Wikipedia talk:WikiProject Mathematics/Archive/2003

Two suggestions: add paragraphs for

• historical info (different historical views, famous contributors, postulates, scientific debate) and
• fields of application

Maybe defer lengthy proofs to the bottom of the page (or a subpage) ? Many readers wil take these for granted, those who want the whole story are willing to scroll forward. Erik Zachte 00:25 Nov 18, 2002 (UTC)

This WikiProject is well thought-out and appears to be consistent with current Wikipedia standards and conventions. In addition to Axel, Pierre, Toby and myself you should also request comment form JakeVortex, tarquin, User:Zundark, User:Gareth Owen, User:Forgottenvector, User:Valhalla, User:Alodyne, User:Steverapaport, User:Jkominek, User:Josh Grosse, User:Archibald Fitzchesterfield, User:Chuck Smith, User:Ram-Man, User:Andre Engels, User:Jheijmans, User:N8chz, and User:Kidburla2002. Also a link to this WikiProject page from the mathematics section of Wikipedia:Wikipedians by fields of interest would be great. --mav 00:46, November 18, 2002 (UTC)

I don't think that it's at all a good idea to try to fine-tune the appearance of HTML constructions on the screen, as with the "double sups to make the limit of integration higher". The reason is that the effect depends heavily on the particular characteristics of the reader's system.

In my case, putting in the double sups made the limit too high, too far from the integral sign (a problem already since HTML doesn't support multiscripts) and way too small. On Chas' system, it was presumably an improvement. Since we can't predict it ahead of time, we should stick with simplicity: one sup. (I take it back if one sup is for some reason illegible on Chas' system. That's a different matter.) — Toby 07:43 Dec 1, 2002 (UTC)

I concur; the double <sup> looks better (IE6, Win98/Win2K), but the single sup is still readable (although just at the edge of confusion for me). The Summation notation is much more bothersome:

∑_{i = 2}ⁿ x

reads ambiguously - is that 2ⁿ? or n_x? i = 2 to n? The alternative, although somewhat non standard, is at least unambiguous (although a bit computer-y). Oh when we will we have our LaTex to HTML conversion (he wailed)? Chas zzz brown 21:28 Dec 1, 2002 (UTC)

For sums in HTML, I prefer nowadays ∑_2≤i≤n x. But I guess the topic is mood now. AxelBoldt 00:00 Jan 8, 2003 (UTC)

We should probably update our style guide for the new TeX feature. One rule that I would like to see there is this: TeX formulas should not be used inline: "Let ${\displaystyle x\in \mathbb {R} }$  be a real number". Because of the size issues, it looks bad, uses unnecessary bandwidth and makes it harder for non-graphical browsers. Similarly, don't use fancy fonts like fraktur ${\displaystyle {\mathfrak {a}}}$  if it can be avoided, so that HTML can continue to be used for all inline formulas. AxelBoldt 00:00 Jan 8, 2003 (UTC)

I concur with the inline comment; it makes it harder (in my opinion) to follow an argument when the font keeps changing. Chas zzz brown 08:50 Jan 8, 2003 (UTC)

I'll start to edit the main page to this effect a bit; feel free to jump in if anything is controversial. AxelBoldt 18:40 Jan 8, 2003 (UTC)

Note on vectors: my textbooks tend to have \mathbf{v}_1 rather than \mathbf{v_1}. (it seems obvious but it got me wondering). One for the style guide here, maybe? -- Tarquin 10:31 Jan 18, 2003 (UTC)

I noticed that we no longer say to leave the differential d unitalicised. I guess that we don't really need an official style, but I'd like to go on the record as saying that I always found texts that didn't italicise it (chiefly from Brits IME) easier to read. -- Toby 09:53 May 3, 2003 (UTC)

The pages for Cyclic group and Klein four-group use the notation C_n to denote the cyclic group on n elements. This seems strange to me; I've never seen this notation elsewhere. The notation I'm familiar with is to use Z_n. Has there been some agreement to use C_n? Dominus 06:29 22 Jun 2003 (UTC)

It's known in Cambridge, perhaps unknown in 99% of the mathematical world. Obviously it is supposed to stop some abuse of notation problems, as in assuming groups are rings, that there is a preferred generator 1, and so on. Charles Matthews 11:44 22 Jun 2003 (UTC)

The following Copied from Village Pump by Theresa knott|Theresa knott 10:59, June 25, 2003 (UTC)

(Start of copied text)

Well, Im obviously not getting along with the mathematicians here; but, I think the "professional" mathematicians are so intent on outdoing each other with their rigorous mathematics that they fail to understand that the non-mathematician is the one who most needs this site, and nearly ALL of the math pages (even on some of the most "simple" and elementary of topics) are nigh-impossible for anyone without the proper training to understand. Kinda a Catch-22 if you see what Im saying.

Its not that I have a problem with rigorous mathematical definitions and proofs, but we also need to have stuff that is "un-professional" "idiotic" "silly", and the like, and of course (most important perhaps), we need "childish" articles on these topics. To be honest, I don't know (and right now I don't care to know) what real, general, and complex functions are. All I know is that every one of my calculus books talks about stuff which either isn't discussed on the wikipedia (or isn't discussed in language which the beginning calculus student is expected to understand).

Now Ill admit, Im not a mathematician. I don't want to be a mathematician. I don't even like math. I don't even understand why math is worth learning. But I do understand that, right now, the wikipedia is about the last place I would go to if I wanted to learn about a mathematical topic. Its not because the wikipedia is inaccurate; but, because the wikipedia seems determidly hostile (in such areas as mathematics) to expressing things "as if a moron had written it"

What Im trying to explain is, a lot of what Im doing in the math section is, to some degree or other, not correct. A lot of it is correct. But some of it definitely isn't. Unfortunately, I have been, more or less, attacked by certain users who remind me of the young John Forbes Nash, with their elitist attitudes, snobbery, and insulting degradation of others. One user actually had the gall to state that he was too busy with his real job, as a real mathematician, to read my crap anymore. He wasn't just referring to my various misconceptions, he was also referring to my inclusion of material which he felt was redundant, redundant to him of course, since he is a "real mathematician".

Let be clear, this wikipedia thing is a lot of work. But the wikipedia isn't going to get better simply by having a bunch of PhDs stroking their phallic egos. What the wiki really needs is a bunch of "ignoramuses" running amuck, trying to learn what the wiki is saying, trying to add to the article with their (frequently incorrect) newfound understandings, and most importantly, BEING CONSTRUCTIVELY CRITIQUED ON THEIR EDITS.

There is a substantial difference between what the wiki claims to be, and what it is. The wiki urges me to "be bold in editing" but the overwhelming response I have gotten, albeit from a handful of more boisterous editors, is a statement of "Get the hell out of here."

Indeed, I have thought about leaving, but I do see some great potential for good here at the wiki, and I do want to improve this site. So I am simply taking a moment to stand up and ask the Wikipedia what it thinks, does it really think that its appropriate to call people stupid because they don't capitalize something (or because they do) or because they forget a comma, or because they get somewhat confused regarding the implicit differentiation of inverse trigonometric functions?

I have made several new friends since I arrived at the wiki this spring; however, I have also met several people who are not friendly. I would like to know what it is that has turned them so sour.

Pizza Puzzle 23:48 24 Jun 2003 (UTC)

Agree, completely agree. The problem is that mathematicians are trained to do things rigorously, and they have to do it that way in order to protect the "correctness" of mathematics. Some may become intolerant to "misconceptions" from non-mathematicians, but I believe most of them are still friendly. Professional mathematicians (not just wikipedian mathematicians) need intakes from non-mathematians (like you, PP) to improve their way of introducing mathematics to general publics. -- Wshun

It should never be acceptable to call anybody "stupid" if they make a mistake; that is attacking the person, not the act. (If I were in charge, all ad hominem remarks would be grounds for banning.) However, we still need to be merciless about bad edits, and if you get constructive criticism, be appreciative, but don't expect it. If you don't know about something, don't put it in. If you're not sure, put it in italics or in the talk page. There are articles that are very good, and unless you understand the content very well, you're more likely to make the article worse rather than better. I have some math background; I can take a look. Stan 04:46 25 Jun 2003 (UTC)

I think I'm the guy that Pizza Puzzle is so annoyed at. And I can assure you I never called him `stupid'. The disputed page was calculus with polynomials and I suggest that anyone following this discussion go check out the history of that page, its associated talk page talk:calculus with polynomials, and pizza puzzles talk page User talk:Pizza Puzzle2 too. From my point of view, I found the page in a very sad state - lots of errors and mistakes - off topic - repetitious - inconsistent notation - strange headings -poorly organised - glaring omissions - all sorts of weird stuff. It looked to me like a page in serious need of a bit of fixing up. So I fixed it up, which is what you are supposed to do yes? Nothing personal in it. I never even paid attention to who had written the thing in the first place, in fact it looked to me like a page that lots of people had dabbled in without paying much attention to what they were doing. It was actually fun to find a maths page that needed something doing to it, since most of them seem to be quite complete.

Anyway I then get a number of notes from pizza puzzle seeming rather put out and asking me to explain what I had done. Which I then did on User talk:Pizza Puzzle2. Subsequently I find that over a period of several days all of the errors and strange stuff that I had weeded out had been reintroduced into the page, plus a bunch of other new errors and oddities so that the page is actually in a much worse state than when I'd first found it. Which was just about enough to make me conclude that wikipedia is a total waste of time™. But I thought I'd give it ONE MORE TRY. So I fix the page back up again (note that I did not simply revert, but considered each part of the article on its merits), and on the associated talk page I explain in detail my reasons for each change (once again) in the hope that this will finally dissuade pizza puzzle from reintroducing them (once again). And yes I was probably a touch short with the guy, mostly because I'd already done all of this - including the explanations - once again. It isn't that I think my prose is so deathless that I can't bear to see anyone tinkering with it. Actually I'm sure the page can still be greatly improved. But to see actual ERRORS reintroduced for no good reason ... well it is more than any sane mathematician should be expected to bear.

user:Hawthorn, please sign your entries with ~~~~

Normally I side with anyone who accuses mathematicians of arrogantly writing stuff which no-one else can understand. However in this case, I find Hawthorn's version makes more sense than Mr. Puzzle's. If PP wants to "add to the article with [his] (frequently incorrect) newfound understandings", he should expect expect to irritate mathematicians. I would advise you both to calm down and deal with the matter rationally. Don't take it as a personal insult when someone reverts your work. You'll have a more constructive debate if you talk for a while before re-reverting. See Wikipedia:Staying cool when the editing gets hot. -- Tim Starling 06:18 25 Jun 2003 (UTC)

(End of copied text)

First let me say where I am coming from. I am reasonably good at maths, though I was taught it by physicists not mathematicians, so I think that I can give some insight. I have to say, PP does have a valid point {though s/he should not get so emotional about it}. I find many of the math's pages somewhat dry, and difficult. I think that on the whole they are too short, have too few examples, and are too formal. I would like to see some verbose text generally talking about the basic principles before a formal definition and proofs. That way the reader can get a feel for the idea before delving in. I am also somewhat worried by notation. I think that some peole are going to be be put off pages if they are unfamiler with notation. Theresa knott 10:59 25 Jun 2003 (UTC)

I remember the set theory edit wars, which ended up with two articles, naive set theory and axiomatic set theory. We could probably do the same thing for other topics, for example having an introduction to XXX article for topic XXX which started with a non-rigorous introduction designed to help beginners to understand the ideas and motivation for the rigorous article on the topic. For example, several of the calculus articles contain non-rigorous treatments which are then followed with rigorous treatments later.

However, there will always be fields of mathematics which are downright baffling for the uninitiated (including, often, other mathematicians who do not specialize in those topics).

Looking forward to reading introduction to topos theory, The Anome 11:14 25 Jun 2003 (UTC) (who has studied some mathematics, but is not a mathematician)

I may just take you up on that ... Charles Matthews 12:23 26 Jun 2003 (UTC)

I have great sympathy for those who want 'verbose'. I want it, too, in relation with any advanced topic which I'm not familiar with. There is always a problem with dense texts in mathematics. That being said, there is no single answer: correct statements aren't actually improved by being made looser and less accurate. I've not been here long, but I can see that there are various 'modes' I have used: historical/genetic, examples, informal talk. I find excess emphasis on the category theory point of view to be unhelpful; but it is also clarifying in its way.

Put it this way, perhaps. The more 'pure' attitudes can sometimes be criticised for failure of NPOV. I wrote about that at multilinear algebra and Nicolas Bourbaki. So, let's do that criticism in a practical way, by editing in the other stuff. I don't think implications of snobbery help. I do think that the wiki way is about things other than de facto standards of definition, which is always a contentious area (cf. tensor).

By the way, I'm a published mathematician - but not recently.

Charles Matthews 11:22 25 Jun 2003 (UTC)

Let's put it this way: I have a tenuous grasp of category theory and am completely lost when it comes to topos theory. Now I think back to myself at age 13, just learning about things like calculus. Just as I needed a way in then, I need a way in for these other topics. It would be useful for many articles to have a header saying (for example, for integral):

Having difficulty understanding this article? Then you might want to learn more about algebra, functions and the theory of limits first.

Do this to enough articles, and we will have a mathematics road map for self-study. The Anome

This is a really cool idea. It would help prevent reiteration of all the prerequisite knowledge in specialized articles, and provide a nice path towards learning difficult stuff. Something like this may even be useful for non-mathematical subjects as well -- certainly the other science articles (physics, chemistry, biology, etc.) would benefit from it, but it could even be applied to articles on history, politics, psychology, or anything else where a foundation of terminology and concepts is necessary in understanding the more complex ideas presented in specialized parts of those subjects. At the very least, some form of "Introduction to terminology" or "Glossary of notations" and the like would be helpful. -- Wapcaplet 12:26 25 Jun 2003 (UTC)

I don't like the idea of putting the "difficulty" notice on articles, though until Wikibooks gets fully on its feet it may be useful. I don't think this idea meshes well with the encyclopedic concept of the Wikipedia. Dysprosia 05:27, 7 Oct 2003 (UTC)

Oh and one more thing.

WRONG: Articles that go "Let there be objects X such that (introduce new notation here without explanation). Then (notation) (notation) (notation) (notation)."

RIGHT: "(Mathematician) invented the concept of X in 18xx to represent (squeezy-pully-twisty things). A simple example, using modern notation is (example). (Explain notation). The idea has now been generalized to (stuff), which has uses in (other fields of math and science). The idea of X can be formalized as follows: let there be objects X such that (notation). Then (notation) (notation) (notation)..."

Not naming any articles in particular. ;-)

The Anome 11:50 25 Jun 2003 (UTC)

Applause! As a maths-untrained person with a yen to learn a little bit about this area from time to time, that is exactly what I would like to see! More strength to your pen, Anome. Tannin

Well, mathematical duckspeak is never going to be awesome teaching. Used between pros it has a high bandwidth; and isn't really so different from other tech-talk. Point is, it's never going to be brilliant prose.Charles Matthews 11:57 25 Jun 2003 (UTC)

That's why it is so important to have an english {as opposed to notation}intor. The Anome 's page layout looks perfect to me. Theresa knott 12:07 25 Jun 2003 (UTC)

I have merged these changes into the suggested structure in the main project. The Anome 12:54 25 Jun 2003 (UTC)

The point is, the quickest and best way to stop somebody from reinserting material which you think is totally wrong, is not merely to state that its wrong, but to give some sort of explanation why its wrong. Most incorrect material can, in some way, be incorporated; as most of it is not only at least an attempt at expressing some correct concept; but generally the user is trying to express it because the concept is not expressed well enough within the article. In short, everytime a user edits a page and "makes it worse" that is a good clue that the article needs improvement. 209.56.25.241

Just as likely, there is a structural problem with a single article, or group of articles. Some comments are like weeds in flowerbeds: they're just in the wrong place. Why should everyone agree on what is relevant? One person's helpful aside is another person's red herring. Organisation of the material can definitely help. Charles Matthews 15:18 25 Jun 2003 (UTC)

Can all these people who are agreeing with Pizza Puzzle please read his revision? It really wasn't more understandable to non-mathematicians. By all means, make mathematics accessible, but don't make it nonsense. I've campaigned in the past for comprehensible maths (see Talk:Tensor product) but I'm not campaigning now. -- Tim Starling 05:39 26 Jun 2003 (UTC)

As one of the people who agreed with him, I have to say- Yes his version was bad. Yes the new version was better. BUT he still makes a valid point. Maths pages need to be accessible to non mathematicians. Theresa knott 08:37 26 Jun 2003 (UTC)

Just wanted to add some general support for comprehensible maths, though I've not been personally involved with any of Pizza Puzzle's edits. Martin 21:46 26 Jun 2003 (UTC)

Well now, generalities are all very well. But if anyone has a general take on how hypertext (with random access) reconciles with the hierarchical way maths is built up, that would be an interesting separate discussion. I've just looked at the backlinks for calculus with polynomials, to assess who might arrive there. Only three: derivative, tangent, chain rule. All of which seem to need work, too: far from clear that there is a consistent level operating. Why no link from the calculus page? There is a 'first principles' proof on the calculus with polynomials page. Not the way I'd do it, given the product rule and induction. And so on. Charles Matthews 09:43 26 Jun 2003 (UTC)

I was totally inactive for a year but I am getting back on Wikipedia and I'm glad to see this wikiproject going. On the issue of readability and pedagogy, here's my 2 Euro cents.

Articles shouldn't be "dumbed down", because that assumes that shows disrespect for the reader by assuming they're dumb. Ignorant, maybe; unsophisticated, maybe; but not dumb. I truly believe that nobody is too dumb for mathematics, especially is they have the basic suriosity that leads them to read the wikipedia article. Now, mathematicians struggle with the same stumbling blocks as non-mathematicians, it's just that it was usually long ago, and they always make it past the stumbling block eventually. It would be helpful if, when writing about a topic, we mathematicians tried to remember what stumbling blocks we had to overcome and how we did it, and wrote about it in the article!

I have background both from mathematics and physics. Encountering most mathematical structures in physics first has the advantage that I am aware of more ways to justify to nonmathematicians why a concept is important. I have a keen interest in the history of mathematics, and I try to bring that to bear on my wikipedia contributions. However, both in mathematics and in science, I think things should be made accessible but without making wrong statements. I can't help it, but incorrect statements just make me cringe and I have to reach for the "edit this page" link. On the other hand, I have very strong feelings about the teaching of mathematics, so I genuinely try to make things understandable.

As for the layout of the pages, I tend to favour historical information near the top, not near the bottom. I agree with The Anome's proposed layout: first a short, gentle introduction, then the formal definition, then (in any order) history, examples, and formal development. In this way, the first paragraph of the page appeals to both mathematiciand and non-mathematicians.

By the way, a perfect example of what we are trying to achieve is function. That page does a pretty good job, but it is horrible on many counts. If I could put my finger on exactly what I don't like about it I'd come in and change it, but it's the result of so many people's work that I'd be wary of doing that, too.

I have created a few pages that start with an abstract definition, or contain little else. The reason is that I didn't want to stick the definition in the middle of a long, pedagogical section of another article. I believe none of these "dry" pages are linked from nontechnical pages, so I think they are not harmful. The motivation is in the longer, general pages.

I watch pages that I contribute significantly to, which means I also watch the talk pages. If someone posts a cry for help on one of the talk pages, I'll probably come to the rescue and, at the very least, add one of those having trouble with this page? Look here first! notes. Maybe I'll go in for a full rewrite.

-- Miguel 15:42, August 13, 2003 (UTC)

I had independently created a page for similiar purposes as this one, because I was not aware of this page. It has some advantages over the format of this page. For the time being, I will informally link it via this talk page: Styles of Mathematics Articles, and leave it open for discussion whether or how it could be integrated or benefited from. - Kevin Baas 19:28, August 4, 2003

(UTC)

A public domain e-text of the book "History of Modern Mathematics" has just been completed. The book was published in 1906, edited by David Eugene Smith, Columbia University. It just has 75 pages, but some of the material may still be useful and valuable. Here's a link to the PDF.—Eloquence 23:05, Aug 10, 2003 (UTC)

The beauty of mathematics is a topic that I would like to see developed on wikipedia. Maybe we can gather a commented list of the most beautiful things in mathematics, from the elementary to the abstract, as a way to communicate to the layman that mathematics is not accounting. -- Miguel 14:38, August 17, 2003 (UTC)

• The page has been listed for deletion by jimfbleak. Please see that page for justification and discussion. —Preceding unsigned comment added by Angela (talk • contribs) 17:09, August 17, 2003

Should we create a template for pages about probability distributions? I know templates exist for various types of content on Wikipedia, but I haven't found any centralised explanation on how to add one to Wikipedia. -- Miguel 15:05, August 17, 2003 (UTC)

Howdy folks. I'm working on a personal project (bits of which might make it to Wikipedia eventually), and am looking for some help with TeX. Specifically, how do I get the "model satisfies" symbol (which is like ${\displaystyle \vdash }$  but with an additional horizontal bar), and how do I get the reverse of both these two?

Thanks in advance,

Onebyone. — Preceding unsigned comment added by Onebyone (talk • contribs) 21:37, October 19, 2003 (UTC)

Hi Onebyone. You probably want ${\displaystyle \models }$  (\dashv is the TeX thing for but it doesn't seem to work here), but I don't know the reverse of the models symbol... Dysprosia 05:51, 21 Oct 2003 (UTC)

Lovely, thanks. I've actually kludged up a reverse models sign using something like {= \! \! | \>} (can't remember exactly what, it's at home), which will do me for the time being. Onebyone 10:03, 21 Oct 2003 (UTC)

Can I raise the question of whether we want iff in definitions? I don't. I think it's offputting to those not pure-mathematical 'native speakers'. And the idea that it's more rigorous is surely shallow.

Charles Matthews 16:28, 21 Oct 2003 (UTC)

In the absence of an explicitly-stated convention, I think it's marginally more rigorous than "if". I have occasionally used "if" in a definition and meant "if but not only if", although not on Wikipedia as far as I remember. I'd suggest that if "iff" is undesirable, the best replacement for the non-specialist reader is "if (and only if)", since the rigorous alternative is to ensure that "if" is never used other than to mean "iff". Onebyone 16:49, 21 Oct 2003 (UTC)

I don't accept the 'rigour' argument, anyway. Using 'if' there is an implied 'one can assert' in front of mathematical propositions - which no one writes unless in a very careful formal treatment. Those who care about this can imagine it all anyway. Better, I think, just to use normal language: 'an X is a Y with property P'. I haven't checked whether the definitions of legal terms on Wikipedia make a point of this type of care. On the whole I think it's wasted: it's hard to imagine the user who needs it. Charles Matthews 17:58, 21 Oct 2003 (UTC)

Well, I agree that the pedantry is not worthwhile if it is off-putting for readers. On the other hand, I'll take no part in any kind of global edit to deliberately introduce ambiguity, even if that ambiguity can generally be resolved from context. You say "I think this care is wasted", but I suspect that for most mathematician authors it will require extra care to remember not to do this rather than extra care to do it!

"An X is a Y with property P" sounds good to me, especially in the standout definition at the top of the article. Nobody writes articles on topics other than maths saying "a person is a saint if and only if they have been canonised by the Church" or whatever. If there's a more formal section of maths in the article, I do think that "iff" and other jargon words should be used in that section exactly as the author would use them in any mathematical writing.

Onebyone 10:35, 22 Oct 2003 (UTC)

So, my understanding is that the Project isn't trying to prescribe, but is looking for some harmonisation. Charles Matthews 19:02, 22 Oct 2003 (UTC)

Hi people. I would like to again raise the question of using mathematical markup (namely the <math> tag) versus plain HTML for mathematical content. I have read what pertains to the problem and I am still not convinced of the point of view explained in the guidelines on the main page WikiProject Mathematics. Here's mostly why.

1. Common ground
   • It seems we all agree that mathematical content should come in a different typeface from standard text, e.g. "Let a be a real number" rather than "Let a be a real number". It is my strong belief that it makes understanding math much easier.
   • The use of mathematical symbols is sometimes inevitable, and sometimes much shorter than plain text, e.g. ${\displaystyle \sum _{i=k}^{p}u_{i}}$  compared to "the sum of all elements in the sequence with indices ranging between ${\displaystyle k}$  and ${\displaystyle p}$ ". (Not to mention that the example above shows that the TeX processing is wrong: it does not treats the formula as inline.)
   • However, I fully support the opinion that the Wikipedia should try to reach the "layman" as much as possible, and that implies favoring text to formulas (with the exception of the item above).
2. Why imho the reasons against using mathematical markup fall short:
   • inline PNG looks bad because it is too big and not vertically aligned. True indeed ! it is ugly, but why stick with it ? Though I am not an expert, it seems simpler to configure ghostscript for size and centering. (Not too small for legibility purposes.)
   • mathematical markup uses unnecessary bandwidth. That seems overrated, since small png files (the ones that could be replaced by HTML text) are ... small, typically a few hundred bytes (in general much more than the text equivalent except in the example above), so one hundred of them in an entry means maybe 50Kb extra. While not negligible, this remains acceptable even for slow connections. Hence it only marginally slows download speed. However I admit that an increasing number of such files might slow down the Wiki server itself unless solutions are taken (see caching below). I'll be happy to learn more about this. Notice that steps against this overflow can be taken by choosing the HTML if possible or else PNG option, at the possible cost discussed just below. Question: shouldn't that behaviour be the default one ?
   • mathematical markup slows down the server because it has to create the png image through the complicated tex->ps->png method, or testing whether it can be converted to HTML first. Now that convinces me much more (and more or less mirrors my experience). Since it is quite true that a lot of inline formulas can be written using HTML, I believe the conversion engine could work much faster (all right ! easier said than done ;-) . If not, see suggestion HTMLmath below.
3. The argument in favor of mathematical markup is simple but stronger. Though my remarks above plead for conversion to HTML, the main reason for using mathematical markup is to obey the same principle that is behind HTML, XML, CSS, etc: separate meaning from display. By using the <math> tag, you indicate that the content is maths, no matter how you eventually display it (and that may depend who reads it too). You can always change the way it is displayed afterwards, depending on technology (maybe we'll have DSL in ten years :-), on your preferences, and so on. If in two years from now all browsers accept MathML, Wikipedia will obviously render math in MathML. What becomes then of all previously written articles ? If they contain expressions such as 'the real number ''x'' ', then they will have to be changed by hand, while 'the real number <math>x</math>' will be translated into MathML automatically and easily (even for more complicated formulas). And that's only one of the uses of the idea of separating content and display. In short, the main reason for preferring mathematical markup is to preserve the future, i.e. to build something that may last.
4. Solutions ? I do not know of course all the pros and contras of all this, but if you agree that mathematical markup has to be built in, but yields undesirable side effects (like slowing down the whole thing or displaying badly), here are suggestions.
   • Caching: (unless it is already done) if bandwidth remains an issue, why not cache the math pages, i.e. keep copies of rendered pages on another server which will (i) free the main server of outgoing flux (bandwidth problems) and computing time (conversion procedure). I then suggest a move towards the HTML if possible or else PNG choice for better display. If finding willing servers is a problem, why not ask math academic servers throughout the globe ? Many of them host mirrors of much heavier archives such as arXiv.
   • One simple thing: make a difference between inline and separate formulas (TeX users will know that). A better solution for all editors would be of course an automatic recognition of whether a math formula is inline or not (not too hard is it ?).
   • HTMLmath: a simple suggestion helping the rendering machine: add a tag (say <hmath></hmath> for instance) that caracterizes the content as mathematical but is written in plain HTML, with, whenever possible, some simple conventions: usual letters should be italicized, ^ means , etc. So that <hmath>x^2</hmath> will be displayed as the HTML <var>x</var>². That idea remains compatible with a future automatic rewriting, while speeding up the procedure for the moment.
   • At the very least, if the suggestion above seems too cumbersome, let us provide a tag that describes the content as mathematical (even without anything extra). Or replacing the <it></it> tag. I propose <mi></mi> for math italic.

I hope I have not bored you too much with such a longish article. Please excuse the newcomer's stubbornness (or maybe intransigence ?). : Pascalromon 23:12, 26 Nov 2003 (UTC)

I'd like to announce a new WikiProject, WikiProject Probability. I started this last week on my user page, and was convinced to move it to a more appropriate home amongst the WikiProjects. It is not quite a list of probability topics, but an effort to catalogue the articles on probability theory and applications, providing a guide (in the form of an annotated table of contents) for those who would like to know more about the topic. I hope such an effort would also expose any defiencies in Wikipedia's coverage of the subject. It is not intended to propose alternate formatting for probability articles. I'd appreciate any and all input from the participants in WikiProject Mathematics. Perhaps WikiProject Probability should even be a sub-project of WikiProject Mathematics?
--Ben Cairns 01:10, 8 Dec 2003 (UTC)