:Tkuvho continues to accuse me of Bourbakism. He feels that the lead of Exterior algebra, because it mentions the universal construction, is "engaging in Bourbakism" (whatever that means). Could someone else please comment on what he means? Is he right and I just don't see it? Or is he just trying to provoke me? If so, it's working and it needs to stop. Sławomir Biały (talk) 12:33, 1 February 2011 (UTC)

I agree that there is nothing Bourbaki-esque about that lede. The Bourbaki treatment can be seen on Google books, on p. 507 of Algebra [1]. In stereotypical Bourbaki style that section starts with a formal definition. It's about the opposite of our article. — Carl (CBM · talk) 12:46, 1 February 2011 (UTC)

The specific case of exterior algebra needs to be discussed separately. As far as Bourbakism is concerned, this type of formalism is a common problem that a number of outside scientists frequently complain about, it is about time to give it a name and see what we can do about it. Now returning to exterior algebra, the shape of the lede as you currently see it is the result of a tooth-and-nail fight of which you may not have followed all the intermediate stages. It took a massive effort just to have a reference to cross product restored. Some additional elementary topics are yet to be restored. Note that it was originally deleted on the grounds that "it is already covered under determinants", which is a typical bourbakist way of looking at things. Similarly, I had to fight to have some of the superfluous category theoretic language deleted, such as the following passage: "In terms of category theory, the exterior algebra is a type of functor on vector spaces, given by a universal construction. The universal construction allows the exterior algebra to be defined, not just for vector spaces over a field, but also for modules over a commutative ring, and for other structures of interest." As a result of my criticism, this has been replaced in the current version by "The association of the exterior algebra to a vector space is a type of functor on vector spaces, which means that it is compatible in a certain way with linear transformations of vector spaces". Note that references to "category theory", "universal constructions", and such have been severely curtailed as a result of my criticism. I am not sure why I am accused of criticizing shortcomings that are not there. Once they were removed following my criticism, they are certainly not there anymore. As far as applying the said "universal construction" to the space of sections, this is a rather advanced topic that requires no fewer than 5 stages to develop: (1) linear algebra, (2) topological stage to define the vector bundle, (3) analytical stage: sections of said bundles to prepare for applying the exterior derivative, (4) forming the infinite-dimensional space of said sections, and finally (5) noticing that the formal algebraic construction applies at the level of the said infinite-dimensional space of sections. Presenting stage (5) as if it were identical with stage (1) is simply mind-boggling and can only be attributed to a Bourbakist mindframe. Notice that I was the first one to state, on this page, that exterior algebra is a great page. It became even better as a result of my criticisms. There is still some residual "functor" jargon to be eliminated. Tkuvho (talk) 13:16, 1 February 2011 (UTC)

Wow. You have really invented a whole slew of facts to support your personal campaign against me. Firstly, the original removal of the cross product from the first paragraph, over my own better judgment, was the result of discussion with Jakob, who felt that it obscured rather than elucidated the meaning of the exterior product. The discussion of the cross product was then re-introduced without any fanfare at all by User:Nageh, and I think in a better way. (Hardly the tooth and nail fight that you make it out to be.) The material on minors was not removed because "it is already covered under determinants", it was removed because it was not covered in the rest of the article proportionally to its coverage in the lead that most participants in the discussion felt that was too long. The wording in the third paragraph was changed days before you made any input at all on the matter (thus it hardly "As a result of [your] criticism..."). Finally, your last comment is wrong on at least two points: (1) that the universal construction is anywhere being mentioned in the article in connection to differential forms (one can use the universal construction, tensor products of modules, tensor products of bundles, or whatever approach one likes to the subject—the only thing the article says is that it is "one of these more general constructions"), (2) that because it is complicated, the lead should not mention it (the language used in the lead doesn't in any way suggest that the generalization is trivial, although perhaps the body of the article could say more about the details). Sławomir Biały (talk) 13:45, 1 February 2011 (UTC)

Bialy, let's leave aside what you call the "campaign" and concentrate on the issues. This is getting tiresome. I was not the one to bring up exterior algebra a few minutes ago. Please consult the end of the previous thread. Tkuvho (talk) 13:48, 1 February 2011 (UTC)

Yes, it is getting tiresome. I do not appreciate the accusations of "Bourbakism". It's really quite irritating (not to mention unfounded in the example that we know you have in mind). Please stop. Sławomir Biały (talk) 13:55, 1 February 2011 (UTC)

Incidentally, if you want to apply the construction to vector bundles or tensor products of bundles, then you are not applying the exterior algebra construction to a vector space (as in the case of the space of sections), but rather applying it pointwise to every fiber. This is exactly the ambiguity that I pointed out repeatedly on the talk page, and it is still there in the lede and can lead the reader to errors. I never called you a Bourbakist. I am criticizing a certain style of writing in mathematics. This is a very common term in the "community". It no longer has that much to do with Bourbaki themselves (which started out before category theory). It was not meant as a personal attack. If it is any help, I apologize for giving you such an impression. Tkuvho (talk) 14:00, 1 February 2011 (UTC)

I think that any interpersonal aspects of this should be moved to user talk pages.

I don't like the idea of using the word "Bourbaki-ism" to refer to "not clear enough". Bourbaki is a particular group of people, and the name Bourbaki has the connotation of the actual writing done by those people, which many mathematicians have had exposure to. The problems people sometimes perceive in Bourbaki's writing are broader in some ways and narrower in others than the perceived problem on Wikipedia articles. Because our problems are not the same as Bourbaki's, we don't want to label our problems with that name. — Carl (CBM · talk) 13:58, 1 February 2011 (UTC)

You are not relating to the way the term is used in the "community". It does not just refer to "not clear", and it does not refer specifically to Bourbaki writing. For instance, Bourbaki did not develop category theory, but everyone knows what I mean when I say that emphasizing category theory in a lede of exterior algebra is Bourbakist. Luckily, the emphasis has been significantly curtailed by now. Tkuvho (talk) 14:02, 1 February 2011 (UTC)

Bourbaki did not emphasize category theory very much, and worked with set-theoretic foundations instead. Indeed, the lack of category theory is a criticism often made about Bourbaki. This is the type of thing that I mean when I say that the criticisms of Wikipedia articles are not the same as the criticisms of Bourbaki. The word "Bourbaki-esque" has to be used to refer to Bourbaki's writing, because that writing is such a well known aspect of 20th century mathematics that it is difficult to separate the name from the work.

On the other hand, topics such as Exterior algebra should mention category theory, because that is the standard language of modern algebra. If a construction is functorial, our article should say so; that's exactly the type of information that our articles are meant to contain. — Carl (CBM · talk) 14:16, 1 February 2011 (UTC)

Carl, you have not been reading the discussion very carefully. Of course it should be mentioned at exterior algebra! What I was arguing is that the lead is not the place for it. At any rate, the current categorical content of the lede is quite minimal, and I see the controversy is taking a toll on some of the participants. If it is deemed uncontroversial perhaps some of the deleted references to elementary concepts such as rank and minor can be restored. This is a minor issue in an otherwise excellent page. As far as Bourakism is concerned, you may not like it but it is routinely used in the sense I used it. I am not sure it is our role to fight custom in this case. Tkuvho (talk) 14:26, 1 February 2011 (UTC)

Please see WP:LEAD. The lead is supposed to summarize the article, much of which is devoted to functorial properties and the universal construction. Sławomir Biały (talk) 14:29, 1 February 2011 (UTC)

OK, well, hope you like my latest change to the lede. Glad you are back. Tkuvho (talk) 14:31, 1 February 2011 (UTC)

Re Tkuvho. Personally, when I hear mathematicians criticize Bourbaki, it is for an overlapping but non-identical set of reasons compared to the reasons people criticize Wikipedia articles. Moreover, in practice, our articles do not resemble Bourbaki's writing very much. So criticisms that our articles are "Bourbaki-esqe" always strike me as somewhere between polemical and naive; either way, it makes me take their argument less seriously. If that's the goal, then by all means keep using the word. I think you be able to convince more people if you phrase your criticisms in other terms. — Carl (CBM · talk) 14:36, 1 February 2011 (UTC)

Bourbakism or excessive formalism?

What term would you suggest then? Excessive formalism? Jargon-filled brow-beating? Somehow they are not as effective. Tkuvho (talk) 14:41, 1 February 2011 (UTC)

Or you might just try to be a little less polemic. You might find that this makes others more amenable to constructive discussion.TR 15:09, 1 February 2011 (UTC)

Let's ask that everybody avoid personal attacks. It may be wise for some participants to take a few days off, for their own good and the project's. The participants have been very valuable members of WP and this project.  Kiefer.Wolfowitz  (talk) 15:20, 1 February 2011 (UTC)

Two quick examples of what might be considered excessive formalism: at natural number, for years the article opened with a definition that spoke of the set (mathematics) of natural numbers. I took the "sets" out of the lede. This was my successful anti-Bourbakist operation. Second example: at first-order logic, I tried to include a sentence in the lead to the effect that "first-order" means quantification over individuals, whereas higher-order involves quantification over sets. Now this is technically not quite correct. Still, a lot of people think this remark clarifies the nature of the term "first-order". But because it was not 100% technically correct, my change was mostly reverted. That's my example of a not completely successful anti-Bourbakist operation. Tkuvho (talk) 17:37, 1 February 2011 (UTC)

I think I'd reserve the term "Bourbakism" for articles that start immediately with the most general possible approach to a topic that doesn't warrant it. On several occasions Bourbaki use monoids where most people would be happy with groups, or when they first develop integration they do it for arbitrary locally compact spaces (which I'm quite happy with, but would be the wrong place to start on wikipedia). I completely disagree with saying that mentioning category theory or functor in the lead of an article is "Bourbakist" and more importantly I disagree that it is wrong. Exterior algebra isn't the article "Prime number", it's an article about a formal algebraic tool. A tool which is commonly used in a functorial way. Almost nobody actually takes the exterior algebra of a vector space (at the very least, people use it for a module over a ring, or a representation of a group). If there is an article whose problem is unnecessary use of jargon, then it's problem is "unnecessary use of jargon", not "Bourbakism". For example, using "set" in the first sentence of the article "natural number" is an unnecessary use of jargon. An infringement that would more merit the term "Bourbakism" would be some sort of high-brow axiomatic description such as "In mathematics, the natural numbers are the standard model of Peano arithmetic." RobHar (talk) 17:48, 1 February 2011 (UTC)

The natural numbers are the free monoid generated by a one-element set: that would be excessive formalism. — Carl (CBM · talk) 20:10, 1 February 2011 (UTC)

Bourbakism is good. --Matt Westwood 19:01, 1 February 2011 (UTC)

Actually the knack is to take out excess "mathematics made difficult" formalism, while not being "anti-Hilbert" (retaining the idea that mathematical concepts are axiomatic and "sharp-edged", not vague). And being entirely accurate in what is said, unless flagged up with language such as "roughly speaking". Charles Matthews (talk) 20:34, 1 February 2011 (UTC)

That's a pretty good summary of the challenge. I think we are in agreement that there is room for improvement in a number of cases. The important thing is not the label, but the recognition that there is a challenge. Keeping an eye on reducing "mathematics made difficult" formalism, combined with some work on introductions and navboxes, would probably go a long way toward making our colleagues in the sciences less frustrated with our pages. Tkuvho (talk) 21:19, 1 February 2011 (UTC)

Just a quick additional comment about Hilbert's axiomatics: we all agree about its fundamental importance. At the same time, it was not necessarily meant to be a pedagogical tool. Peano tried to apply the purely axiomatic approach in his own teaching, with disastrous consequences documented at our page for him. I would ahistorically call that Bourbakism, because that's the way the term is used in the "community". People have pointed out above that this is may not be related to Bourbaki proper, which is also a good point. Tkuvho (talk) 09:25, 3 February 2011 (UTC)

Wikipedia, also, is "not necessarily meant to be a pedagogical tool". It's a reference site, primarily.

The issue of long chains of logical dependencies is an expository one, inherent in axiomatic subjects, and it is natural for us to try to solve it by means of wikilinks. We should continue to do that (no choice in fact); it has been noted that in the medical area we tend to assume people will follow the links if they need definitions, while professionally-written material uses a great deal more paraphrase into layman's language. I think we could make some progress here by working towards a "style guide" paragraph or two on how to use paraphrase in mathematics articles. There is an obvious issue of finding an appropriate register of language, and mathematicians have much less practice than physicians in that matter. Charles Matthews (talk) 10:49, 3 February 2011 (UTC)

In my view, this issue of "long chains of logical dependencies" that Charles mentions above is a key one here. These long (and exacting) chains in mathematics can be extremely tedious and time consuming to follow (as every mathematicians becomes painfully aware when they try to read any mathematics outside their specialty). The length of such chains in mathematics is significantly (rough guess, at least an order of magnitude?) longer than in other fields, and that non-mathematicians greatly underestimate this difference, leading to considerable frustration. It would be interesting if there were some objective measure of the average length of such chains in various fields. Paul August ☎ 14:31, 3 February 2011 (UTC)

Dependency bot

The above discussion gave me an idea — let us have a new bot which looks at the lead of an article and assigns it a number which is the smallest natural number greater than the numbers assigned to the articles to which it is linked. If it is not possible to calculate such a number due to a closed loop in the links, then it would report that fact and give a list of the links in the loop. This tool could be used to try to break circular definitions and reduce the depth of searching which readers have to do to understand the lead. JRSpriggs (talk) 13:24, 3 February 2011 (UTC)

That would not be too difficult, technically speaking. It could be done by starting at a given article and chasing links until there are no more. Unfortunately, my time at the moment is committed, but I'd be very interested in seeing the results.

One concern I have is with loops (even in the lede) of a "see also" kind. For example,

• Recursion theory is a branch of mathematical logic.
• Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory.

However, without actually generating some numbers, it's impossible to say how common that issue would be. — Carl (CBM · talk) 13:35, 3 February 2011 (UTC)

My suspicion is that such loops occur in almost all cases. From an accessibility point of view this is not really a problem since such links typically inform the reader of parallel articles on closely related subjects, one of which may in fact be more appropriate for the specific info that the user was looking for. (Knowing "what to search for" already requires quite some familiarity with a subject.)

Moreover, such links are useful since people come from different backgrounds, some readers will be familiar with A but not B will others will be familiar with B but not A. If A and B are similar in some sense, then both these groups will be well served by the leads of A and B pointing out the similarity and linking to the other article.TR 14:09, 3 February 2011 (UTC)

This particular issue is resolved to a certain extent by navboxes. While it is obviously not a solution to all ills, a hierarchical structure of a navbox can help the reader break out of a logical loop. Thus, we could create a navbox for linear algebra with three levels, beginner, intermediate, and advanced; here rank, minor, determinant, cross product would go at beginner level; exterior algebra and other college-level topics would go in intermediate level; advanced topics could connect to differential graded algebra, etc. This way a reader who is having difficulty with "exterior algebra", instead of getting frustrated with links that lead to other intermediate or advanced topics, could go where he should go first, namely the elementary topics which are prerequisites for exterior algebra. Two people involved in this discussion have already created navboxes. Give it a try! Tkuvho (talk) 14:28, 3 February 2011 (UTC)

I don't see exterior algebra as a college-level topic except possibly for a few exceptional students are a few very strong universities. Maybe this is a matter of different universities doing things differently, but I think of the algebra content of a "typical" undergraduate mathematics degree as including just the basic group, ring, and field theory, some basic linear algebra (maybe through Jordan canonical form), and probably a little basic Galois theory. I wonder if there is any information on what topics really are common at the undergraduate level. — Carl (CBM · talk) 14:47, 3 February 2011 (UTC)

I agree that it would be the rare college level student that would be taught this. In fact the same might be true for the average topology graduate student. I don't recall seeing this, nor does a quick glance in my three graduate algebra books (from the late sixties, early seventies) find any mention. Paul August ☎ 15:16, 3 February 2011 (UTC)

I agree, it is not really an undergraduate topic. Obviously whether or not it is taught depends strongly in the interests on the faculty. My argument in favor of navboxes is independent of the issue whether exterior algebra is an undergraduate topic (replace "intermediate" level in the navbox by "advanced", and "advanced" by "research" :) ). Tkuvho (talk) 15:18, 3 February 2011 (UTC)

Affine Grassmannian

The article on affine Grassmanians AGr(n;k), i.e. the k-dimensional affine linear subspaces of an n-dimensional vector space need some additions. For example, it says that as a homogeneous space it can be realised as

${\text{AGr}}(n;k)\cong E(n)/\left[E(k)\times O(n-k)\right]\,.$

At first it didn't even say what O(n−k) was, never mind link to the article. (It's the orthogonal group and E is the Euclidean group.) I think this expression needs explaining. I'm half way to understanding it, but not completely. You start with a k-dimensional subspace passing through the origin, say S₀. You can move that onto any other k-dimensional affine subspace, say A₀, by a Euclidean transformation; so we start with E(n). But different Euclidean transformations take S₀ to A₀; look at the image of the origin when you take S₀ to A₀. That's why we quotient out E(k); we get a map A₀ → A₀ given by different Euclidean transformations taking S₀ to A₀. This is where I start to get stuck. I can see that the O(n−k) term comes from the different choices of original subspace instead of S₀. But that's just the ordinary Grassmannian Gr(n;k) and not O(n−k). Could some one possibly explain to me where O(n−k) and then add the explanation to the article itself? — Fly by Night (talk) 16:27, 4 February 2011 (UTC)

Take a set of all lines in R³, for example. E(3) acts transitively on them, so you have to find what transformations leave a fixed line in place. There are naturally two kinds of them: euclidean transformations of the line itself and (improper) rotations of the space around that line as an axis. Thus the isotropy group is E(1) × O(2) — Kallikanzarid^talk 18:51, 4 February 2011 (UTC)

I see, but how would you phrase that in terms of my S₀ and A₀? In terms your more general approach, what is the general theorem at work? If you have a Lie group G acting transitively on manifold X by α : G × M → M, then M is isomprphic to to the quotient G / G_x, where x ∈ X and G_x ≤ G is the isotropy subgroup of x? This reminds me of the first isomorphism theorem which says that if φ : G → H is a homomorphism then φ(G) ≅ G / Ker(φ). Is that where the proof comes from? If not, could you leave me a link or a reference? I need to understand this for some work I'm doing; but I'm more of a geometer than a group theorist. Thanks. — Fly by Night (talk) 21:03, 4 February 2011 (UTC)

"If you have a Lie group G acting transitively on manifold X by α : G × M → M, then M is isomprphic to to the quotient G / G_x, where x ∈ X and G_x ≤ G is the isotropy subgroup of x?" Yes, but please note that it is a quotient of manifolds, isotropy group is not required to be normal. It makes sense if you think about it :) I am not very familiar with the subject myself, for a rigorous explanation refer to homogeneous space; the second volume of Kobayashi–Nomizu has a chapter about homogeneous spaces, but I haven't read it myself yet. — Kallikanzarid^talk 22:04, 4 February 2011 (UTC)

Great, thanks. When one of us has read that chapter we ought to improve the article I mentioned at the top too. I didn't mention normal subgroups. As far as I recall G_x ≤ G means that G_x is a subgroup of G. While $\scriptstyle G_{x}\,\triangleleft \ G$ means that G_x is a normal subgroup of G. Thanks again. — Fly by Night (talk) 01:37, 5 February 2011 (UTC)

Plücker coordinates

There seems to be a big flaw in this article. The space of lines in P³ is a projective concept. Yet Plücker coordinates are defined in terms of a Euclidean structure defined on R³, e.g. the construction uses a scaler product. Cross products and scaler products depend upon the choice of Euclidean structure and are not projectively invariant. Is it just me, or does that seem a little alarming? — Fly by Night (talk) 02:09, 5 February 2011 (UTC)

The article as I read it explicitly argues that the coordinates are projectively invariant despite the non-invariant setup. —David Eppstein (talk) 02:28, 5 February 2011 (UTC)

Really, maybe I missed that. Could you point me towards that? (The article doesn't contain the word invariant). — Fly by Night (talk) 02:53, 5 February 2011 (UTC)

The part in the geometric intuition section about "up to a common (nonzero) scalar multiple". —David Eppstein (talk) 03:13, 5 February 2011 (UTC)

You should think of R³ is an affine coordinate patch of P³ (that is, it is just P³ minus the plane at infinity). Io describe lines in P³, it's enough to describe those in R³, and then add in the ones at infinity (e.g., take the projective closure).

That said, I'm not defending the approach taken by the article, though, which I find to be quite awkward. I think a better way to define the Plucker coordinates is to think of the space of lines in P³ as Gr(2,4). Planes through the origin in R⁴ are defined by simple two-forms in $\wedge ^{2}\mathbb {R} ^{4}$, which are uniquely defined up to scale, so there is a one-to-one correspondence of Gr(2,4) with the set of simple two-forms in $\mathbb {P} \left(\wedge ^{2}\mathbb {R} ^{4}\right)$ (this is the Klein quadric). The coefficients of a 2-form in a basis then define the Plucker coordinates. The article should probably discuss this approach more explicitly. Sławomir Biały (talk) 13:00, 5 February 2011 (UTC)

Applied mathematics

Input needed at Talk:Applied mathematics, where Michael P. Barnett (talk · contribs) has proposed various re-writes of the lead paragraph of the article. My own view is that his writing style is poor, his proposed leads are rambling and do not summarise the article, and he makes several unsourced claims; in short he is proposing to replace the current brief and clear lead paragraph with a POV mini-essay. But that's just my opinion - views of other editors would be useful. Gandalf61 (talk) 10:30, 5 February 2011 (UTC)

In his comment on the talk page, Charles Matthews found a charitable tone, which is worth emulating. I was unable to find the kind words needed before editing yesterday, and so I did not explain my edits on the talk page.

Yesterday, I expanded the lead with a sentence or two describing the activity of applied mathematics, that is formulating and studying problems in other (empirical or more empirical) fields, and noting that this activity had given rise to topics in mathematics, that then became the subject of study for their own sake (in the activity of pure mathematics). My expansion failed to cite the conventional sources that my edit summary mentioned, e.g. von Neumann, Kantorovich, etc. What is important is that applied mathematics not be limited to a collection of techniques: Both the techniques and the practical activity need to be mentioned.  Kiefer.Wolfowitz  (talk) 12:24, 5 February 2011 (UTC)

Triangulation

The situation regarding the articles titled ABC triangulation XYZ, for various values of ABC and XYZ, seems less than satisfactory. In particular:

• Triangulation
• Polygon triangulation
• Point set triangulation
• Triangulation (geometry) (just moved from triangulation (advanced geometry))
• Triangulation (topology)

How much difference is there between the topics of these articles? Should some be merged? How should they link among each other? Should we have a disambiguation page titled triangulation (mathematics) that would link to these and also to triangulated category and Delaunay triangulation and upper triangular matrix (apparently "triangulation" sometimes means putting a matrix into that form)? Michael Hardy (talk) 22:25, 6 February 2011 (UTC)

The first one you list, triangulation, is completely unrelated to the rest: it's about locating objects by measurements from three other objects, and the other four are all about some sort of simplicial complex. The next three are all about similar topics (complexes where the cells are actual Euclidean triangles in the Euclidean plane) so are in that sense different from the fifth in which a triangle is something more abstract. And, although mathematically they are similar, polygon and point set triangulations are quite different from the computational point of view. But triangulation (geometry) seems kind of useless to me since it is trying to be something of a catch-all and we already have triangulation (disambiguation) for that. For the same reason I don't see a justification for creating a new triangulation (mathematics) article: how would it differ from triangulation (disambiguation)? —David Eppstein (talk) 22:59, 6 February 2011 (UTC)

It's not at all unrelated to the rest, and it's not about "locating objects by measurements from three other objects". It's about locating objects by measurements from two other objects in the simplest cases. Surveyors use triangulations of the surface of the earth; geometers speak of triangulations of the plane; the latter is merely a more abstract thing. Michael Hardy (talk) 04:30, 7 February 2011 (UTC)

Well, at the very least triangulation (mathematics) would omit the non-mathematical topics. There are several cases where XXXX (mathematics) is a disambiguation page and XXXX is also a disambiguation page, and in which this particular division of labor is clearly useful. For example partition (mathematics). Michael Hardy (talk) 23:20, 6 February 2011 (UTC)

Actually, it is desirable to have directions or distances from four or more known points to a new triangulation station. This gives one enough redundancy to isolate a gross error (if any) and make an estimate of the magnitude of minor errors. JRSpriggs (talk) 07:38, 7 February 2011 (UTC)

FP nomination

Two animations related to maze generating algorithms have been nominated for FP. See Wikipedia:Featured picture candidates/Maze Generation 2.--RDBury (talk) 08:20, 7 February 2011 (UTC)

Also, the previous nomination, WP:Featured picture candidates/Non-intermediate phases of BML Traffic Model, is about to close so please take a look if you haven't already. It does happen that pictures aren't promoted simply because there aren't enough votes.--RDBury (talk) 08:35, 7 February 2011 (UTC)

Groupoid algebra up for deletion

The brand-new article Groupoid algebra has been nominated for deletion.  --Lambiam 19:30, 7 February 2011 (UTC)

Adjoint representation disambiguation links

Greetings! This month, we have a large number of links to the disambiguation page, Adjoint representation - 61 links, to be exact. We at the Wikipedia:Disambiguation pages with links project would appreciate any help you could give us in fixing these ambiguous links. Cheers! bd2412 T 00:41, 8 February 2011 (UTC)

Shouldn't these two be merged? — Kallikanzarid^talk 22:24, 8 February 2011 (UTC)

Not necessarily. Charles Matthews (talk) 23:06, 8 February 2011 (UTC)

Gyrovector space

Project members might want to keep an eye on links that feed into gyrovector space. Someone has been trying to do quite a bit of WP:UNDUE promotion of this article, which perhaps includes some legitimate mathematics, but also appears to include some crackpot ideas. Sławomir Biały (talk) 13:32, 8 February 2011 (UTC)

Peer Review for Logarithm

I have nominated logarithm for peer review. Please talk here. Thank you all, Jakob.scholbach (talk) 21:41, 9 February 2011 (UTC)

De Groot Fourier Transform

The new article De Groot Fourier Transform has some very strange statements. E.g.,

DGFT is an method with two variables: groot and power.

I find myself doubting that "groot" is actually used as a parameter. The only reference in the article doesn't seem to talk about an analog of the Fourier transform at all.

I have the feeling that this is an elaborate hoax, but this is not a field that I'm familiar with. Can someone else take a look? Ozob (talk) 02:55, 12 February 2011 (UTC)

The referenced work is a masters thesis, Localization and Classification using an Acoustic Sensor Network, by de Groot. The Wikipedia article is pretty much a direct copy of Appendix D in the thesis (page 110), and the work is copyrighted with the notice:

All rights reserved. No part of this thesis may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior written permission of the above-mentioned.

Notability aside, it's likely a copyvio. Cheers, Ben (talk) 03:42, 12 February 2011 (UTC)

If it's a master's thesis, it was probably put there by the copyright owner, so it would not be a violation. But maybe it's OR. Michael Hardy (talk) 04:40, 12 February 2011 (UTC)

I have marked it for speedy deletion under WP:CSD#G12. In any event, even if the author did release this under the GFDL, it is still clearly original research. This at least saves time at AfD. Sławomir Biały (talk) 13:52, 12 February 2011 (UTC)

Proposal for all articles

WP has improved its math articles greatly since just 3 years ago, when reading an article on a topic one did not already know involved nested (and sometimes circular) link chasing for definitions (links that refer to articles with more links, and so on). I propose that editors try to put a WP:HAT on each article that does not define all its terms, with something like, "This article might be easier to read if you read article A first", in the case that terms come up that can best be understood by reading prerequisite article A, instead of the reader having to chase links for definitions. This might be something like a bottomless pit leading into philosophy of math, but it might also back link to an article the reader is already familiar with, breaking the "infinite" regression back. Remember what Hawking said about what the flat-earth-on-the-back-of-a-turtle-woman in the audience said to Bertrand Russell when he asked her upon what did the turtle upon which the earth rested rest, "its turtles all the way down"[2]. PPdd (talk) 05:32, 12 February 2011 (UTC)

This is a perrenial proposal. I'm against silly notes like this. They violate WP:HAT and are rarely if ever written in a tone appropriate to an encyclopedia article (they directly address the reader). Besides, they shouldn't even be necessary. A well written lead should establish the context of the article, including Wikilinks, so that readers can navigate from those. There has also been a recent proposal to increase the use of navboxes, which also serve a similar purpose. Sławomir Biały (talk) 13:15, 12 February 2011 (UTC)

I have added an FAQ entry about this one. PPdd, this proposal has come up many times before. Every time someone's found an article where this is a problem, the right fix has always been to revise the lead or some other part of the article. Ozob (talk) 15:03, 12 February 2011 (UTC)

FAQ is good (especially for late comers to here like me), but it might also specifically mention Bullet point #8 here[3] and this[4]. PPdd (talk) 15:17, 12 February 2011 (UTC)

The difficulty is that highly technical terms, in math at least, cannot be simply explained in a few words. Moreover, adding definitions of every term used quickly makes a paragraph incomprehensible, because the main point of the paragraph is lost among all the side points. (I also note that you were the one who added that section to the MOS a couple days ago [5]). Hatnotes are used for disambiguation, not for prerequisites. — Carl (CBM · talk) 15:22, 12 February 2011 (UTC)

Another related proposal regards "suggested prerequisite for more easy comprehension", which is subtly different from a "more general treatment" hat. PPdd (talk) 15:17, 12 February 2011 (UTC)

The standard way that we handle prerequisites is by judiciously linking to them in the lede section, and also by adding "introduction" or "background" sections to the article, as with Diagonal lemma. Remember that our articles are intended to be references, not detailed introductions like lecture notes. — Carl (CBM · talk) 15:26, 12 February 2011 (UTC)

help with an svg file

I keep having trouble with inkscape—could somebody please help me out with this image: ? I want the black rectangle be replaced by a z and the extraneous red phi removed. Thanks! Jakob.scholbach (talk) 14:48, 12 February 2011 (UTC)

I'll take a look and see what I can do. RobHar (talk) 18:31, 12 February 2011 (UTC)

Looks like I fixed it. I deleted phi (hopefully the correct one), and converted the text to path (that's what you need to do to when some text is just showing up as a big black box; you can just select everything in inkscape and click on "Path → Object to Path" and it should work out). RobHar (talk) 18:49, 12 February 2011 (UTC)

WPM at its best—thank you! Jakob.scholbach (talk) 21:31, 12 February 2011 (UTC)

Proposal re definitions for all articles

This has likely been covered before on talk, but I propose a general suggestion to add a "Definitions" section at the bottom, for terms defined in the article, for ease of reference. An opposition to this proposal might be that a user can do a search in the article, but this likely produces numerous results (the first of which should be the definition, if a definition has been made in the article. PPdd (talk) 15:59, 12 February 2011 (UTC)

Are you proposing that every article should repeat the formal definition of all the terms it uses? That's the point of wikilinks: the first use of a term will be linked, and the reader can follow the link the get a whole article on the other topic. If we want to summarize the definition within the article, it's better to do that in the regular prose, not in some section at the bottom. We can assume that the reader will actually read the article... — Carl (CBM · talk) 16:05, 12 February 2011 (UTC)

Very often the definition of the concept that the article is about is in the first sentence or otherwise near the beginning of the article. Michael Hardy (talk) 18:26, 12 February 2011 (UTC)

Category rename

There is a proposal to rename the category Recursion theory to Computability theory that hasn't received any response yet. Please comment there if you have any thoughts on the matter.--RDBury (talk) 08:19, 13 February 2011 (UTC)

The category was renamed yesterday. — Carl (CBM · talk) 13:04, 15 February 2011 (UTC)

Fundamental solution

Comments on Talk:Fundamental solution indicate a need to explain the relationship with Green's function. This is one of those interfaces between traditional language and contemporary mathematical language that has been discussed here. That would be part of the issue only, though. Charles Matthews (talk) 12:24, 15 February 2011 (UTC)

Wikipedia talk:Make technical articles understandable

Following the promotion of rhodocene to FA status, some discussion has started again at Wikipedia talk:Make technical articles understandable. That guideline is written in a way that does allow for some technical articles, although it was written to encourage all articles to be as accessible as possible. There have been some useful conversations here recently about accessibility, and people who contributed to those may be interested in following the discussion on the guideline page. — Carl (CBM · talk) 13:00, 15 February 2011 (UTC)

Target audience in WPMath assessment template

Hey all. In looking through the discussion at Wikipedia talk:Make technical articles understandable mentioned by Carl in the previous section, in particular some comments of User:Sławomir Biały on the "target audience" of an article, I had a crazy idea: we could add a field to the Maths rating template banner we put on talk pages that holds the "target audience" of the article. It certainly seems like the target audience of an article is something that it is important to establish. Editors who have spent a long time on certain articles end up having to justify the work they've done to editors who have just shown up and are unhappy with the level of exposition. And that's fine, but it would help if the "seasoned" editors of the article had some way of pointing to an established consensus of what the "level" of the article is. I think there are several other ways this would help. The types of "levels" could be something like "Basic", "High school", "Undergraduate", "Advanced undergraduate", and "Graduate" (where the last should be used sparingly, and the specific terms used could be made more international or otherwise clarified). The approach of "one level down" that Carl has been talking about at Wikipedia talk:Make technical articles understandable would provide a guideline for how to assess the "target audience" of a given article. For some other articles, one would also want to use the subject's popularity to "lower" the level. Thoughts? RobHar (talk) 14:46, 16 February 2011 (UTC)

I don't see any reason why we, as a wikiproject, couldn't designate a "target audience" for an article. On the other hand, I am certain that some editors feel that every article should be aimed at a high-school audience (at the extreme fringe, editors sometimes argue that esoteric topics shouldn't be covered at all). So all the we could do is say, "this is what we think about it"; we can't force anyone else to listen.

A separate issue is that it takes a huge amount of work to go through and actually tag articles with this information. Let me tell you...

I have a different suggestion: any article that is marked "Top" or "High" priority should be written to be understandable by someone with no more than high school mathematics experience. "Mid" priority articles should be written so that at most freshman and junior topics are required. Articles marked "low" priority could be handled on a case by case basis. This would give an easy rule of thumb, and it uses the existing priority ratings that we have. — Carl (CBM · talk) 15:17, 16 February 2011 (UTC)

That's a pretty nice suggestion. Is there any way we could go about expressing this rule of thumb explicitly somewhere? I think that would be helpful. RobHar (talk) 15:32, 16 February 2011 (UTC)

One option would be to add it to the maths rating template. We could add a short section below the rating information that says something like this for Top/High:

And like this for Mid:

And like this for Low (if we need anything)

These could appear automatically inside the rating template based on the priority rating. — Carl (CBM · talk) 15:44, 16 February 2011 (UTC)

I like the idea of target audiences -- or at least think it's worth a shot. I strongly disagree with linking that to article importance. Some very important parts of math are esoteric, and some unimportant things are easy. CRGreathouse (t | c) 21:30, 16 February 2011 (UTC)

For example, Rhombicuboctahedron is rated Low-priority, but it should be accessible to a general audience. Homological algebra is Top-priority but probably can't be made accessible to general audiences (or even most undergrads?) in any meaningful way. The best we could hope for is a lede that could be understood by high-school students. CRGreathouse (t | c) 21:38, 16 February 2011 (UTC)

I agree with that high priority things can be more advanced, but I think that in practice our High-priority articles should also be a high priority for accessibility, even if they are advanced; list of High priority articles. Easy unimportant things are fine; I don't think that "Low" priority has any reflection on intended accessibility.

I'm not sure that Homological algebra should really be Top-priority; I would think that Topology should be Top-priority, and homological algebra should be High or Mid priority. — Carl (CBM · talk) 21:43, 16 February 2011 (UTC)

(ec)I'm a bit wary of identifying a single target audience. The background knowledge is not by any means a linear scale. Typically, the target audience will consist of a divers group of people with different types of background knowledge. For example, take any an article about Lie algebra's. Interest readers could be (advanced) undergraduate mathematics students with a fair amount formal mathematical knowledge about rings, vector spaces, etc. But they also could be interested physicists, with only very vague knowledge of formal mathematics (they probably could not reproduce the definition of a group), but with a fair amount of practical experience with some real life examples of Lie groups like SO(3), and maybe even with the concept of an "infinitesimal generator". Some engineers coming into the topic might have yet a different set of reference knowledge.

An important part of making an article accessible is to reach out to this different audiences. A danger of identifying a single target audience is that in writing the article a certain prior knowledge is assumed that is reasonable for the identified audience, but is completely unreasonable for other interested groups.

One thing I often like to do when writing technical articles is to profile a couple of different types of persons that might want to look up that article. In writing the article, I try to include things that one of these fictitious readers may have heard about (but not necessarily all of them).TR 22:08, 16 February 2011 (UTC)

Well, in both my original suggestion, and Carl's suggestion, I don't think there would be a problem with Lie algebra. In my suggestion, it would be clear (at least to me) that "Undergraduate" should be an upper bound on its level (by "undergraduate" I mean someone who has gone through say a typical freshman science program at an american/canadian university, and maybe some linear algebra). That this should be level is precisely for the reasons you cite. In Carl's scheme, since Lie algebra has high priority, in fact the suggested level would be high school background audience. More generally, with my suggestion, the argument that a given article is of interest to a diverse group of people means that its "target audience" should be a low level; and in Carl's scheme, math articles that are of interest outside of pure mathematics are typically rated high priority (in fact, that is one of the rules of thumb listed on the assessment page for rating something high). So, I'm not sure the problem you are bringing up would really show up much at all. RobHar (talk) 02:00, 17 February 2011 (UTC)

(ui) I like the idea of having some kind of "level" indicator in the maths rating tag. And I agree that while the importance is strongly correlated to the expected level, it should be used as a guideline only. One issue is that the majority of math article still don't have a rating tag at all yet. Another is that many math articles vary in what they expect the reader to know, so an article might need a different levels for different sections. However, as a baby step to see if the idea might work, how about creating a new category Category:General audience mathematics articles and adding the articles that should be readable at a high school level of math? A category like this would be incorporated into a ratings tag scheme anyway. And it won't be much time and effort lost if the idea turns out to be impractical.--RDBury (talk) 03:51, 17 February 2011 (UTC)

I was just looking at the list of Most viewed math articles to see if could be used as a starting point for the hypothetical category from the previous paragraph. A few issues occurred right off the bat. First, biography articles should probably be considered general audience without have to say so. Second, there really aren't that many articles on the list with no advanced math at all. For example Circle, which you would this is a pretty basic topic, has a section on representations in the complex plane. I certainly wouldn't throw out the section because not everyone knows what a complex number is; that information will be useful to those who do and the rest can skip the section. So it should be stressed that a general audience tag should be taken as a guarantee that someone who graduated high school will be able to understand every word.--RDBury (talk) 04:39, 17 February 2011 (UTC)

online copies of cited references

I'd appreciate if people citing math papers in WP articles could make an effort to include non-paywall links to copies of the papers when such are available. The papers are often on the authors' personal websites or preprint sites like arxiv, and at other times can be found through citeseer or by googling the title, but sometimes they can be a bit obscure. I try to add such links when I come across them, but that's just a drop in the bucket. Thanks. 71.141.88.54 (talk) 01:27, 17 February 2011 (UTC)

I agree (and I try to do this when I can). Unfortunately, the trend of putting papers online is relatively recent, and most papers before the 1990s won't be available. It also seems to be less common in Europe; many European mathematicians don't have any personal website they could even think about posting papers on.

A separate issue, which I expect we will see more soon, are the "black market" scanned copies of books that can be found by appropriate google searches. I think we have to avoid these on Wikipedia, since they are almost always copyright violations. Readers who want them can probably find them anyway. — Carl (CBM · talk) 01:57, 17 February 2011 (UTC)

One issue that WP, for some good reasons, regards an on-line PDF as a less reliable source than a printed book. It is nice to have these in the External links section though.--RDBury (talk) 03:26, 17 February 2011 (UTC)

Yes, I know there are a lot of unauthorized book scans floating around and I'm not suggesting we link to those. I'm mostly talking about papers that are posted online by the author, to their own homepage or to a preprint server. Those should be usually considered presumptively authorized and authentic unless actually in dispute. Citeseer can be slightly trickier but I think it's generally ok to use those links unless there's concrete reason to think some particular link might have a problem. There are also quite a few scanned books at Project Euclid and those are also authorized as far as I know. There are a bunch of old French math papers at numdam.org, and dblp.uni-trier.de is sort of a German version of Arxiv for computer science papers. 71.141.88.54 (talk) 04:51, 17 February 2011 (UTC)

As far as I know DBLP stores a lot of bibliographic information for computer science papers, but does not store the papers themselves. The other thing to watch out for here is that in some cases the free versions may have been placed online prior to journal refereeing and so may contain inaccuracies compared to the non-free versions. Or they may not, but it's not safe to blindly put a link to a free paper with the same authors/title assuming that it's automatically good. —David Eppstein (talk) 06:24, 17 February 2011 (UTC)

I think unless there's a known problem with a preprint, we should link to it, just making sure to label it as a preprint. Even if there's a known problem, we should probably (subject to reasonable judgment about the specific issue) link anyway but mention what the problem is. Again, this refers mostly to preprints where the online copy is somehow under the author's control, so if the problem was really bad, the author wouldn't have left it on the web at all.

Also, if there's not a good non-walled copy of the paper but there is a JSTOR scan, we should include that, since lots of public libraries subscribe to JSTOR while usually only academic libraries will subscribe to Springerlink and the like. JSTOR improves accessibility over journal publisher sites in that regard. 71.141.88.54 (talk) 06:53, 17 February 2011 (UTC)

I agree, in the majority of the cases peer review leads only to minor corrections, which rarely effect the statements that an article is referenced for. If PR does lead to major changes, most authors also update the preprint. I don't think there is reason to be overly careful. (although if possible on should always check).TR 09:23, 17 February 2011 (UTC)

David--you're right about DBLP, it appears to be more like Citeseer in that it has links to fulltext on other sites. I was thinking of ECCC (eccc.hpi-web.de), which has a lot of online material but is limited to complexity theory. 71.141.88.54 (talk) 07:02, 17 February 2011 (UTC)

This is clearly not just an issue for WikiProject Mathematics, but is relevant to all citations to academic journal papers regardless of academic field, so this discussion should be raised/moved/flagged up somewhere more general. Wikipedia Talk:Citing sources, perhaps? Qwfp (talk) 08:03, 17 February 2011 (UTC)

I think the general practice is to link document identifiers if they are available. The "cite xxx" and "citation" templates have parameters specifically to support DOI, PubMed, and Bibcode identifiers. Other identifiers can be linked using the "id=" parameter of these templates and using templates like {{arxiv}} ,{{MR}}, {{JSTOR}} or {{Zbl}}. Using these specialized templates is preferred to using the "url=" parameter to link to any of these databases/archives.TR 09:18, 17 February 2011 (UTC)

Yes, that's what I generally do. But these link only to full-text on the official journal sites. Google Scholar often links paper titles to open-access versions when available, but I tend to look for the doi and use that in {{cite doi}}. This thread has made me consider also adding a link to the end something like [preprint], when such is available. Qwfp (talk) 10:29, 17 February 2011 (UTC)

For referencing preprints on the arxiv it is better to use "id={{arxiv}}". Note that this will link to the abstract page rather than directly to the pdf. This gives readers the choice what format they want. (usually both PS and PDF are available). Also note that only DOI links, will send you directly to the journal page, MR, JSTOR, PubMed, bibcode, etc. will provide a link to the article's entry in the respective database/repository.TR 11:30, 17 February 2011 (UTC)

True, good point, though the sites these templates link to are of use only in certain academic fields. In my particular field of medical statistics the only two of those services that are really relevant are JSTOR and PubMed, which provides open-access abstracts but only links to the official site for the full text. The other services are almost never used at present. The placing of preprints or postprints on university websites is increasingly common, however, but there's little point creating a template for these. Qwfp (talk) 11:52, 17 February 2011 (UTC)

Poincaré conjecture and accessibility

Continuing the accessibility trend of late, there is a conversation visible on my talk page [6] about Poincaré conjecture. Since this is one of the Millennium Prize problems, it really should be as readable as possible up top. I made a minimal change to the lede to point out the fact, which is well known to confuse students, that the 3-sphere is the surface bounding the 4-dimensional unit ball (rather than, say, the 3-dimensional solid from grade school geometry). My change was reverted. Maybe someone else can find a better wording? — Carl (CBM · talk) 12:31, 17 February 2011 (UTC)

Rewrite of lead at "Linear algebra"

A couple of editors are attempting to rewrite the lede at Linear algebra. I reverted the first try here (as I didn't think it was an improvement) other edits have been made since. Other views welcome. (I'm traveling all day today and unable to give much attention to this.) Paul August ☎ 11:24, 19 February 2011 (UTC)

That article is in such poor shape that we should do everything we can to encourage the energies of new editors. Almost any attention to the article would be most welcome. At present, the lead is probably not ideal, but I think it's more constructive to get people focused on expanding the article, rather than worrying over the color of the bikeshed. Sławomir Biały (talk) 13:12, 19 February 2011 (UTC)

Lists of integrals

Am I the only person on Wikipedia who is actually monitoring Lists of integrals? The page is viewed 1900 times a day and supposedly has 49 watchers. Just today, substantial vandalism was left untouched for more than 13 hours. Xanthoxyl ^< 02:46, 20 February 2011 (UTC)

Sorry but how can you tell how many people are watching a page? BrideOfKripkenstein (talk) 03:56, 20 February 2011 (UTC)

External tools at the top of the history. Xanthoxyl ^< 04:50, 20 February 2011 (UTC)

On my user page you'll see an easy way to tell how many people are watching. But I may not be watching all the pages that I'm watching. (Apologies to Yogi Berra.) Maybe Xanthoxyl is the only person monitoring that page. Being the only person watching a page has happened to me sometimes. Michael Hardy (talk) 07:35, 20 February 2011 (UTC)

Page moves and renaming

Hi

As a result of my nominating a page (Dehn plane) for deletion. Consensus was that the name was incorrect as it could not be sourced and the deletion discussion is here Wikipedia:Articles_for_deletion/Dehn_plane.

My move, based on the deletion discussion, was discussed here Talk:The_Dehn_plane#Bold_page_move

Several moves later it was left at Non-Legendrian geometry.

Now a single editor has gone against consensus and changed it back to a badly titled "The Dehn plane"

Firstly "The" should not be used, secondly consensus was against using Dehn plane and thirdly it seems as though some editors are deciding that their way is the right way even though it is against consensus.

I fully appreciate being bold, but something has to be done about this. There is no proof given so far that shows a convincing argument for using Dehn plane in any apart of the title. It has so far only produced one neologism from one source.

Chaosdruid (talk) 21:24, 20 February 2011 (UTC)

What we really need more urgently is someone fluent in German to read Dehn's paper and sort this mess out. The secondary sources are some combination of wrong, confused, and self-contradictory. (But yes, fixing the name issue is a good idea too: the standard terms for Dehn's two examples are "semi-Euclidean geometry" and "non-Legendrian geometry"). Sławomir Biały (talk) 21:33, 20 February 2011 (UTC)

I see this discussion is continuing in a new section below Wikipedia_talk:WikiProject_Mathematics#To_boldly_go_against_the_consensus Chaosdruid (talk) 19:28, 21 February 2011 (UTC)

Curve (geometry)

At best the title of this new article is confusing since it's not about Curves in the mathematical sense. I thought flexible strips used in drafting were called splines, from which the mathematical term was derived; please confirm or correct me on this. It seems like we should have an article on them, whatever they're called. We also have a rudimentary article on Elastica theory which covers a mathematical model of these things.--RDBury (talk) 01:24, 22 February 2011 (UTC)

The article as it is currently written seems to be about a particular product ("flexible curves") produced (and probably trademarked) by a company. Since the specific product clearly isn't notable, there is probably very little worth merging anywhere. I would support redirecting to curve (or deleting, since disambiguation seems unnecessary). Sławomir Biały (talk) 01:50, 22 February 2011 (UTC)

We have the article flat spline about the general notion. I went ahead and boldly redirected curve (geometry) to curve. Sławomir Biały (talk) 01:53, 22 February 2011 (UTC)

Absurdity constants, Suppes, Church, and Currie's paradox

I recall something about "absurdity constants" (not absurdity "constraints") in relations to Suppes' Logic, Methodology and Philosophy of Science, Church's thesis, and Curry's paradox, but that is all I remember. Can anyone help with this for the absurdity article? PPdd (talk) 05:39, 12 February 2011 (UTC)

I'll try to look at it next week, although I may have lent my copy to a colleague.  Kiefer.Wolfowitz  (talk) 15:01, 12 February 2011 (UTC)

I have a different book by Suppes, whose index lists no "absurdity". Sorry I couldn't help.  Kiefer.Wolfowitz  (Discussion) 17:38, 22 February 2011 (UTC)

Thanks, but note - my memory might be wrong; that is where I best recall seeing "absurdity constants". Since I was a student both of Church and Suppes, my (errant)memory might be biased. PPdd (talk) 15:20, 12 February 2011 (UTC)

There certainly appear to be a number of Google hits for "absurdity constant" in the literature. See, for example, Gabbay, Dov (2004). Handbook of the History of Logic. Amsterdam: Elsevier. p. 191. ISBN 9780444516237., in the chapter "Paraconsistency and Dialetheism":

"For example, in both classical and intuitionist logic there is an absurdity constant, ⊥, such that for all β, ⊥ → β is a logical truth."

-- The Anome (talk) 20:20, 22 February 2011 (UTC)

Talk:Rake (angle)

Hi

I have just added the maths project banner to Talk:Rake (angle)

I think it is within your scope but would appreciate someone checking that !

Thanks Chaosdruid (talk) 02:26, 22 February 2011 (UTC)

From the edit history, it appears that this was originally about a part of motorcycles. Now it has lost that connection and appears to be merely a definition of a synonym of vertical angle (angle from the horizon) or zenith distance (angle from vertical). It needs a category, but does not appear to me to be about mathematics. In short, it is a mess. JRSpriggs (talk) 03:46, 22 February 2011 (UTC)

Am I wrong in thinking it should merged with the corresponding entry in Wiktionary?--RDBury (talk) 16:23, 22 February 2011 (UTC)

The original page is here [7] and only mentions bicycles in the second example.

I do not think it should be solely about motorcycles, that material was added afterwards, as it is clearly about more than just motorcycles. It seems crazy that there are already so many different rake pages linked from Rake.

The page was expanded (almost hijacked) until it was solely about motorcycles and then the material was moved to the bicycle and motorbike geometry page leaving the redirect. Chaosdruid (talk) 04:31, 23 February 2011 (UTC)

I think RDBury has a point. How much is there to say about this thing, beyond its definition? A definition is not enough to justify an article. --Trovatore (talk) 04:35, 23 February 2011 (UTC)

Well the main point I would make is that the angle of rake is mostly used to describe either ships prows/bows/other features and motorcyles/bicycles. I suppose this could be the page soley for ship's angle of rakes? (all the rest having their own pages rather than being wiktionaried) Chaosdruid (talk) 05:24, 23 February 2011 (UTC)

It just doesn't sound like there's enough there for an article. --Trovatore (talk) 09:42, 23 February 2011 (UTC)

Existential theory of the reals

Existential theory of the reals is an orphaned article: nothing links to it (except the list of mathematics articles). Some links to it could be created and it would bear expansion.

It's in three categories (maybe others should be added?): Category:Real algebraic geometry, Category:Mathematical logic, Category:Computational complexity theory. Michael Hardy (talk) 16:54, 23 February 2011 (UTC)

Potential merge to semialgebraic set. Charles Matthews (talk) 18:06, 23 February 2011 (UTC)

It's a very important topic in the computational complexity theory of real-number computation. I don't think that merge would do that aspect of the subject justice. On the other hand, the existing article is in bad shape. —David Eppstein (talk) 18:22, 23 February 2011 (UTC)

It was in even worse shape before I edited it. (I think?) Michael Hardy (talk) 23:00, 23 February 2011 (UTC)

I was thinking of linking it to "elementary theory of the real numbers" but I discovered we have no such article! Moreover, elementary theory is rather monosyllabic. It would be helpful to fill these gaps if anyone gets a chance. Tkuvho (talk) 14:32, 24 February 2011 (UTC)

The elementary theory of the real field is the theory of real closed fields. Algebraist 18:56, 24 February 2011 (UTC)

Ah, thanks. Should there be a redirect from Elementary theory of the reals? Apparently elementary theory should be connected to real closed field then. Tkuvho (talk) 20:15, 24 February 2011 (UTC)

Directing it to "elementary" rather than "existential" doesn't seem to make sense, since that's an essentially different problem. It's about sentences that begin only with existential quantifiers, and one can imagine statements like the one about NP-completeness changing if one allowed universal quantifiers. Michael Hardy (talk) 00:48, 25 February 2011 (UTC)

I didn't mean that "existential" should be redirected to "elementary", but rather that there should be an extra redirect to real closed field from elementary theory of the reals, as well as a "see also" cite of elementary theory of the reals at existential theory of the reals. Tkuvho (talk) 06:06, 25 February 2011 (UTC)

What would be the point of a see-also link that is redirected to an article already prominently linked from the first sentence of existential theory of the reals? —David Eppstein (talk) 06:21, 25 February 2011 (UTC)

I see the link was added two days ago. Thanks for pointing this out. Tkuvho (talk) 08:26, 25 February 2011 (UTC)

Singular value decomposition is up for review

The article singular value decomposition is up for A-class review. It needs both reviewers and editors. Sławomir Biały (talk) 14:14, 24 February 2011 (UTC)

To boldly go against the consensus

The page Dehn plane contains a discussion of an example of a plane where the parallel postulate fails. The example satisfies Legendre's theorem to the effect that the sum of the angles in a triangle is π. The page has now been moved back to non-Legendrian geometry, even though the geometry discussed here is eminently Legendrian. This is the kind of committee decision we are getting famous for. Tkuvho (talk) 12:42, 21 February 2011 (UTC)

What is most troubling is how unreliable the content there should be regarded. The naming issue should be a totally peripheral matter. Sławomir Biały (talk) 12:48, 21 February 2011 (UTC)

The current content is reliable. Tkuvho (talk) 13:55, 21 February 2011 (UTC)

Boldly going against the consensus? No, that is not how wikipedia works. We make bold edits, they are discussed and consensus is formed.

To make a "bold edit against consensus" means that the editor believes that consensus does not matter.

It would be better to have read the talk pages and deletions discussions which were available on the talk page, not yet archived, and then start more discussions that to simply ignore the consensus that had previously been achieved. Chaosdruid (talk) 19:31, 21 February 2011 (UTC)

Although Tkuvho feels confident that the article's contents are reliable, I still feel like better verification is desirable. I think more discussion and better sources would help, rather than continuing to argue over the title. Present day sources that include "semi-Euclidean geometry" and "non-Legendrian geometry" might be good places to attempt to verify the article's content, as well as to write a better article. Also sources discussing "non-Archimedean geometry" can be used with some care. Sławomir Biały (talk) 19:36, 21 February 2011 (UTC)

In the mean time, I suggest that the article be moved back to Semi-Euclidean geometry as a reasonable compromise until the article actually gets sorted out. Unfortunately, admin powers seem to be required to do this now. Sławomir Biały (talk) 19:46, 21 February 2011 (UTC)

Yup, the last page move created lots of problems with double redirects and so forth. It is likely that the page couldn't be put back to "Dehn plane" for those very reasons also. Chaosdruid (talk) 19:58, 21 February 2011 (UTC)

(ui) For a little context, the article recently survived an AfD here. This is a good topic for an article but what we have at the moment needs much work or perhaps a restart from scratch. Hilbert gives a long discussion of the Archemedian axiom in geometry and it's relationship to the parallel postulate and the sum of angles in a triangle, citing Dehn's paper. It appears however that "Dehn plane" plane is a noelogism, or at least not notable as a phrase. There also seems to be some confusion on the term non-Archemedian, as used in modern English, and non-Legendrian as used in 19th century German, I think it will take someone reasonably fluent in the latter to determine what Dehn actually meant since mathematical language changes significantly over a hundred years. So it may well be that the geometry is "Legendrian" in the modern sense but not what Dehn meant. I personally think the article should be moved to Non-Archimedean geometry which is definitely not a neologism, see the Springer EoM entry for example.--RDBury (talk) 23:40, 21 February 2011 (UTC)

Hi RD, thanks for your interest. The AfD discussion you mentioned is based on the false premise that the example discussed here is non-Legendrian. The error resulted from the conflation of two examples discussed by Dehn, as I explained a week ago in detail at Talk:Dehn plane. The property of being non-Legendrian has nothing to do with the property of being non-Archimedean. Both terms have been stable since at least Dehn's time. The point of Dehn's example was not that the geometry is non-Archimedean (the existence of such geometries is much older), but rather that it violates the parallel postulate. Moving this to "non-Archimedean geometry" makes no sense. Tkuvho (talk) 03:08, 22 February 2011 (UTC)

Thanks for the clarification, maybe a new article is in order then.--RDBury (talk) 16:30, 22 February 2011 (UTC)

One immediate problem is that the contents of the page do not correspond to its current title, but (literally) on the contrary. Can we have a consensus for moving this to "Dehn's plane" or "dehn's counterexample"? Tkuvho (talk) 17:13, 22 February 2011 (UTC)

There are still problems with the double redirects caused by the page moves, the bots are possibly getting confused. I have asked Tkuvho to take a look at them as he was the last to move. Chaosdruid (talk) 16:18, 25 February 2011 (UTC)

New disambiguation

The new article Sum of squares (disambiguation) includes a number of maths topics and hence might be worth checking. Melcombe (talk) 17:27, 25 February 2011 (UTC)

Wijsman's decomposition

I just needed a beautiful theorem which lots of people know but is not written down anywhere (asfaik) in an accessible way including elementary examples. Suppose a probability space $(\Omega ,P)$ is invariant under a compact group $G$ of transformations on $\Omega$. Suppose for simplicity that only the trivial subgroup leaves all elements of the space fixed (otherwise we must divide it out). Assume smoothness. Then the space is essentially the product of two independent probability spaces: one space carrying the maximal invariant, the other being the group itself with Haar measure. There is a neat elementary example in the Monty Hall problem.

The result is also much used in ergodic theory, it's called the ergodic decomposition.

Question: what to call it, what to link it to? I'd like to start writing the article but I'm a mathematical statistician, not an analyst or ergodic theorist or whatever.

There are connections to sufficiency, to invariance (in statistics), to experimental design, and so on. Everywhere where symmetry can be used to simplify statistical models or statistical reasoning. Multivariate normal distribution and multivariate analysis.

References:

R. Wijsman (1990), Invariant measure on groups and their use in statistics

P. Diaconis (1988), Group representations and their applications in statistics and probability

Richard Gill (talk) 15:54, 22 February 2011 (UTC)

Maybe ergodic decomposition is a suitable name for it. Or Wijsman's decomposition? Can you clarify what you mean by "carrying the maximal invariant", and can you tell us a few concrete examples? Those might actually shed some light on what it should be called and which other articles should link to it. Michael Hardy (talk) 23:45, 26 February 2011 (UTC)

Graphical comparison of musical scales and mathematical progressions AfD

The above article is up for AfD here. I've had my say but there is some new discussion basically asking for more expert opinions, so please have your say if you can bring some mathematical expertise to the issue.--RDBury (talk) 21:49, 26 February 2011 (UTC)

R. Catesby Taliaferro

R. Catesby Taliaferro is a stubby new article, doubtless imperfect. Do what you can. Michael Hardy (talk) 00:49, 27 February 2011 (UTC)

Any idea whether he pronounced it "Tolliver"? That's the usual pronunciation from the Southern US, but Yankees usually don't know that, to say nothing of folks from other countries. But I wouldn't want to add that unless we can find out. --Trovatore (talk) 00:56, 27 February 2011 (UTC)

The infamous MHP problem ended up in arbitration

After constant editing conflicts for years, a discussion archive probably running several volumes as printed books and 2 failed mediations the article has ended up in arbitration now.

Maybe it is of interest for some of the editors here or they even want to provide an assessment/opinion.

Wikipedia:Arbitration/Requests/Case/Monty Hall problem

--Kmhkmh (talk) 22:06, 20 February 2011 (UTC)

It is probably useful to point out that Arbcom has historically avoided making decisions about the content of articles; they only deal with editor conduct. The actual disagreements about the content have to be handled on the article's talk page. — Carl (CBM · talk) 22:44, 20 February 2011 (UTC)

yes, they emphasized already that they intend to focus on potential misbehaviour of editors rather than content issues. However most involved parties are already arguing content nevertheless and there are content issues at the core of various long standing conflicts between authors.

Another thing that might be advisable is reevaluate the article's excellence status after the arbitration is completed, since the article has changed rather significantly (not necessarily for the worse though).--Kmhkmh (talk) 00:27, 21 February 2011 (UTC)

Please see the hilarious preliminary statement by Alanyst!  Kiefer.Wolfowitz  (Discussion) 19:54, 21 February 2011 (UTC)

Alanyst almost cost me a mouthful of coffee and a new keyboard. Gandalf61 (talk) 16:08, 28 February 2011 (UTC)

Categorical bridge

Categorical bridge has been prodded. Michael Hardy (talk) 04:33, 21 February 2011 (UTC)

I couldn't find any sources for it, so deleted it. Dreadstar ☥ 00:00, 1 March 2011 (UTC)

Boolean logic

Would someone please monitor. I'm at 3RR, and I can't say the edits I'm reverting are vandalism, just completely, and obviously, inappropriate. — Arthur Rubin (talk) 16:05, 27 February 2011 (UTC)

MTAA discusion

There is a discussion underway at Wt:MTAA that concerns this project. Sławomir Biały (talk) 17:46, 28 February 2011 (UTC)