Wikipedia talk:WikiProject Mathematics/Archive/2004/Jan-Aug

"This article assumes knowledge of" notices
Is it really that necessary to put those "This article assumes knowledge of yada yada yada and blah" notices at the top of pages? If the aim is to help educate the potential reader, it's rather inefficient, unhelpful and redundant in my opinion. Education material should go to Wikibooks. Reference material should stay here. Thanks Dysprosia 09:05, 13 Feb 2004 (UTC)


 * It's a less-than-ideal solution to a genuine problem. Perhaps we could induce a bit of momentum towards top-down organisation of the whole Project, and get a better overall view, or even consensus.
 * In my opinion, and based on the fact that mathematical coverage here is getting fleshed out as the weeks and months go by, we could probably also define a more consistent view of the bottom-up 'needs'. There could be a single page telling people things like 'A depends on B' by major topic. One can't really label that exclusively as education; pro mathematicians also are in a constant struggle outside their speciality with questions like "I think this is answered by some bit of algebraic geometry but where does one look for the language and basic statements?" and "I don't understand why they look at X - why is it suddenly fashionable?". These are just upmarket versions of undergrad issues on organisation and motivation, and as soon as one hits the axiomatic approach there is a perceptible requirement to deal with them.


 * HTH


 * Charles Matthews 11:31, 13 Feb 2004 (UTC)

Top-down organization is a good idea... perhaps we can instead say "This article is part of the subtopic series/topic/whatever of topic", instead of the "assumes knowledge of"? Dysprosia 22:37, 13 Feb 2004 (UTC)


 * Hmmm ... that would work if you could be sure that manifold would be in the differential geometry series because serious differential geometry assumes knowledge of manifolds. Now quite a few people might say 'we look at manifolds for other reasons' (eg dynamical systems on them). This is actually fairly typical: the Lebesgue integral would be in both the Fourier analysis and stochastic process series. Taken to its logical conclusion, the map looks tree-like: the 'leaves' are the major research areas, which draw on auxiliary subjects (e.g homological algebra), which are based on more elementary subjects, and so on back to a small number of 'root' topics such as trigonometry, school algebra. Depending on one's philosophy of mathematics, this might give a completely unified map, perhaps with naive set theory as the 'root'. You then find that much of the combinatorics side has been left out in the cold, so in a sense this is too POV. I think it does correspond reasonably well to what a lot of people in the field understand to be the natural organisation. Charles Matthews 08:55, 14 Feb 2004 (UTC)

Ring theory pages
I would like to reorganize some ring-theory-related pages a little bit, specifically these pages:


 * Algebra over a field
 * Division algebra
 * Rig (algebra)

I would like to redo them as follows:


 * Move algebra over a field to algebra (linear algebra). Most of the links to this page are currently wrong, so I suspect the current page title is misleading.
 * Add a page algebra (ring theory), that talks about (associative) algebras over an arbitary base ring, and mention that associative algebras are the special case of algebras over a field.
 * Add a page for nonassociative algebras, to talk about the general theory of nonassociative algebras. While associative, Lie, and Jordan algebras are special cases, the general theory has a much different flavor.  Move the discussion of nonassociative division rings here.
 * For division algebra, move the discussion about associative division algebras to division rings, which it currently overlaps with. Move the discussion about nonassociative division algebras to nonassociative algebras.
 * Redirect rig (algebra) to semiring, and mention that the term is sometimes used for semirings with zero and one. This is also not standard terminology.  Semiring theorists call semirings with zero and one rigs approximately never.  As far as I can tell, the term is primarily used by category theorists. -- Walt Pohl 16:56, 13 Mar 2004 (UTC)


 * Well, this is mostly OK by me. The non-associative stuff looks a bit as if it was imposed by a Cayley number fan. With due respect to Cayley, it's mostly as Walt says, and once Lie algebras and Jordan algebras are mentioned, the rest of the non-associative stuff is rather specialised. Charles Matthews 16:18, 17 Mar 2004 (UTC)

MediaWiki Side Tables
A week or so back User:Fuelbottle created the MediaWiki pages Template:quantity, Template:change, Template:space and Template:structure, containing side-tables of links, and used the msg: function to display the relevant side-table on each of the pages listed underneath each of these categories on the main mathematics page. More recently User:TakuyaMurata has removed the side-tables from all of the articles in the quantity and space categories. Net result is that some articles have side-tables, but others do not. Can we discuss, and maybe reach a consensus, on whether these side-tables should be (a) removed across the board; or (b) re-instated; or (c) maybe retained in some modified form ? Gandalf61 13:03, Mar 28, 2004 (UTC)


 * I would vote for (a) removed across the board. I also posted a reference at Request for comments.-- Taku 00:29, Apr 1, 2004 (UTC)


 * I agree - these boxes do nothing except take away space that would be better suited for tables and images that add content to the articles. Footers would be better if this type of navigation is needed at all, but frankly a link to the subject article which in turn has such a list would be better. --mav 07:41, 1 Apr 2004 (UTC)


 * I appreciate the effort Fuelbotgtle put into making the side tables, but I don't think they contribute much to the pages. -- Walt Pohl 08:44, 1 Apr 2004 (UTC)

Really (frankly) WikiProject Mathematics should have addressed navigation needs and issues quite some time ago. It seems that picky discussions always are going to take priority over crude needs for the general reader to find things. Well, such is wiki life: much easier to complain that sheaf theory is hard to understand, than to do something for the calculus student. More fun to lay down the law about the perfect article, too.

From where we are, though. There is a subtopic structure now fairly much in place. Footers are definitely better. They would be worth adding systematically, in areas where (i) the existing article coverage is already fairly complete, and (ii) there are likely to be readers needing hints on where to go, rather than just a typical List of X topics. So, which areas are those?

Charles Matthews 07:51, 7 Apr 2004 (UTC)


 * I am ambiguous for either (b) or (c). There are advantages and disadvantages to both side bar and footer.  Side-bar is more prominent, footer is less intrusive.  I appreciate the effort User:Fuelbottle put into making the side tables, and I think they are a great contribution to the pages.  I think the mentioned actions of User:TakuyaMurata were uncalled for, rude, subtracted from the overall clarity and navigability of the Mathematics pages, and added nothing. Kevin Baas 16:34, 7 Apr 2004 (UTC)

I have now changed Template:quantity, Template:change, Template:space and Template:structure into footers. They look better now, and I think they are a good way to navigate the main topics. The last few days someone have created Template:Linear_algebra and Template:Calculus, I think these work ok for navigating subtopics, but if they were footers they could include more topics. Fuelbottle 20:25, 7 Apr 2004 (UTC)
 * I like a sidebar at the top of the page better -- (1) it shows related topics right away (put impt stuff up high where more people will see it) and (2) I think it's easier to read a vertical list than a row of items. FWIW, and thanks for your work on this. Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)

My 2 cents (I know no one asked...):

I don't just think the sidebars (or footers) are possible to work, I think they're necessary in some form. I think the people who are saying, "well, all these people have to do is go to the main topic page, read it, and find a bunch of list pages" haven't really thought the issue through completely. Pretend for a moment that you are learning calculus or linear algebra for the first time (I know...for many of us, this was a long time ago, but pretend). You have essentially no context in which to place articles, aside from the discussion given at the main page. But the most important point is something that I think Charles already pointed out, and that is that math is a cumulative subject with highly complex logical dependencies among topics. One cannot possibly understand the article on Fourier analysis without first knowing what a vector space or Lebesgue integration is. It's true that links are very helpful within an article (click the link if you don't know the term), but this can be very confusing after a while to the reader. For one thing, the reader has no idea the distance between his or her own knowledge and the knowledge needed to read the article; links can't provide this. For another, even with links, the reader may end up kind of blindly wandering around, not knowing the best order of topics that has proven pedagogically sound in the past. Yes, it's true, wikipedia is not a textbook, but the way I see it, in the "ideal wikipedia", it should be theoretically possible for a reader to understand any article by reading simple articles leading up to more complex, in a logically depending fashion. Providing sidebars/footers or organisation of this type isn't writing a textbook at all -- it's just making a tool available so that the existing information is more usable for everyone. After all, I'm thinking there could be sidebars/footers for category theory, homological algebra, or relatively obscure fields, in time. The longer one stays in math, the more one realises how little one knows, and trying to learn a new field without some kind of guidance to the topics and their logical interdependence is difficult for pros, so it certainly won't be easy for most calc students, say.

By the way, it doesn't seem to me there's any reason that an article can't be in more than one series -- e.g. manifolds was mentioned, why can't this be in differential geometry, differential topology, and so on? This would make it difficult to have sidebars, though, and even with footers it could get cluttered if it's used too often.

Revolver 09:26, 8 Apr 2004 (UTC)


 * What I think is that (a) wikis do overlapping and parallel systems quite well (redundancy isn't a serious criticism), and (b) centralising, as a point of view, really is POV here (might be my POV). There just needs to be some reasonable agreement on what would be 'clutter' on a page. One footer is OK, surely. More than that ... I'm not sure. So, I get a picture of 'ideal footer' as containing 'stratum before' as well as 'on the same level as these other pages' info. Charles Matthews 09:46, 8 Apr 2004 (UTC)

Reminds me of a quote in Lang's algebra book, I think -- "Unfortunately, it's impossible to present a body of mathematical topics while maintaining a total order", or something equivalent. Really, the whole logical dependence thing seems to me to be something like a directed graph...just throwing out ideas, maybe a single footer, showing (a) the major topics (rarely more than 3 or 4) that are good idea to be familiar with to understand this, (b) similar articles on the same level/topic, and (c) major topics that lead from this. In the hypothetical manifold case, it would seem to me both diff geom and diff top could be part of (c), at least each of these in the modern formulation. If readers want to go "up" or "down" a level, fine, but they only need a handful of places to go. Up close, they may want to be pointed to trees, but at a distance, directions to forest make sense. Revolver 10:02, 8 Apr 2004 (UTC)

Dynamical systems
Not sure if this is the best place to raise this, but our coverage of dynamical systems and chaos theory is pretty inadequate compared to the treatment of subjects like algebra and graph theory. Even the main article at "Chaos theory" suffers from some vagueness - it defines a chaotic orbit, but doesn't really define the terms it uses (dense orbit, sensitive dependence, etc). There are a lot of holes even in relatively basic topics (Poincaré map,box-counting dimension, and James A. Yorke, for example) and there are some other key articles (bifurcation diagram) that have very brief descriptions.

I've filled in a couple holes (the dynamics definition of orbit, for example) and I'll try to fill in some others, but there's a lot of work that needs doing and some of it will definitely require more background than I have.

Isomorphic 00:20, 14 Apr 2004 (UTC)


 * Agreed that those topics need work. I'll put something on my to-do list. -- Is anyone interested in moving chaos theory to nonlinear dynamics and making chaos theory a redirect? (At present the redirect goes the other way.) "Chaos theory" sounds advertising hype, to my ears. Within the field, people call it "nonlinear dynamics" if I'm not mistaken. Not a content issue, I know, and therefore rather trivial. Happy editing, Wile E. Heresiarch 03:58, 15 Apr 2004 (UTC)


 * I understand, from reading Strogatz: Nonlinear Dynamics, and a little red book on Chaos Theory which I forget the name of, that Nonlinear Dynamics and Chaos Theory, although related, our distinct fields. Nonlinear Dynamics is theoretically prior, but does not discuss Chaos Theory topics, such as the application of ergodic theory.  Perhaps Chaos Theory is heirarchiacly "under" Nonlinear Dynamics, but I believe it is a topic large and distinct enough in itself to deserve it's own page and treatment.  Furthermore, as pointed out earlier, Chaos Theory is a (relatively new) part of Nonlinear Dynamics, and Nonlinear Dynamics is not Chaos Theory. Kevin Baas 17:15, 15 Apr 2004 (UTC)

There must be bits of nonlinear dynamics that are not about chaos, though. What about all that 'qualitative theory of differential equations'? Well, big in the 1950s, I guess. The usual thing would be, yes, nonlinear dynamics as top-level (most inclusive) article, section in that talking about chaos theory to set it in its context (cf. singularity theory &rarr; catastrophe theory for the big-in-the-1960s analogue); and then 'please see main article chaos theory' from there.

The point about gaps is of course a good one. Sign of the times when WP starts looking less like a Cantor-set encyclopedia, mostly gaps. I don't believe we have the basic Frobenius theorem on matrix powers, which is linear dynamics, yet.

Charles Matthews 14:50, 15 Apr 2004 (UTC)


 * I understand, from reading Strogatz: Nonlinear Dynamics, and a little red book on Chaos Theory which I forget the name of, that Nonlinear Dynamics and Chaos Theory, although related, are distinct fields. Nonlinear Dynamics is theoretically prior, but does not discuss Chaos Theory topics, such as the application of ergodic theory.  Perhaps Chaos Theory is heirarchiacly "under" Nonlinear Dynamics, but I believe it is a topic large and distinct enough in itself to deserve it's own page and treatment.  Furthermore, as pointed out by Charles, Chaos Theory is a (relatively new) part of Nonlinear Dynamics, and Nonlinear Dynamics is not Chaos Theory.


 * If substance is at all restricted to the geometry of the medium, then wikipedia will always be "like a Cantor-set" - fractal (perhaps multifractal) and in a constant state of flux; emergent - like a dissipative system.

Kevin Baas 17:20, 15 Apr 2004 (UTC)


 * Charles, I think qualitative theory of differential equations would be a great title. It is true that chaos is only one of several possible behaviors, but all the expositions I've seen describe it in the context of other behaviors, and they usually spend quite a bit of time talking about transitions from non-chaotic to chaotic behavior. Also, they typically say something like "here's a quick review of what linear equations can do, and now let's move on to what's peculiar to nonlinear equations"; it seems WP could do likewise. Anyway, there is a lot to do here. Happy editing, Wile E. Heresiarch 15:25, 16 Apr 2004 (UTC)

In putting up the bios for Lefschetz and Pontryagin, I noticed they both moved into that area at about the same time, after the work in topology for which they are also known. I guess at the time the theory started out asking for periodic orbits, which is like a conventional topological question, in that you might be able to prove existence theorems. Then, I guess, you get the Poincaré return map near to a periodic orbit, as a cross-section near a fixed point; and it is the mapping that induces that is typically the source for the discrete-time iterations that also are studied. Also J. E. Littlewood worked on the Van der Pol equation at that time. Smale went into Anosov flows and suchlike shortly after his topological work on the Poincaré conjecture. That's about global structure of flow on manifolds, and builds on Morse theory. When computing became more of commodity, things (it seemed) changed in the direction of being able to look much more closely at given examples; rather than having to be guided by mathematical analysis; there were more things that came up that were clearly true, but not provable. I never went into this field much; so post-1970 I have just heard the jargon that everyone else has. Charles Matthews 15:41, 16 Apr 2004 (UTC)

User:Charles Matthews/WikiProjectMathematics thoughts
I have posted a discussion document at User:Charles Matthews/WikiProjectMathematics thoughts; and invite people to comment (maybe there).

Charles Matthews 15:21, 28 Apr 2004 (UTC)

What to do with references?
Hi, Charles. You seem to be the cult leader for the mathematicians (!) around the Wikiland. So I will post my questions here, and hopefully I can get a feel on the consensus, if any.

1. Wikipedia's recommended style goes against the mainstream tradition in the mathematics community. Which one should we use?
 * Doe, John; Doe, Jane (1900). Some paper.  Some Journal 1, 1–99.

versus
 * Doe J., J. Doe, Some paper. Some Journal 1 (1900), 1–99.

2. Wikipedia requests references from authors. And I did try to stick with their guidelines. But somewhere along the line I must ask myself: why bother with all the details if they are not going to help the target audience, which are mostly internet surfers who have no interest in digging up the real sources? Why shouldn't we just give them a general reference (some textbook) and be done with it? I fully understand that no one ever forced me or anyone to provide any references. But I still think it would nice if we can agree on a guideline here and get it out of the way.

What are your thoughts?

[bow] Peter Kwok 02:44, 2004 May 27 (UTC)


 * Well my thoughts are to not confuse the ==References== section with the ==Further reading== section. Use the first for actual references used to create the article and use the second for more general books people can read in order to get more information on the subject. But I leave this to the people actually working on this set of articles. --mav 05:31, 27 May 2004 (UTC)

Ummm ... well, this is just on my own behalf. The use of references to original papers should be fairly limited; it helps to cite the paper with the first proof of a theorem, not least because it makes clear that 'proved in 1935' is saying something about the publication date, rather than when a proof was first found. I don't think we have a standardised citation style. As mav said, other references are probably there to help with background reading &mdash; rather than try to give a full bibliography of a subject. There is some general pressure on WP to be ever more academic and scholarly; but footnoting and supporting everything with sources goes against the normal, good survey style. Charles Matthews 08:20, 27 May 2004 (UTC)


 * 1. I assume Peter is refering to Cite your sources. I use this style in the few articles that I've written (for consistency), but I don't really care.


 * 2. Mav's point is a good one, which I intend to use in the future. Charles is also right that many references destroy the flow of the text. In my opinion, statements that are in "any good textbook" do not need to be referenced just put one or two good books at the end of the article. More obscure statement should ideally be referenced, so that the reader can check them. The underlying reason is that I'm personally rather distrustful towards the Wikipedia articles (no offense to anybody, but it's just too easy for a mistake to slip in and remain unnoticed), so I feel I need to double-check some statements and it helps then if a reference is provided. By the way, I don't agree that the target audience is "mostly internet surfers who have no interest in digging up the real sources," especially not for the more specialized articles in mathematics.


 * Jitse Niesen 11:22, 27 May 2004 (UTC)

Okay, I think that settles the issue of using general references-- at least for basic results that should be included in most textbooks.

As for the style issue, I don't see any consensus yet. Not that it is an urgent issue now. But the longer it is put off, the harder to convert the references later-- especially when the servers are soo-oo sloo-ooo-oow. For now, I will go with Wikipedia's recommended style, but I will keep an open mind in case things change in the future. Thank you all.

Peter Kwok 18:24, 2004 May 27 (UTC)

Proposal on Chinese surnames
I was updating some information for Chern and encountered a typical problem in writing Chinese suranames. In most regions that use traditional Chinesee people put the last name last, just like the western names. However, in most regions that use simplified Chinese (except Singapore) people put the last name first. When the two styles are mixed, like Dan Sun and Zheng Sining in the Chern article, it becomes confusing. (In this case, Sun and Zheng are surnames. But sometimes Dan Sun is written Sun Dan; and Zheng Sining, Sining Zeng!)

This has been a well-known problem for identifying Chinese on passports. So what people sometimes do is to capitalize or put a red underline under the surname in passports. I propose that we do the same here and
 * capitalize the first instance of the surname of each Chinese mathemtician in an article-- at least when there is reasonable suspicion for ambiguity.

You can see whether capitalization is useful in the Chern article.

Thanks, Peter Kwok 20:20, 2004 May 28 (UTC)

P.S. I mistakenly added an entry for "Dan SUN". Later I created another entry for "Dan Sun". So the former should be deleted now.


 * I took care of this deletion for you - I'm not sure if this followed policy but it seemed alright.
 * Derrick Coetzee 00:33, 29 May 2004 (UTC)

Thanks, Derrick. Peter Kwok 22:02, 29 May 2004 (UTC)

I think, speaking only about usage in mathematics, that it is standard to have surname last. (When it comes to weiqi, this would be wrong, in my view! But the point would be to use here the name commonly expected.) Charles Matthews 05:40, 5 Jun 2004 (UTC)

Do we have to begin every article with the word "In"?
I mean, yeah, it is a good style, but not the good style, right? How about a little tolerence for people who sometimes want to put the "in" part at the end of the first sentence (or not using it at all)? Peter Kwok 19:01, 2004 Jun 29 (UTC)

Yes, it becomes dull. There are a few other ways. But in general: the first sentence is important to define the area; the first paragraph should be able to stand on its own as a summary. Charles Matthews 19:06, 29 Jun 2004 (UTC)

I concur with Charles that we should keep this policy. Although it is banal, it has substantial benefits, not the least of which are consistency and contextualization. Kevin Baas 22:49, 2004 Jun 29 (UTC)

I have no problem with providing a summary in the first paragraph. But I also think that some kind of varieties can't be bad, especially when the first sentence already specifies the context. Right now people just go around and "fix" the first sentences of almost all mathematical articles so that they all begin with the word "In". This kind of practice only creates frustration and doesn't add value to the articles or to the readers. Since there is no ownership in Wikipedia, I think it is more important for all of us to be more tolerant of other people's style and focus more on the content instead. Peter Kwok 15:12, 2004 Jun 30 (UTC)
 * Well, although I'm guilty of this myself, one shouldn't get too attached to one's "style"...as articles get edited over a period time, the style seems to morph from the original contributor's (if there was one major initial contributor). And, it's difficult to draw a line between style and content. I understand your concerns about how these little unwritten conventions can get boring or annoying. But, I think they're helpful if they're not applied blindly.
 * My own opinion is that differences in style or formatting tend to distract from content. It's not that any one choice of style is really bad, but when it's consistent, it's one less thing for the mind to worry about when reading. Keep in mind, one reason it may seem banal is because many of us are looking at many articles every day, editing over and over.
 * Re: "In mathematics,..." yes, it appears (it IS) banal after a while, but the reason it's there is to give a random reader contextualisation. If an article just launches into cohomology, or functional analysis, or even undergrad ODE's, a random reader may not be able to tell the general subject area, i.e. they may not even recognise that the article is mathematics. Of course, most people who manage to get to these articles will know it's mathematics, but a lot of people wander around exploring, or hit the random page button, or (most importantly) may reach the article because of an incorrect disambiguation.
 * Myself, I've wandered into some of the physical science, chemistry, engineering articles and actually not known what subject they fell under. It's easier in those areas to give more specific areas (i.e. physical chemistry, electrical engineering, cosmology, etc.) because even the general public is familiar with these terms. Most people have no idea of the subject areas in mathematics, beyond "arithmetic", "algebra", and "geometry" (all high school level). Very few will know that "topology" or "combinatorics" or "knot theory" are areas in mathematics (topology has another meaning in English, and knot theory sounds like something you learn while sailing on a boat), so beginning with these terms might not do much more than saying nothing.
 * My general opinion is this: the first sentence should be useful and agreeable to both a random wandered and a person dislocated from a bad disambiguation. This usually amounts to a short definition or description, beginning "In mathematics". Not every article has to start that way. There's no need for the article on functional analysis to read, "In mathematics, functional analysis..." when "Functional analysis is a branch of mathematics which..." The first paragraph (or, introductory paragraphs) should be useful and agreeable to anyone who has the remotest chance of really understanding part of the article, and it should lay out the essential facts that you would want someone to read if they never got past the first paragraph. Then, the rest of the article can begin to assume where the typical reader is.
 * Revolver 00:08, 1 Jul 2004 (UTC)

&gt; Not every article has to start that way

Thank you. That's all that I am saying. No one is going to tell a story about Little Red Riding Hood before he gets to the point. And everybody (including myself) agrees that the first sentence should put everything in context. The only problem is: do we have to all write exactly the same way? For God's sake, this is supposed to be an encylopaedia, not a piece of application form. Yes, there will be random readers who have no prior knowledge of the subject and may not immediately recognize the context. But all they need to do is to read through the first&mdash; I am not asking for even the second, just the first&mdash; sentence. Is that too much to ask for?

Readers are only one side of the equation. There are users (i.e. editors), too. Wikipedia allows users to freely edit articles. Everybody's work may be overwritten over time unless he wrote something that nobody ever reads. We all know that before we contribute. But isn't it exactly why it is more important to nourish mutual respect among users? Right now I find it hard to work in an environment where style police who have nothing new to add just run around to make other people write like them. (No, Charles, Kevin, and Revolver, I am not talking about you. But I suspect that veterans like you guys are already aware of what's going on.) What IF I do the same to those style police? Wouldn't they be pissed off as much as I am? Peter Kwok 15:43, 2004 Jul 1 (UTC)


 * I think there is a house style; and I think there is also a wiki style, based on general tolerance, and not insisting on matters inessential to salvation. One way to look at it, is that style changes alone aren't so much; an edit to change the style is certainly better if it also adds some substance. Charles Matthews 16:12, 1 Jul 2004 (UTC)

So, for instance, a change in style that allows an argument to read more clearly or an example to be better understood is good "style change"; making a notational change that (the editor believes, at least) makes an equation read easier on the eyes or be more transparent, is good; reorganising sections so they follow a more natural order is good; changing tex or math expressions to conform to what's usually used is okay;, but...making cosmetic changes, rewriting a paragraph without making it much different or better, or constantly changing "generalisation/generalization", "neighbourhood/neighborhood" is prob not necc. Revolver 20:27, 1 Jul 2004 (UTC)


 * Fair enough. I don't deny that some style changes are good, or even necessary, and I don't mind people overwriting articles with richer and better content.  It is the ones that added no substance got me.  I regard the "In mathematics" changes as cosmetic and think that we should give people more leeway on that issue.  If you disagree, fine; but let's draw a line somewhere.  Now some people even begin to change journals' standard abbreviations to long names, which is not even recommended by Wikipedia!  Not to mention replacing HTML-styled formulae with &lt;math&gt; tags, or adding a line in the article which won't show up in the display, etc.  (The intensity has been increased recently.  I believe some of the later changes were made just to get me after I expressed my disagreement.)  Do those cosmetic changes really do the readers any good?  Even though it is not exactly vandalism, however, this kind of style vandalism is just as demoralising.


 * If this place really believes in the "everything goes" philosophy, then do let things go. However, if this place believes in maintaining a house style, then maybe we need some kind of guidelines or governing body to give users some protection.  Right now I feel that I am being targetted up to the point that it is intolerable.
 * Peter Kwok 22:57, 2004 Jul 1 (UTC)


 * I see this is a thing with you and User:Michael Hardy, who is more or less a founding Wikipedian. It is unlikely that this is anything personal, actually. As you are both good contributors, I hope you will just leave this for a few days, first. Charles Matthews 07:20, 2 Jul 2004 (UTC)


 * I understand why you said that. But after waiting a few days, then what?  Style vandalism is not going to go away.  I am not asking to put a restraint order on a certain individual&mdash; I am just asking to regulate a certain behaviour.  May that viloator be Michael or me or even you or whoever, I just think that certain conducts are doing more harm than good to this place even though they might be unchallenged in the past.


 * I read the WP pages and have already learned all about "be bold", "edit and don't just talk about it", and that kind of things. But we all know it is how flame war (or, in Wikipedia's case, edit war) starts.  I could have gone into a mud fight and rebutted line by line to see who was a better stylist.  I could have even mass reverted articles.  But I didn't.  It is pointless to committ myself into making the place better if the place is not even what it advertises to be.  I want to make things better.  And in order to make things better, we need rules.  I just come here to share knowledge as a hobby, not to compete with people to see who has more time and higher seniority to have the last say in style.  And I can't freely express myself if there is no rule to prevent style vandalists from targetting newcomers and defacing one's work without adding any new and meaningful substance.  This kind of behaviour defeats the purpose of Wikipedia and is a big turn-off for serious contributors.


 * I will take your words for now. But, man, if people don't get serious about this issue, then this place is no fun any more.
 * Peter Kwok 17:51, 2004 Jul 2 (UTC)


 * If you actually want me to discuss this with Michael Hardy, at any point, I will. You can send me email. Charles Matthews 18:07, 2 Jul 2004 (UTC)

Comments on Peter Kwok's concerns
I agree with your statement that mutual respect is important. I have always been polite and respectful to you, and moreover, when I noticed your existence I was glad to see another person contributing articles on mathematics, and that remains my evaluation of your work on Wikipedia.

You seem to think that I have targeted you some how. I have not. I do not edit articles without intending some identifiable improvement.

You wrote: "Right now I find it hard to work in an environment where style police who have nothing new to add just run around to make other people write like them."

Would you tell me who those people are? You seem to think I am one such person. I have contributed a far larger number of new articles on mathematics than you and most others, and a far greater amount of substantive mathematical content to article initiated by others.

I also do minor edits such as a small spelling or punctuation correction in a long article. I did several of those in the article you created on the LYM inequality. You stated on the discussion page that those edits contribute nothing. I disagree. But if you don't agree that they contribute anything, that is not a reason to infer that I was personally targeting you. After I created uses of trigonometry, jengod made some small changes for which I saw no need. It is possible that that person knows some reason of which I am unaware why the changes were improvements, and it is also possible that they are not. Even if I disagreed with those edits, I would still conclude only that another person disagrees, and not that I am being targeted or attacked.

As for moving "In mathematics..." to the beginning, there is a reason for that that I tried to explain to you earlier; I did it because I think the article is in several respects better that way, and I would be specific about that if you appeared to be interested.

You wrote: "I don't deny that some style changes are good, or even necessary, and I don't mind people overwriting articles with richer and better content. It is the ones that added no substance got me.  I regard the "In mathematics" changes as cosmetic and think that we should give people more leeway on that issue.  If you disagree, fine; but let's draw a line somewhere."

Do you regard "cosmetic" as meaning unnecessary or bad? Making an article esthetically better makes it easier to understand and to remember. You wrote: "Now some people even begin to change journals' standard abbreviations to long names, which is not even recommended by Wikipedia!" ... because some readers may otherwise not understand the abbreviation. If you disagree with that, you could say so, rather than acting as if there is something personal about it.

You wrote: "I believe some of the later changes were made just to get me after I expressed my disagreement." On this point I have good news that will reassure you. You suggested that I may be among those doing this. But I have not done this. When I disagree with the way someone edits or with their opinions about how others should edit, I address the actual content of the disagreement, saying why I think what I think. I do not personally attack them. You wrote, "Do those cosmetic changes really do the readers any good?". I would say that if they do no good then they are _not_ cosmetic. "Cosmetic" by definition means they make an esthetic improvement in the article, and therefore they do some good.

You wrote "If this place really believes in the "everything goes" philosophy, then do let things go. However, if this place believes in maintaining a house style, then maybe we need some kind of guidelines or governing body to give users some protection."

_Some_ guidelines are in the style manual: usually the title word or title phrase is highlighted at its first appearance, one eschew's superfluously capitalized letters in section headings, etc.

You wrote: "I could have even mass reverted articles." Did the things you object to happen in more than one article? You have mentioned only one to me. What were the others, if any? - Michael Hardy


 * Michael - I'm sorry that my offer, made above, to deal with Peter's comments above by email was not taken up. This is really not a good discussion. I personally do think you have been stepping over the line recently, in edit summaries, and in other ways (I am not happy with a style change you made recently in something I wrote). Appeals to how many edits you make obviously carry a certain weight; but they don't actually make up for a constant refrain that others lack 'common sense', etc. 'Open sentence' is standard usage in parts of philosophical logic - whatever you may think of it. And so on. I think you should accept that irritation has been caused, and try to work out how to go forward from here. There is nothing to be gained by 'winning' such an argument. There is also a guideline on escalation. We have to accept that there will be friction, from time to time; and not treat such occasions just as a rebuttal-fest. Charles Matthews 19:00, 14 Jul 2004 (UTC)

Clarification: I am not one of the founders of Wikipedia
I fear one of Charles Matthews' comments may be construed by some to mean I am one of the founders of Wikipedia. In fact, Wikipedia was founded early in 2001 by Larry Sanger and Jimmy Wales; the latter has put about $500,000 of his own money into the project. I first edited articles here in October of 2002, if I recall correctly. Axel Boldt was for some time the only person extensively editing mathematics articles here, and I surmise that he is the original creator of the list of mathematical topics. Michael Hardy 01:50, 15 Jul 2004 (UTC)

Typesetting of mathematical formulas
I know it doesn't really matter, but I am always confused by how to write sentences with math in them and saying things like "where m is the mass, b is the buoyancy, and c is the charge") etc. Some people stick commas inside the tex markup and treat the whole thing as a continuous sentence:

If an equation, such as



a + b = c, $$

is encountered, then c is the sum of a and b.

some people treat the equation like a graphic, with lots of extra words necessary to keep it in complete sentences:

Summing two numbers is represented by the following equation:



a + b = c $$

In this equation, a and b are the summands, and c is the sum.

Some people put variable descriptions in a bulleted list below the equation, etc. Can we have a little blurb about a nice method of formatting sentences? I just want some advice for a clean style for myself. - Omegatron 16:05, Jul 20, 2004 (UTC)

Links to surnames of mathematicians are often very bad things
Just as the untutored lay person knows who is being referred to when one mentions Shakespeare or Einstein by surname only, so mathematicians know who is being referred to when one mentions Abel by surname in the context of a math article. But a link to Abel is (of course) a link to the son of Adam and Eve who was killed by his brother in the book of Genesis. And how could anyone expect a link to Study to be a link to an article about the mathematician Eduard Study? Sometimes a math article, or substantial parts of one, are intended to be read by people who know little about mathematics, and in such cases linking to "Euler" does not inform the reader as well as if one links to Leonhard Euler. Consequently I think in most cases first and last names should be used. Michael Hardy 02:04, 1 Aug 2004 (UTC)


 * There appear to be two points about this:


 * (a) that surname-only links may be ambiguous to the reader or require disambiguation as wikilinks;
 * (b) that fuller names in links carry more information to the reader anyway, in the absence of the problems noted under (a).


 * I'm sympathetic to the first point, as I imagine most people are. I find the second point less convincing, really; if there were no link then surname-only does offer much less, but the point is weakened when there is a page to refer to. It is partly a generation and background thing, but I'm happy with Swinnerton-Dyer, just as much as with Peter Swinnerton-Dyer who is really Professor Emeritus Sir Peter Swinnerton-Dyer, Bart. when it comes down to it.


 * Charles Matthews 16:47, 3 Aug 2004 (UTC)

The main reasons that it became standard to use only surnames for references in published text, have been for considerations of space, and the tediousness of typesetting. That is, they were publisher-centric. However, since, Wikipedia is (essentially) free from such constraints, we can afford to be more reader-centric. Thus, more use of full names is a good thing. The presence of a link lessens but does not eliminate the benefit to the reader of fuller names. Of course, judgment is required to know when more information is too much information. Paul August 15:48, Aug 24, 2004 (UTC)


 * I don't think it's just a matter of publisher-friendliness. Readers take additional time to read long names too, and there becomes a time when "Leonhard Euler" looks uselessly long to them. So perhaps in introductory articles, the first appearance of Euler could be written "Leonhard Euler", and the next ones can be just "Euler". Otherwise really-big-names like "Euler" could stay as surname only. (Surname-only links like Study or Abel are another matter and should always be avoided, indeed, IMO.) --FvdP 19:18, 29 Oct 2004 (UTC)


 * Note that according to policy, a link is only given when a name is first mentioned or when it is used in a new context. Thus, asking that every link use the full name isn't inappropriate &mdash; the ones that aren't links, which is most of them, can go right ahead and use just the surname. Link redundancy and first-name-redundancy coincide.
 * That said, an advanced article is justified in excluding the first name of well-known mathematicians, even from links, since it can reasonably expect a more experienced reader. Derrick Coetzee 23:18, 29 Oct 2004 (UTC)

The case for LaTeX
In recent days, I have been adding $$...$$ to every inline math expression I have encountered, starting with articles in Category:Curves and category:Bundles (mathematics). At the time, I thought that the HTML wikitext markup for equations was provisional, and that by TeXifying expressions, I was improving the articles. I didn't know about the existence of the Wikiproject Mathematics page. I'd like to offer my apologies for breaking convention.

That said, I'm perfectly astonished that HTML wikitext markup for inline equations and variables is an official recommendation (not truly "official," but you know what I mean.) I think it's a bad idea, so allow me to flesh out my case here. My proposal is that we should use $$...$$ markup for any and every expression related to math, including formulae, single-letter variable names, and all inline expressions. Here's why:

Now, if you're using a graphical browser, right-click on the previous image and view its file name. Then compare that file name to the one on the WikiProject Mathematics page (where I got it from.) The filenames are exactly the same--5aa3fbdb28e2859859317b8a9d316fa9.png. So server space is not wasted for common expressions like variable names, either, even if they are forced to render as PNGs. There will be only one copy of the PNG file for $$\,\!\theta$$, and anyone viewing our math articles will have it cached. But it is true that mixing inline PNGs with ordinary article text can have a somewhat jarring effect; this is unavoidable, and I happen to not mind it at all (I have seen textbooks that have odd line spacing due to inline math expressions; they still sell well.) One possible compromise is to avoid forced PNG rendering unless absolutely necessary (that is, do not use "\!\," or other "artificial" spaces if you can possibly help it), so the user will see the maximum amount of inline HTML. They can still use their preferences to turn PNG rendering on, so we should expect that PNG versions of all of our expressions, equations, and variable names will exist.
 * 1) Content != presentation. The entire reason that XHTML and CSS were created from the ashes of HTML 3.0 was to separate presentation from content.  We can see the effectiveness of that design decision right here in the Wikipedia: I can change the "skin" of the site (which is just a CSS file) and the look of the site changes automatically, in spite of the fact that the content of every page remains the same. Doing this required tags that were solely devoted to presentation, like ..., ... , and  ...  to be removed from the standard.  They force presentation and content to mix.  So why do we require mathematical expressions to be represented in the exact same manner?  Why should a variable name be "italic?"  What, precisely, does that indicate to the user?
 * 2) Consistency. TeX is capable of creating beautiful PNG representations of math expressions, but the fonts and styles it uses for PNG do not match the fonts and styles used for the present "wikitext math" style.  TeXifying everything will make all variables and equations look consistent.  We won't be able to avoid TeX for more complex formulae anyway; we might as well let TeX choose the font for us.
 * 3) TeX allows the user to decide. If we put all math expressions (including inline expressions and even variable names) in the $$...$$, any user will be able to change the look of all math-related pages with a single tweak to their preferences.  They can view everything as HTML unless absolutely necessary, or they can view everything as PNG for maximum clarity.  That all users' default preferences are not set to the latter is no reason to avoid LaTeX markup.
 * 4) TeX allows the admins to decide. If, in the future, some brave developer decides to replace our LaTeX engine with MathML or some other more fitting standard, they can write a bot that automatically converts all LaTeX expressions on every page.  Alternately, they may decide to change the default fonts for TeX (I don't know if this is possible, but I assume that it is), and again, all math expressions in the Wikipedia will respond to the change.  Neither scenario is possible with "wikitext math," which would have to be changed by hand.
 * 5) PNG images are small. That's the entire point of PNG, and why we use it in the Wikipedias in preference to GIF files.  An expression like $$\int_0^\infty e^{-x^2}\,dx$$ only takes up 680 bytes; this post I am typing is much larger.  It would be difficult to achieve better compression without throwing away image quality!  In a giant page full of these types of expressions, the bandwidth "wasted" downloading the PNGs is negligible compared to the bandwidth required for (1) the article text, and (2) the Wikipedia logo in the upper left corner.
 * 1) TeX can emulate inline HTML, anyway. One objection to the use of LaTeX markup (and, in my opinion, the most legitimate one) is that some browsers cannot view inline PNG, and the resulting alt-text is incomprehensible.  This is true; however, the MediaWiki LaTeX engine creates inline HTML already!  Compare:
 * 2) *HTML style: f(x) = a0x2 + (a1x)cos &theta;
 * 3) *TeX inline HTML: $$f(x) = a_{0}x^2 + (a_{1}x) \cos\theta$$
 * 4) *TeX with forced PNG rendering (with \left, \right, and \!\,): $$\!\,f(x) = a_{0}x^2 + \left( a_{1}x \right) \cos\theta$$

I admit that such a proposal will require us to avoid the more traditional style; $$x \cos \phi$$ renders as "squashed" inline HTML, and would require parentheses if we did not allow artificial spaces: $$x(\cos\phi)$$ or $$(x)\cos\phi$$ or $$x * \cos\phi$$, etc. It's easier to simply allow PNG rendering for unsatisfactory expressions, but nevertheless, this proposal does address the inline objection.

I'm not surprised that my sentiments have been expressed before: Wikipedia talk:WikiProject Mathematics/Archive1 (see comments by User:Pascalromon.) I echo his/her sentiments, but I don't think we need changes as drastic as those that he/she proposed. So how about it, everyone?

Ardonik 19:26, 2004 Aug 3 (UTC)


 * You write I happen to not mind it at all. If most people agreed, we wouldn't be having the discussion, though. Wiki tends to look provisional, and there's a reason (it is). Now, work on format is constructive; but I don't know enough TeX to be happy with it. We have a kind of compromise at present. I expect it to remain until there is a clear technical shift in rendering, making inline TeX the obviously right way to go. Charles Matthews 21:52, 3 Aug 2004 (UTC)

The beauty of TeX is that we can avoid inline PNGs (which I am not opposed to avoiding) and still reap the other benefits of TeX mentioned above by keeping inline expressions in tags. As for not knowing TeX, you don't have to! You add a lot of useful math content to the Wikipedia, Charles, and I figure that the job of less math-literate people like me is to follow in your footsteps, tweaking things here and there. TeXifying equations is one way to do that. Perhaps it would be to everyone's benefit to mark the "old style" as provisional, so as to encourage intrepid Wikipedians to update it at their convenience to the "new format" without shunning the old style completely? --Ardonik 22:28, 2004 Aug 3 (UTC)


 * I think inline PNGs are ugly. I don't mind the use of tags if they are properly translated in inline HTML; in fact, I prefer to type $$f(x)$$, rendering as $$f(x)$$, to f(x) , rendering as f(x) [side remark: I am surprised to see that both expressions render differently; on my display, I prefer the latter]. Unfortunately, not all mathematical expressions are translated into HTML, and I think that these expressions should be either translated by hand to HTML, or put on a separate line. -- Jitse Niesen 20:19, 4 Aug 2004 (UTC)


 * I will admit that it often takes some degree of coaxing to convince TeX to leave some simple expressions as HTML (for instance, using \(space) seems to invariably cause PNG conversion.) TeX isn't perfect, but I still think the advantages of keeping expressions TeXified more than outweigh the disadvantages.
 * If the community consensus is to avoid inline PNGs, then the next step is to discuss strategies for keeping TeX from PNG conversion. I am assuming that the conversion program ultimately responsible is latex2html.  As seen from this page in the official manual, there are any number of ways to induce image conversion, but there appears to be no option by which one can force HTML output.  (Can someone who is more familiar with the world of TeX correct me on this point?)  That rules out convincing the developers to change program parameters; I think we'll just have to come up with a list of TeX features to avoid or replace in order to ensure inline HTML generation.  But now is the right time to discuss such things, and this is the right place to do it.
 * Ardonik 07:39, 2004 Aug 5 (UTC)

Use of \mbox
We can use \mbox{ } to force spaces without inducing PNG conversion. Compare: Can anyone think of any other HTML syntax that TeX can't handle without PNGs?

Ardonik 11:21, 2004 Aug 5 (UTC)

TeX/HTML currently incompatible
On line bundle, I attempted to view the article using all possible choices of user preferences, and none of them were able to convert things like the "Z/2Z", "RP2", "CP2", etc. (blackboard bold, fractions, etc.) to inline HTML. When strict HTML was selected, of course it returned tex code. The point is that there is no way to use inline math mode while avoiding PNGs. TeX and HTML simply "evolved" from different origins and haven't quite become compatible. I expect this problem will be solved in time. In any case, there's no telling that the solution won't require detailed combing over and editing in the future, anyway. So, I agree completely with you in principle, but think it's too early to work in practice. And I don't think it's that big a deal...it will be a lot of work to make the switch when HTML and TeX become compatible, but with enough people working on it, shouldn't be a problem. Revolver 21:02, 5 Aug 2004 (UTC)


 * If the \frac notation cannot be used inline, then we should employ a forward slash instead. TeX understands it; see http://turing.une.edu.au/~amth247/Lectures_2003/Lecture_03/lecture/, and in particular the section of fractions and roots.  It recommends that the slash notation be used in favor of \frac wherever it would make an equation easier to read; thus "Z/2Z" would become $$Z/{2Z}$$.  In order to prevent the "RP" and "CP" in line bundle from rendering inline as PNGs, it suffices to avoid switching to fonts like \blackbb (and it makes perfect sense that HTML would not be able to handle those.)  Again, we can reap the benefits of TeX without generating PNG files.  --Ardonik 02:33, 2004 Aug 6 (UTC)

If the community consensus is to avoid inline PNGs, then the next step is to discuss strategies for keeping TeX from PNG conversion....That rules out convincing the developers to change program parameters; I think we'll just have to come up with a list of TeX features to avoid or replace in order to ensure inline HTML generation. But now is the right time to discuss such things, and this is the right place to do it.
 * Maybe so. I don't know, maybe this comes from seeing articles evolve over months or a couple years, but I don't think this is a urgent problem in any case. Try to avoid the most obvious problems (e.g. I think blackboard bold should be entered as bold for the moment) but it's nothing to get too uncomfortable over. For now, it's probably enough to sit back and wait for the inevitable HTML/TeX compatibility to happen, and then let things sort out. None of these articles are really going to look like they do at present in 2-3 years, anyway. Adding good content and improving some of the weaker "elementary" articles (fundamental thm of calculus, etc.) seems far more important. (BTW, why is FTC listed first in the "calculus" box, before derivatives even?) Revolver 21:15, 5 Aug 2004 (UTC)

Of course I agree with you that adding content is more important than worrying about style, but by formalizing a system now, we ensure that future Wikipedians will know what guidelines to turn to when creating new math and science articles, and that people like me will know how to TeXify articles without ruining them. A thousand times over do I prefer consensus to inaction. --Ardonik 02:33, 2004 Aug 6 (UTC)
 * It's not urgent (what is urgent in this Wikipedia?) but I feel that we do need to address it. LaTeX is not some relatively new technology waiting for extra features to be added by enterprising programmers.  It is mature and fully featured; latex2html itself was around before 1993.  There is nothing to wait for.  The TeX tools were designed to empower those who love math, and now that they have been enabled in the MediaWiki projects, they are at our disposal.  They do everything we want.  What reason do we have to avoid them?
 * P.S. FTC? Calculus box?  --Ardonik 02:33, 2004 Aug 6 (UTC)
 * Fundamental theorem of calculus. Look at the "topics" box on the right. FTC is the first topic. Revolver 19:55, 6 Aug 2004 (UTC)

Honestly, what do we stand to gain by waiting? --Ardonik 03:37, 2004 Aug 6 (UTC)
 * I agree that $$f(x)$$ is more logical than f(x), and that content is more important than format, but I also agree that the HTML version looks better. Supposedly this will all be resolved when mathml is working.  Should we just wait until then?  (and how long will that be, anyway?) - Omegatron 02:47, Aug 6, 2004 (UTC)
 * Well, we have "experimental" MathML support right now, but as for how long we'll have to wait before MathML becomes a widespread standard, the answer is perhaps indefinitely. How could a company that failed to correctly support even CSS 1 be bothered with adding MathML support?  Sure, Mozilla might get it eventually (or someone might develop a fork of Mozilla that supports it), but until aforesaid company makes Mozilla or Firefox the default desktop browser, few people will be able to view MathML.  Additionally, when MathML support is fully enabled, we won't be able to take advantage of it without putting our expressions in  tags first, so we will be better off TeXifying our expressions now than continuing to use raw HTML and piling up the amount of conversion that will need to be done later.


 * A few points. (1) Actually there is a free plug-in for Explorer available and Mozilla et al. have already a reasonable support for MathML (but you need to download some fonts). (2) What happens to &lt;math&gt; is determined by a home-grown transformation that might be changed if desired. (3) MathML is not really functional right now. I think the last point is important. There should be at least one way to see the ideal end-result. -- Jan Hidders 11:22, 6 Aug 2004 (UTC)


 * Yeah, I used the MathML player when I was still in IE. It seemed to work fine, and is free.  MathML is probably the ideal future solution, but ideals are commonly nonviable.


 * Maybe we can make some sort of compromise? add an attribute "inline" to the math tags (, etc. )to make it format as HTML if at all possible, or in small-lettered, center-aligned TeX if not?  And when converting to HTML, change the span.texhtml { font-family: serif; } to something that renders prettier?  Perhaps just leave it in the default font? - Omegatron 13:36, Aug 6, 2004 (UTC)
 * From what I can gather, TeX's chief weakness is its inability to guarantee the generation of inline HTML (by default, of course; user preferences would always be able to force PNG generation.) I am convinced that this can be worked around, but I openly admit that the solutions (like using \mbox{ } instead of a space) are cumbersome.  Another weakness is that the inline HTML is rendered in a different font than the HTML that surrounds it.  Only the developers can fix this problem, as they control the MediaWiki CSS.
 * At the same time, responders seem to generally agree that there are tangible benefits to preferring the markup to ordinary HTML.
 * I see the workings here of a possible compromise:
 * Content and accuracy are more important than anything else. Compared to these, the beauty of a page's math should be an afterthought.
 * (I'm afraid I can't agree that considerations of beauty "should be an afterthought". Of course content and accuracy are of paramount importance, but if an article is so off-putting, that it isn't read, well … Paul August 16:34, Aug 24, 2004 (UTC))
 * Allow people to continue creating and formatting equations in the "wikitext math style" currently described on the WikiProject Mathematics page, but recommend use of the tag for future entries.
 * When using LaTeX, the "house style" will be to avoid generating PNG images for inline equations and variables. Anyone TeXifying wikitext math must be careful to preserve the HTML format for all inline expressions and variables; when this cannot be done, they should leave the expressions and variables as they are. Conversely, if the TeXification of a page's math expressions is done correctly, there should be no reason to remove it.
 * The WikiProject Mathematics page will feature a tutorial on how to keep LaTeX from generating images so that Wikipedians can share tricks like \mbox{ } with others. I can help to write this.
 * Expressions on their own line may freely be converted to PNG, so house style will be to prefer that complex expressions remain on their own line whenever possible.
 * Convince the developers to use a prettier font-family, font-weight, font-style and font-size for inline HTML conversion (what specific settings would be ideal I do not know.)
 * Does this sound like a reasonable set of guidelines? Would anyone be opposed to them, and if so, what can I do to improve them?  --Ardonik 19:10, 2004 Aug 6 (UTC)

"Well, the ideal solution would be …"
Well, the ideal solution would be to just have any and all articles that use mathematical expression to jettison HTML entirely and have the whole thing be a LaTeX file. This would eliminate all the problems. (I'm being facetious, of course...but also trying to indirectly point out what the problems are short of doing this.)

From what I can gather, TeX's chief weakness is its inability to guarantee the generation of inline HTML.
 * It's a bit more than that. For people who dislike the ugly "discontinuity" of alignment between HTML and PNG, and find it personally disruptive, solving this problem would still these people to choose "always HTML" and so give up inline PNG images altogether. But why should they have to do that?

The guidelines sound alright. I still believe that for relatively simple things, it's best to leave in HTML as we've always done. I'm talking about the greek letter "&pi;", for instance. Or, single variables, like "x" or "y". Nothing gets me more than seeing a variables that stands out nearly TWICE AS TALL as the text size I'm reading. For more complicated inline expressions, I have a lot more tolerance and understanding. But, even something like Z/2Z, doesn't seem to need texifying. Of course, I'm sure I draw the line much farther than most other people.

Revolver 19:50, 6 Aug 2004 (UTC)


 * Here is where you and I disagree--I think anything related to math should be TeXified, so as to indicate that the information being marked up is math and not prose. I've already outlined my reasons for preferring this, so I'll have to accept that we will differ on this point.  But remember that with inline HTML generation, the user should not see any drastic difference between &amp;pi; (&pi;) and $$\pi$$ ($$\pi$$).  The only real difference to the user will be that they can change the look of the second one on the fly with a single change to their preferences.  --Ardonik 20:48, 2004 Aug 6 (UTC)
 * Your assertion is just not true. Obviously, you have never attempted to do this on IE personally, or you wouldn't claim this. Here's the problem: too many math expressions are not changeable (or won't change) to HTML. So, even after changing preferences, the user is STILL bombarded with a ton of inline math expressions, esp. at articles like curve and a lot of the category and algebraic topology articles. These things can't be changed to HTML, and given that there will always be a wide variability in the size people choose for their fonts, someone will be left looking at disruptive text. Revolver 17:45, 24 Aug 2004 (UTC)

Crazy idea
This may seem like a crazy idea, but it would be something I would be willing to contribute time toward. There is a company which makes a semantic interface onto LaTeX (Scientific Works), which you can enter into directly (not WYSIWYG, but logical interface). It takes very little time to enter stuff, about as fast as using a word processor. Then, there is a viewer that comes with it which is free for anyone to download on the internet. So, once you make a file, you just direct someone to download the viewer and view the file with the viewer. There is absolutely no TeX code involved at all.

While this is clearly not workable for the wiki pages that people work on, it might be possible to do periodically for some of the more important math and technical pages, I'm thinking of Wikipedia 1.0 in particular and its updates. The number of articles here wouldn't be too much, it would be much better visually, and both the wiki-HTML-PNG version as well as the Works version could be available for people to choose.

Otherwise, I'm just starting to think, while the CD-ROM viewers of 1.0 will have the option of which way to see it, the people reading the paper version will not.

Revolver 20:10, 6 Aug 2004 (UTC)


 * The best way to integrate any document-viewing plugin is with XHTML's tag; say, something like

 alternative text (i.e. inline HTML for the proof)


 * sort of like an "applet" for math pages.
 * Yet I would still prefer the current system of integrated LaTeX to this--the user doesn't have to know that we're using a LaTeX back-end, and we can swap it out with something more effective (read: MathML) at any time. It's definitely not as easy to use as a WYSIWYG editor, though.
 * Ardonik 20:57, 2004 Aug 6 (UTC)

My own two cents: In principal, I completely agree with the idea of writing all math code in TeX. That being said, I must object to actually doing this at present. I personally think that all inline TeX&mdash;whether rendered as HTML or PNG's&mdash;looks terrible. More than once I've avoiding reading a math article (let alone bothering to edit it) simply because I don't want to get a headache trying to wade through the changes in font sizes. In principal, the TeX->HTML shouldn't look bad, but it does. Yes, I know this can be fixed by a simple change to the wiki CSS file, but no one seems to be doing this. In the meantime, I'd much rather have a article that I can read rather than one which is semantically "correct".

Point 2: I think the real push should not be towards getting everyone to TeXify everything, but rather towards getting the wiki developers to implement MathML output. I believe that MathML is a viable solution now! Not some distant future. MathML looks reasonable in Mozilla browsers and plugins are available for other 'less competent browsers'. If you ask yourself why there isn't better browser support for MathML, the answer is pretty obvious: there just isn't much demand for it. What's needed is a site like Wikipedia, with its large quantity and quality of math content, to start outputing things in MathML to increase demand. Who should we be talking to, to push this matter?

In the meantime, I will continue to use pure HTML for everything inline simply so I can read it. I will starting inputing TeX as soon as wiki starts outputing MathML. As to having to rewrite all the articles when this happens, I don't think it's such a big deal. It's not like it has to be done all at once. Articles are getting edited all the time, they can be converted piece by piece. And until they are, it's not like they're going to be unreadable.

Fropuff 04:08, 2004 Aug 8 (UTC)


 * For changes to the CSS file you could do a request at the wikitech-l mailing list . I suspect that if you make clear that this is a common complaint in the math community there will be a quick response. I'm not really an expert on CSS matters, so I cannot do this myself. As far as real support of MathML goes, see the discussion on this in this newsgroup last week (in August 2004) with subject "Status of MathML support". -- Jan Hidders 09:51, 8 Aug 2004 (UTC)


 * Fropuff, you think that neither TeX's PNG rendering NOR its inline HTML look good? Honestly, is the serif font on your browser that ugly?
 * I've performed an experiment in the interest of furthering this conversation. I have just TeXified the entirety of the determinant article, trying as much as I could to keep inline statements from rendering as PNGs.  I will disclose now that in four areas, I failed to accomplish this task, though not for lack of trying:
 * The \approx symbol in TeX apparently forces PNG output, in spite of the existence of the &amp;asymp; entity in HTML. I could not find a suitable replacement for this.
 * I was unable to specify a bold font for the "R" characters in $$\textbf{R}^n$$ without generating PNGs. From the documentation I read today, it seems that the command to do this is \textbf, but it apparently has the same effect as \mathbf in the MediaWiki.
 * The correct way to prevent $$|A|$$ from looking spaced out is to use the \left and \right commands, but for reasons unknown to me, $$\left| A \right|$$ displays as a PNG: $$\left| A \right|$$.
 * I couldn't find an inline sqrt or a square root symbol. Using \sqrt{} guarantees PNG output.
 * Anyway, here are links to the old version and the current version. Compare the way they look.  Except for the places I mentioned above, how similar are the two articles?  Do those of you who dislike TeX's HTML output still dislike the text that you see?
 * It took me several hours of browsing through manuals and latex files to fully TeXify the article (I'm still learning TeX, too), but if any of you feel that I've mangled it or inserted something contrary to fact, please revert my changes.
 * Ardonik 11:33, Aug 8, 2004 (UTC)


 * Determinant is somewhat messed up. The first two expression render differently of the last two... IMO major, i.e. long, expressions should (be allowed to) render as PNG and be placed in a new line, for clarity; there should be no "tricks" when writing so that it is easy to edit and convert to some later format; expressions and/or single letters/symbols inline with text should be  also, although uglyer it is more clear.--Nabla 12:40, 2004 Aug 8 (UTC)

I honestly think the old version of the determinant article looks far better. If there isn't a whole lot of inline TeX, the effect isn't too bad, but take a different example with a higher density: compare the current version of Representable functor to the last unTeXified version. Again, I think the old version is far more readable.

"Honestly, is it the serif font on your browser that's ugly?" No, I actually approve of the serif font. It's the size that bothers me. PNG's are too large, the text of the TeX/HTML is too small (hard to read in fact). When the two are used side by side its just a mess. I know this may sound nitpicky, but I honestly get a headache trying to read that stuff.

Fropuff 14:26, 2004 Aug 8 (UTC)


 * I agree with Fropuff that the inline PNGs are very ugly and with Ardonik that it would be preferable to use tags to deliminate maths expressions. The discussion that Jan pointed to shows that we will probably not have MathML output in the near future. The only satisfactory resolution, as far as I can see. is to improve the translation of  environments to HTML, so that for instance $$|A|$$ automatically renders as |A|. -- Jitse Niesen 18:19, 8 Aug 2004 (UTC)

Is it just me, or do the HTML sup constructs show up really low? Compare x2 to $$x^2$$. This makes articles that contain many superscripts very hard to read because the superscripts are hard to distinguish from regular text. TeX/HTML renders the superscripts much better in my opinion. Gadykozma 14:14, 27 Aug 2004 (UTC)
 * The both 2's look to be at the same height for me - the bottem of each "2" just below the top of the "x". Paul August 16:33, Aug 27, 2004 (UTC)
 * The TeX version looks awful -- the x of x^2 protrudes far below the "baseline" of text. The HTML version is balanced in height and more readable. Revolver 09:00, 31 Aug 2004 (UTC)
 * Maybe it was a linux problem, or the specific version of Mozilla/Galeon I usually use. Now I'm on windows and both look fine. Gadykozma 18:59, 1 Sep 2004 (UTC)

A clarification
A Clarification -- one more reason I prefer HTML. Besides lots of things not being able to render in HTML, there is another big problem. Many people urge me to change my preferences. But then a lot of expressions I wish were KEPT in TeX get changed to HTML when I don't want them to!! This happens for example at the article pi. Long, single-line expressions get chopped up and rendered often in a silly manner. Besides, for single-line, I WANT TeX. Why should I be force to give it up?? Revolver 09:04, 31 Aug 2004 (UTC)


 * Good point. The preference "HTML if possible or else PNG" renders fractions as HTML, which looks terrible (at least in my browser). A possible solution is to change the software so that all single-line expressions are rendered as PNG, even if they could be rendered as HTML. With single-line expressions, I mean lines that contain only a $$...$$ construct, and possibly white space. I do not know how feasible this is technically. What do people think of this idea? -- Jitse Niesen 10:22, 31 Aug 2004 (UTC)

Its strange nobody seems to have mentioned the project for a paper version of wikipedia, Paper Wikipedia. This seems very relevant to the question whether LaTeX or html markup is to be preferred. Gadykozma 18:23, 5 Sep 2004 (UTC)

Editing the articles on set theory.
Although I've been editing for about a month, I've just discovered this page.

I've been doing more and more edits to the articles on set theory, and I'm contemplating rewriting the article Set. I posted some discussion concerning my proposed changes at Talk:set and Talk:naive set theory but so far no one has responded. Perhaps no one is watching these pages, or has nothing to say regarding my posts ;-) However, at the risk of being accused of not being bold, I'm reposting them here, just in case anyone cares. If not I will go on blissfully editing to my hearts content - until someone objects.


 * (The following comments and proposal is now pretty much moot, as I've made the changes I proposed below. Paul August 21:00, Aug 27, 2004 (UTC))

''I think there is too much overlap between the articles Set and Naive set theory.

''In reviewing the change history for Set, I find that the earliest versions of this article (can anyone tell me how to find the original version, the earliest I can find is as of 08:46, Sep 30, 2001) contained the following language prominently placed in the opening paragraph:

''"For a discussion of the properties and axioms concerning the construction of sets, see Basic Set Theory and Set theory. Here we give only a brief overview of the concept." (The articles referred to have since been renamed as Naive set theory and Axiomatic set theory resp.)

''As subsequent editors, added new information to the beginning of the article, the placement of this "brief overview" language, gradually moved further into the article, until now it is "buried" as the last sentence of the "Definitions of sets" section. Consequently I suspect that some new editors are unaware that some of the material being added to this article is already in, or should be added to Naive set theory or even Axiomatic set theory (e.g. Well foundedness? Hypersets?).

''If it is agreed that, Set is supposed to be a "brief overview" of the idea of a set, while Naive set theory and Axiomatic set theory give more detail, I propose two things:


 * 1) ''Add something like: "This article gives only a brief overview of sets, for a more detailed discussion see Naive set theory and Axiomatic set theory." to the opening section of the article Set.
 * 2) ''Move much of what is in the article Set to Naive set theory or Axiomatic set theory.

''Comments?

''Paul August 20:23, Aug 16, 2004 (UTC)

''I have moved the sections on "Well-foundedness" and "Hypersets" to Axiomatic set theory, which I think is a more appropriate place for them - based on the idea expressed above that the Set article shold be a "brief overview". Paul August 07:34, Aug 18, 2004 (UTC)

I should have added a third item to my proposal:

3. Rewrite the remaining parts of Set in a more elementary style. (The idea being that Set would be at the elementary/high school level, Naive set theory would be at a high school/college level and Axiomatic set theory at a college/graduate school level)

If you want to look at a first draft of a rewrite of Set, see: Paul August/Set.
 * I've now completed my rewrite of set Paul August 21:00, Aug 27, 2004 (UTC)

lastly, a couple of questions about notation. Why is "{}" preferred over &empty; for the empty set? "{}" looks kinda ugly to my jaundiced eye. Also is A\B preferred over A - B for set theoretic difference?

Actually I've got lots more questions, (especially about markup - are there any standards?) but that's enough for now. If this is not really the right place for all this, then my apologies. Paul August 03:47, Aug 19, 2004 (UTC)


 * Have at it. Your changes sound good to me. I think &empty; is far more common than {}. I've always preferred A - B to A \ B, but the latter seems more common and is used (presently) in the article Complement (set theory) &mdash; Fropuff 05:03, 2004 Aug 19 (UTC)

(Note: I've taken the liberty of moving the disccussion on  "{}" versus &empty; which used follow here to the following new section below.  Hope that's koser ;-) Paul August 18:14, Aug 24, 2004 (UTC))

A friend of mine recently pointed out to me another article that should be considered in a revision of our set theory coverage: Language of set theory. It's a poor article currently, but you might be able to take it somewhere. I was thinking perhaps that it should highlight how other mathematics can be built using set theoretic language (for example, how relations, functions, and ordered pairs are expressed as sets.) Isomorphic 18:05, 19 Aug 2004 (UTC)
 * Yes this article needs some help. I'll see what I can do. Paul August 21:00, Aug 27, 2004 (UTC)

Notation for the empty set: "{}" vs. &empty;
(Note: I've taken the liberty of moving the disccussion on "{}" versus &empty; from the previous section to here.  Paul August 18:14, Aug 24, 2004 (UTC))

Why is "{}" preferred over &empty; for the empty set? "{}" looks kinda ugly to my jaundiced eye. Paul August 03:47, Aug 19, 2004 (UTC)
 * … I think &empty; is far more common than {}. Fropuff 05:03, 2004 Aug 19 (UTC)


 * The reason that some prefer {} over &empty; is that many popular browsers such as explorer and konqueror cannot display &empty;. -- Jan Hidders 08:46, 19 Aug 2004 (UTC)


 * hmmm all my browsers Safari, OmniWeb, IE (all on Mac OSX) display it fine. Paul August 12:29, Aug 19, 2004 (UTC)


 * My IE under Windows XP doesn't and neither does Konqueror (on Mandrake Linux). For the record: IMO we should use &empty; anway. In fact, I think that if looks are important there is no problem as long as there is a free, open source browser that can be easily installed on several platforms, is standards-compliant and displays the article as it is suppposed to look. But that's just me. :-) -- Jan Hidders 13:06, 19 Aug 2004 (UTC)

Based on the above It looks like there might be an emerging consensus that &empty is better than {}. any objections? I wouldn't mind going around and changing {} to &empty. But it's a little work, and I don't want to do it if anyone is just going to change them all back. Paul August 20:17, Aug 22, 2004 (UTC)


 * You have my vote. But we/you should probably first try to formulate a policy on the project page. That gives you something to point to when watchers of articles who didn't follow this discussion start complaining. Formulating such a policy and trying to make it sound sensible is IMHO a good sanity check to see if this change is ad-hoc or can be fitted in the broader picture. -- Jan Hidders 21:46, 23 Aug 2004 (UTC)


 * Jan makes a good point. I've frequently included HTML entities for various symbols in my posts, and sooner or later someone will come along and change them because they don't display in browser X (almost always IE). A few of the named entities that won't display in IE (with default fonts on my Windows 2000 system) include
 * &amp;empty; (&empty;), &amp;notin; (&notin;), &amp;lowast; (&lowast;), &amp;otimes; (&otimes;), &amp;lang; (&lang;), &amp;rang; (&rang;), and &amp;alefsym; (&alefsym;)
 * The unnamed symbols that I most frequent want are U+210F (&#x210F;) and U+21A6 (&#x21A6;). These I've avoided using altogether as I think support for them is probably worse (although they both dispaly fine in my default browser). My personal vote is to say anything in Unicode is fair game (it's valid HTML after all), but I may be in a small camp on this one. -- Fropuff 23:04, 2004 Aug 23 (UTC)


 * It's very annoying that on some browers I use (I use multiple computers and multiple browsers) many of the set theory articles or just articles with lots of HTML set theory notation are completely unintelligible, because they read as "A (BOX) (B (BOX) C) = (A (BOX) B) (BOX) (A (BOX C)), unless A = (BOX) or B = (BOX).", or worse "(BOX) (BOX) A = A if and only if A = (BOX)". With many of these, I don't even bother to read them, I just leave. I suspect lots of other readers do as well. Revolver 17:29, 24 Aug 2004 (UTC)
 * Having said this, there are some symbols that are impossible to render HTML (intersection?) and so I often end up using it anyway. Revolver
 * So Revolver, does this mean you prefer we stick to using "{}"? Paul August 18:14, Aug 24, 2004 (UTC)
 * For now, yes. It's not as good as < >, but it's better than << (BOX) >>. Revolver 07:32, 26 Aug 2004 (UTC)
 * I'd say it is better to use the TeX version ($$\varnothing$$) than {}. This is, at least, both standard notation and universally visible, if somewhat ugly when set inline with normal text. -- Fropuff 21:48, 2004 Aug 27 (UTC)
 * Well I also like $$\varnothing$$ better than {}, just about anything would be. Should this be the preferred way?  Paul August 23:56, Aug 27, 2004 (UTC)

I make a very strong vote against &amp;empty;. Why? Almost all our readers use IE, which doesn't support it! I like $$\varnothing$$, because the software can render it according to user preferences and HTTP browser information, which is the best solution for everyone (if it doesn't do this now, at least the potential is there). Derrick Coetzee 01:39, 28 Aug 2004 (UTC)


 * Agreed. I'm only wondering if there is a difference for you between $$\varnothing$$ ( $$\varnothing$$ ) and $$\emptyset$$ ( $$\emptyset$$ ). On my Mozilla (under the pref. "HTML when possible" for math) the latter renders better. -- Jan Hidders 01:56, 28 Aug 2004 (UTC)
 * The same difference there is between $$\epsilon\!\,$$ and $$\varepsilon$$, between $$\phi$$ and $$\varphi$$ and between $$\sigma$$ and $$\varsigma$$. &mdash; Miguel 23:21, 2004 Dec 3 (UTC)
 * Oh, yikes, Firefox's math HTML rendering is inconsistent with TeX! &mdash; Miguel


 * Depend's on what you're preferences are. When they both render as PNG's I like the \varnothing one better. But certain preferences will convert \emptyset to the HTML &amp;empty;. So maybe that's the better one to use. -- Fropuff 02:17, 2004 Aug 28 (UTC)


 * For me, under Safari for any math rendering preference setting:
 * &empty; (&empty) looks like a circle with slash - my preference
 * $$\varnothing$$ ( $$\varnothing$$ ) looks like a circle with a slash- a little bigger circle, slightly more horizontal slash - my second preference.


 * With either "recommended for modern browser" (not sure what this pref means exactly) or "Always render PNG", then
 * $$\emptyset$$ ( $$\emptyset$$ ) looks like a rather ugly oval taller than wide with slash. - don't like this one much, but better than "{}"


 * While with "HTML if possible or else PNG"
 * $$\emptyset$$ ( $$\emptyset$$ ) looks the same as &empty.


 * How does IE render $$\emptyset$$ ? Paul August 04:18, Aug 28, 2004 (UTC)


 * IE, with default preferences renders both $$\emptyset$$ and $$\varnothing$$ as PNG's. The former looks like a tall, skinny oval with a slash through it, and the latter as a circle with a slash through it. -- Fropuff 04:33, 2004 Aug 28 (UTC)


 * Given all this, I vote for $$\emptyset$$, because it yields HTML where settings allow it and works in IE. It's also very common in LaTeX documents. Do we have consent? Derrick Coetzee 04:38, 28 Aug 2004 (UTC)


 * I support a $$...$$ based solution. Personally, I would prefer \varnothing over \emptyset, but if the majority style here is \emptyset, I can stick with that, too. FWIW, in my LaTeX documents I usually have a global redef in the global preamble, as in, and then use \emptyset later on. BACbKA 23:25, 3 Dec 2004 (UTC)

I think the notation {} is too confusing. We should use some variation on the slashed O sign, even if it doesn't render properly everywhere. Gadykozma 05:03, 28 Aug 2004 (UTC)

In my opinion {} or { } is better because it still has a connection to the set notation due to the braces. whereas $$\emptyset$$ is a completely new symbol and the connection with emtpy set has to learned and cannot be inferred. MathMartin 22:28, 3 Sep 2004 (UTC)


 * If by "completely new" you mean "widely used in papers for decades"... keep in mind this is the default LaTeX empty set symbol. Derrick Coetzee 23:12, 29 Oct 2004 (UTC)


 * This was my personal opinion (I should have said so). Of course we should use the symbol which is most common, if this is $$\emptyset$$ so be it. MathMartin 21:41, 22 Nov 2004 (UTC)

I would say that {} is the empty set, while $$\emptyset$$ is a symbol for it. Which notation to use should depend on the context. &mdash; Miguel 18:01, 2004 Nov 26 (UTC)

Out of curiousity could you provide an example where it is better to use $$\emptyset$$ than {} ? MathMartin 22:00, 3 Dec 2004 (UTC)


 * Sure: $$\{\emptyset\}$$ is more readable than $$\{\{\}\}$$. &mdash; Miguel 23:06, 2004 Dec 3 (UTC)

Avoid notational conventions! Sometimes "{}" works better, sometimes "&empty;" works better; sometimes TeXvc works better, sometimes it doesn't. There are special circumstances; if a common browser cannot render a version, then it's justified to warn writers against that version. Still, the only basis for debate in that case is to determine whether the special circumstance obtains, and the only conclusion to draw is that the number of options is lowered by one. Of course, people that are interested in æsthetics are free to discuss their personal preferences as much as they like; I have my own opinion on this matter, which I'd be happy to chat about on my talk page or even by email. But Wikipedia does not need a standard for every notational debate. -- Toby Bartels 23:55, 3 Dec 2004 (UTC)

&cup; symbol displays as box?
Someone edited the set article, changing each set union symbol "&cup;" (i.e &cup) to an uppercase U, because they were displaying as boxes. Is there a problem with rendering &cup;? It looks ok for me (Safari, IE, OmniWeb on MAC OSX). Does anybody else have problems with this? Paul August 19:48, Aug 31, 2004 (UTC)


 * The right thing to do if your browser does not display "& cup ;" is to use $$\cup$$, never to replace it with "U". &mdash; Miguel 23:41, 2004 Dec 3 (UTC)

Schaun MacPherson
At User_talk:ShaunMacPherson, I have invited that person to discuss on this page his implicit decision to move hundreds of articles titled ABCD's theorem to ABCD's Theorem with a capital T, and similarly for conjectures, lemmas, axioms, etc. In case anyone can be more effective in persuading him that I can, I mention that here. (If you are Schaun MacPherson and do not wish to pursue the matter, please feel free to delete this section.) Michael Hardy 20:40, 31 Aug 2004 (UTC)


 * Personally, I don't think the word theorem, lemma etc. should be capitalized in this context. But it's a minority view. A number of editors threw out my preferences and capitalized them. Gadykozma 23:51, 3 Sep 2004 (UTC)