Wikipedia talk:Manual of Style (mathematics)

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[edit] structure

Sometimes people say that this is an encyclopedia as a reason for excluding certain information that is considered too specialised/difficult. I don't see their point. I have seen some mathematics articles that suffer from too narrow a perspective, like laplace operator, which completely ignored generalization to forms and still ignores a discription in terms of covariant derivatives so it would apply to all tensors. Also I have seen some mathematics articles which are now physicist territory, like Noether's theorem and Lagrangian. I think that a good article should start at it's highest level and then explain how lower levels are special cases of it. These lower levels may then also have their own page if necessary. And if something has application to physics or anything else, these should then be treated. BTW The laplace article is still very far from decent since it does not say anything usefull about the (general) Laplace operator etc etc. Any comments?MarSch 18:47, 25 Mar 2005 (UTC)

You mean an article titled derivative should start with a general definition that encompasses the derivatives of first-year calculus, the derivatives of Schwartz's theory of distributions, and Radon-Nikodym derivative, and all the others, and only after that mention special cases? That seems incredibly silly to me. Michael Hardy 02:15, 3 Jun 2005 (UTC)

Hi MarSch. You need to put this on Wikipedia talk:WikiProject Mathematics if you want poeple to notice this. I would also suggest splitting it into several paragraphs, to make your point more clear. Oleg Alexandrov 19:06, 25 Mar 2005 (UTC)

I agree with MarSch. I would ask more specifically: what is the difference between a Wikipedia and a Wikibook? It seems to me that a sufficiently well-structured collection of articles on wikipedia would be just as useful to learn from as a wikibook, no matter what level of knowledge the reader currently has. In fact, I would go further: I think the division into "encyclopedia" and "textbook" is a by-product of historical technical limitations in publishing, which are now being broken down. I welcome the development of wikipedia into a source of material at a textbook level of detail. (However, I will try to restrain myself from writing such content if the consensus falls against it.) Dmharvey Talk 14:46, 2 Jun 2005 (UTC)

Violently agree with Dmharvey. In fact, WP is arguably better than a book, since its more conducive to research. One can dig more widely more quickly than one would ever hope to with a book. One neat idea is of a "wiki neo-book" which would be nothing more than a curious list of article titles that should be read in a certain order.

Note, however, that a number of structural problems need to be addressed in order to accomodate this kind of expansion. I've already belabored on one such issue on Wikipedia:WikiProject Mathematics/Proofs, but similar issues loom. The structure of an article becomes extremely important if it is to be readable. I also have uneasy feelings about subtle vandalisms, intentional or accidental, and my personal ability to manage my watchlist. I'd like to have some permanent way of stating "I've examined this formula, and agree that its correct". But I think this talk would best be for Wikipedia talk:WikiProject Mathematics and not here. linas 00:40, 3 Jun 2005 (UTC)

I am, unlike others, for peaceful resolutions! :)

The current wikipedia policy is to keep encyclopedia articles separate from books. This is not the place to argue against it; the consensus so far seems to be that this separation is good.

The advantage of a collection of loosely integrated articles (such as Wikipedia), over books (such as WikiBooks) is that you don't need to worry about global consistency, you don't need tight integration, and each article can be read rather independently of others. You also don't need to worry about mistakes in proofs. So, encyclopedia format removes a layer of complexity present in books, and as such, gives more flexibility and makes it harder to make mistakes.

By the way, MarSch's main point was not about books. It was about writing a math article top-down starting with the most abstract and going toward particulars. I would say everybody else disagreed with MarSch, see Wikipedia talk:WikiProject Mathematics/Archive7#Structure of math articles. Oleg Alexandrov 01:56, 3 Jun 2005 (UTC)

OK. Clarification of my point of view: I agree with the outcome of Wikipedia talk:WikiProject Mathematics/Archive7#Structure of math articles, that is, I think an article (particularly its introduction) should be accessible to as wide a variety of people as is possible, and then people should be able to meander to material that matches their level of knowledge/experience.

However, I tentatively stand by my position that in principle there need be no difference between a book and an encyclopaedia. I could be persuaded to change my mind. I am, after all, a complete newbie, and, I like to believe, open-minded. Perhaps someone can suggest a place where this has been discussed, so I can educate myself. Thanks. Dmharvey Talk 02:26, 3 Jun 2005 (UTC)

Try Wikipedia:Village pump (policy) if you would like a community-wide discussion. Oleg Alexandrov 04:43, 3 Jun 2005 (UTC)

Hi Oleg, I did have a look there, but it seems they only have archives going back two weeks at the most, and I couldn't find anything to answer my question.

In the meantime however, I did think of at least one reason why a textbook is different from an encyclopedia: textbooks often have "homework problems". (This thought was prompted by the Polygon Sum Conjecture discussion.) So far I haven't seen a set of exercises at the end of any WP article, and I concede that they probably don't belong there. (Well maybe, I need to think about that some more.) Someone once said that there is no substitute for doing a Hartshorne exercise every day (referring to the book Algebraic Geometry by Robin Hartshorne). Dmharvey Talk 11:47, 3 Jun 2005 (UTC)

I would like to mention that even I don't agree with myself anymore about the top-down approach. Bottom-up is the way to go, but now it is mostly bottom. I would like the encyclopedia to be more comprehensive. --MarSch 13:02, 3 Jun 2005 (UTC)

The difference between textbooks and encyclopaedias is that an encyclopaedia consists of loose articles. For instance, an textbook on (elementary real) analysis may have a chapter on univariate functions with sections on continuity, limits, derivatives, etc. However, an encyclopaedic article on continuity talks about continuity of univariate functions, multivariate functions, functions between metric spaces, functions between topological spaces (cf. continuous function). This is why it is easier to learn from a textbook than from an encyclopaedia. All IMHO, of course. -- Jitse Niesen 20:35, 7 Jun 2005 (UTC)

[edit] History section

Would like to see the Guideline recommend the inclusion of a History section - many mathematical fields and concepts have a rich and interesting background - see fractal, chaos theory or group theory for examples. Would be good if we could reach a concensus on the position of the History section - my preference is near the beginning of the article, straight after the intro, but in some articles (such as complex number) it appears near the end. Gandalf61 09:15, Jun 2, 2005 (UTC)

I second that. --MarSch 13:48, 2 Jun 2005 (UTC)

I also agree; although I have no preference about the location of the history section. Dmharvey Talk 14:34, 2 Jun 2005 (UTC)

Agree w/ Dmharvey. linas 00:40, 3 Jun 2005 (UTC)

[edit] the "informal introduction"

Perhaps we could add a section giving an example of an informal introduction for continuous functions, e.g.: "In the case of the real numbers, a continuous function corresponds to a graph that you can draw without lifting your pen from the paper." (This was a working definition at the beginning of a calculus class I once taught.) Dmharvey Talk 14:48, 2 Jun 2005 (UTC)

Agreee, all math articles should have an informal intro. Again, potential structural problems abound: if all articles have intros, invormal overviews, formal defnitions, a set of theorems, possibly a diagram, a history section, references, ouch, it risks getting dense and overwhelming. linas 00:40, 3 Jun 2005 (UTC)

Each article should have an introduction and it should be informal but correct. I dislike however the terms "loosely speaking", "jocularly" or some such. I like to say "in some sense". That means that I am being informal and not going to go into something technical right now, yet precise. --MarSch 13:08, 3 Jun 2005 (UTC)

The very point of the informal introduction is to drive the point home. Any means are fine for that. If you get a spark light up in the mind of the reader, you hooked him. If the price to pay for that is hand-waving, so be it. That can always be rectified later with the formal defintion. Oleg Alexandrov 15:50, 3 Jun 2005 (UTC)

My experience (both in WP and without it) is that often it is impossible to give an informal introduction that is nevertheless "correct" (whatever that means — let's not even go there.). That is, sometimes there is a person who will learn something useful from an informal introduction that is somewhat incorrect, yet will learn nothing from an introduction that is actually precise. This is the kind of person I would like to make sure is covered, which is why I don't mind if an informal introduction is somewhat incorrect — as long as it is made clear, by whatever means, that they are not getting the whole story.

I think the example I gave with continuous functions is an excellent example. There are high school kids who know what graphs of functions are, and given the definition "can be drawn without lifting a pen from the paper" will immediately understand a lot about continuity. If you gave that person an epsilon/delta definition, let alone an "inverse image of open sets" definition, they would learn precisely nothing. Dmharvey Talk 17:06, 3 Jun 2005 (UTC)

I like intuitive definitions like "can be drawn without lifting your pen". This is informal yet precise. Things that can be visualized make the best introductions. The epsilon-delta def needs to be preceded by another informal description, like "the closer you get to the point a, the closer the function gets to the limit b"--MarSch 18:34, 3 Jun 2005 (UTC)

[edit] writing style section

There are various issues of writing style that I see crop up every now and then. I have put one of them on the "how to write..." page. Please feel free to add your own favourites. Dmharvey Talk 1 July 2005 15:32 (UTC)

Thanks for this. There probably are a lot more we could add. — mjb 02:57, 9 August 2005 (UTC)

With consensus I would add that the construction "then if" is especially annoying. Why can't people just state their theorems as hypothesis-conclusion, with the stage set in a previous sentence? Orthografer 16:49, 7 June 2006 (UTC)

[edit] Encyclopedic vs conversational tone

Lately I've been working on removing spurious "note that…", "it should be noted that…" and similar phrases from Wikipedia articles. I noticed these phrases crop up a lot in the math articles. It seems to be a side effect of the conversational, second-person, lecture-like tone taken in a lot of the articles. I have mixed feelings about this writing style; it is often found in textbooks and can help the reader understand a difficult subject by holding their hand through an explanation, so I don't want to suggest that it be abandoned. However, it does run counter to the detached, 'encylopedic' tone considered ideal in Wikipedia articles, so I want to encourage authors to avoid going overboard with conversational clichés. In a lecture situation where the listener is more open to having their attention redirected, it is typical and comfortable to hear certain phrases like "note that" repeated often. But in prose, where exposition is more linear, it tends to be jarring (especially if it happens often), and reflects either poor organization (crucial points shouldn't be afterthoughts) or a lack of confidence in the reader's willingness to continue reading. Therefore, I tried to add a bullet point to this effect.

I've seen examples of math articles written very much in a conversational, lecture style, and others that are written very much in a detached, encyclopedic style. I don't remember which ones they were, though, so if someone feels like mentioning examples or further improving the guideline, please have at it. Thanks — mjb 02:57, 9 August 2005 (UTC)

I agree with the above. In the same vein, I think we should discourage the use of the "editorial we". Paul August ☎ 03:57, August 9, 2005 (UTC)

I am not as averse to the conversational tone as other people here seem to be. I would make a distinction between prose that is, for example, giving an overview of the current state of knowledge of a subject (in which case the encyclopaedic tone works well), and prose that is, for example, leading the reader through a proof of a theorem (in which case the conversational tone works better). In the first case, constructions like "note that...." are usually spurious and can be rewritten without much trouble. However, I think it is more difficult to remove these clichés in the case of explaining a proof, where the author is trying to draw the reader's attention to logical relations between parts of the proof.

Also, the difficulty with discouraging the "editorial we" is that it forces more frequent use of the passive voice, which I am also stylistically opposed to.

Nevertheless, I appreciate the sentiments that people are expressing here and I'd like to hear more opinions. Dmharvey Talk 10:16, 9 August 2005 (UTC)

See Wikipedia_talk:WikiProject_Mathematics#.22Tone.22.2C_pronoun_use.2C_etc._in_math_articles (current version) and the related Talk:Knot_theory#You.2FMe (current version) and Talk:Braid_group (current version) for discussion on this topic. I was unaware of the discussion here, otherwise I would have directed people here instead. --Chan-Ho (Talk) 05:47, 14 May 2006 (UTC)

[edit] TeX vs. non-TeX

Recently, User:Jitse Niesen reverted edits by User:MathKnight to spectrum of an operator, citing this article as the reason for the revert. The things that were reverted were primarily the TeX-ification of plain-markup formulas, for example, the conversion of the plain-markup

T ∈ B(X)

to the TeX formula

.

I don't really like this revert at all, and I don't like the plain-text markup, for several reasons. TeX formulas can be converted to plain html, or not, depending on one's settings of Special:Preferences. Thus, if the page is marked up with TeX, the user can control conversion to HTML by changing thier preferences. By contrast, if a formula is in HTML, it's stuck there forever, and can't be TeX-ified. Thus, the general WP reader has far more control over TeX formulas than plain formulas. (Disclaimer, I am sensitive to this issue because my browser seems to be lacking fonts with the ∈ symbol, so it looks like a dumb square in my browser.) I would like to see a policy spelled out here that explicitly enourages the use of TeX, and discourages the use of plain HTML for math markup. linas 6 July 2005 00:57 (UTC)

A similar discussion was just taking place today concerning Fermat's little theorem or maybe it was Proofs of Fermat's little theorem. I also would like something spelled out. Perhaps the discussion at Wikipedia:How to write a Wikipedia article on Mathematics#Typesetting of mathematical formulas could be modified. I would like to see something that says "All equations should ideally be done using TeX, except inline equations where the PNG rendering would disrupt the text flow." It sort of says that already, but it's not very insistent. I know not everyone agrees with this, please jump in and give your opinion. Dmharvey Talk 6 July 2005 01:59 (UTC)

It all depents. If the TeX formula is inline, and becomes PNG, it must not be allowed. On my laptop the PNG images look huge, and look bad surrounded by text. On the other hand, if the formula is on a separate line (displayed formula), it is preferable to have them PNG I think. Oleg Alexandrov 6 July 2005 03:29 (UTC)

Yes, but it is exactly the inline formulas where this is a problem. The display formulas already are mostly in TeX, and aren't a problem. Have you tried changing your formula display preferences, to see what this page looks like? linas 6 July 2005 04:04 (UTC)

I believe editors better keep the preferences set to default when it comes to displaying formulas. Then we will see the same things as the readers. Now, if I change my preferences to render all formulas as PNG, I think things will look worse. If I force all of them HTML, they will also look worse, as html does not render well some math formulas. Oleg Alexandrov 6 July 2005 04:36 (UTC)

This is a topic that returns regularly, see for instance Wikipedia talk:WikiProject Mathematics/Archive4(TeX). Of course this does not mean that it is not worth having, for instance, I didn't realize that some people do not have a font for ∈ which must be very annoying. However, PNG in running text looks very ugly to some people (including myself). I think that past discussions have showed that there is not a good solution at the moment which makes everybody reasonable happy.

However, it may be possible to change the software so that a decent solution will be possible. One alternative is to support MathML, and I'd love to find out how feasible that is, both on the server side and on the client side. The other possibility is to improve the routines that convert the TeX to HTML. It should be possible to do a better job, and then we could use <math> tags everywhere. -- Jitse Niesen (talk) 6 July 2005 19:34 (UTC)

Help_talk:Formula#Maynard_Handley.27s_suggestions — Omegatron 02:18, 1 November 2005 (UTC)

(The link right above is a bit of a mystery to me: can anybody please explain?)

I agree with most of the above. Having started a small sub-article myself recently, I wan't sure what to do with the "central dot" for function notation. The HTML "central dot" (&sdot;) is understood by e.g. Firefox but not by e.g. Internet Explorer. So I decided to use TeX. I hoped that WP would be smart enough to render this in HTML for browsers that support the HTML &sdot;, and leave the PNG for those that don't. Alas, it looks like it's not so smart ATM.

The guidelines in this manual of style do not make it clear enough what one should do. In fact, it looks like they encourage quite the opposite: "However, still try to avoid in-line PNG images". I think this is missing the point entirely, as one should not think-ahead and write math depending on how it will look like on this or that browser. I'll be even more radical and say that there should be just *one* correct and accepted way of writing math, and all the burden of rendering should be put on the server-side. The server should be able to display the correct thing depending solely on the formula, on the browser used and on the user settings. This should be transparent to authors and readers alike. Hope this makes sense, I can be more specific if unclear. PizzaMargherita 19:42, 1 November 2005 (UTC)

[edit] Downsampling a too-big graph

See also Wikipedia_talk:WikiProject_Mathematics#graphs

Hello. In the discussion of graphs on Wikipedia:How to write a Wikipedia article on Mathematics, it is suggested to make the graph too big, then downsample it. I understand the concept but I'm not familiar with the commands. Can someone state the commands that are needed to do that? I think it would help a lot if we can bypass the need for reading through man pages or whatever to find it. Thanks for your attention to this topic & happy editing, Wile E. Heresiarch 01:14, 11 July 2005 (UTC)

I HATE when people force you to read through man pages.  :-) I added some menus. Anything else? - Omegatron 01:44, July 11, 2005 (UTC)

For Windows users, You have to install Ghostscript to open .ps files in the GIMP. I linked to the instructions but those instructions aren't the best. You should really set enviroment variables instead of copying the file to your system directory. You need to right-click My Computer --> Properties --> Advanced tab --> Environment Variables --> New and create variable names and variable values as such:

GS_PROG

C:\Program Files\gs\gs8.51\bin\gswin32c.exe

GS_LIB

C:\Program Files\gs\gs8.51\lib

Though your path name may vary. I don't really want to put all these instructions in the middle of the text, though. Maybe this information should go under the GIMP or Ghostscript articles, and we can link to that? It's too "how-to", though, for the WP. - Omegatron 14:41, July 22, 2005 (UTC)

I agree, let's move the graphs to its own page. - Omegatron 18:59, July 22, 2005 (UTC)

Every time I upload a picture with one of these methods, I include more and more detailed instructions. They should really just be made general, go in the graph section instead, and save me a lot of work. Here are the lastest, though: Image:Butterworth response.png - Omegatron 17:20, July 23, 2005 (UTC)

[edit] Too much HTML?

It was just recently when there was an argument of TeX vs HTML, where it was reaffirmed that in general PNG images inline are not that preferrable. However, it seems that recent changes to this manual of style push that too far. Now it reads that one should not use LaTeX inline to start with, which I think is a bit too much. Opinons? Oleg Alexandrov 15:35, 9 August 2005 (UTC)

I don't know if you're referring to my edits or what. When I was adding headings and reorganizing, I tried to qualify the statements about PNG images (I made it more clear that they're dependent on user prefs), and in the process, I noticed that there were conflicting guidelines about when it was OK to use LaTeX. The 'Using LaTex markup' section said inline LaTeX was discouraged and gave some reasons why, but then went on to advise people on what to do if they did want to use LaTeX, whereas the 'Very simple formulas' section was very strongly against LaTeX inline. I tried to reconcile the statements but could not really ascertain what was considered ideal, so I changed the latter section to match the less-prescriptive tone of the former. — mjb 15:52, 9 August 2005 (UTC)

I think Oleg referred to your changing "Having formulas as in-line PNG images, as above, is generally discouraged" to "Having LaTeX-based formulas in-line, as above, is generally discouraged". The problem is not with having LaTeX-based formulas using <math> tags, but with formulas which render to PNGs.

I do not like the addition of "Article authors should avoid referring to "we" or addressing the reader directly." as referring to "we" is normal style for mathematical articles and recommended in at least one style book. I'm also rather surprised by the warning to write "&lt;" instead of "<". Does the latter really cause problems in some cases? -- Jitse Niesen (talk) 18:53, 9 August 2005 (UTC)

Yes, this is exactly what I meant. I am happy with Jitse's changes now. Oleg Alexandrov 20:19, 9 August 2005 (UTC)

Yes "we" is normal style for mathematics articles, but I don't think it is necessarily appropriate for an encyclopedia. What style book recommends it? I think that "conversational style" and "addressing the reader directly" are more appropriate for didactic material, but less appropriate for reference works. I especially dislike the "editorial we" (perhaps because it reminds me too much of the royal we ;-) — Paul August ☎ 20:41, August 9, 2005 (UTC)

I agree with the above conclusion that there is no method currently that makes everyone happy. I like the idea of improving the automatic TeX to HTML rendering (as the current stuff is horrendous and part of the reason I've been doing HTML inline), but how feasible is it to change the wiki software like this to render HTML that everyone will deem acceptable? I see a lot of "force render"s because the HTML conversion is so awful.

I used to be opposed to HTML rendering until I found better fonts to use on my machine. This may or may not continue to be a problem in MathML, depending on the implementation. We also have to wait until most people have MathML by default in their browsers before we can make a major push to convert to it. There is also the issue that MathML (like most XML) tends to be extremely verbose and may make editing and writing a hassle. Perhaps writing everything in TeX and doing automatic conversion to MathML will be better, so long as the rendering is much better than the TeX to HTML rendering that we have now.

Finally, I would like to use this opportunity to push for some diagramming standard for Wikipedia, as I am a big fan of abstract nonsense and feel somewhat naked without being able to easily include commutative diagrams in my articles. I know that I can create static images, but my real desire is to create diagrams that can easily be edited by other users. Either xypic or some sort of SVG standard would be a godsend. Thanks for listening. - Gauge 03:19, 21 August 2005 (UTC)

• Is there a list of recommended browser fonts, and how to get them? I'm running Debian, I thought I'd installed every font I could find... but ∈ still doesn't render. Might be a browser issue, not a font issue? linas 18:14, 21 August 2005 (UTC)

• I believe that the web server and the web browser exchange a list of capabilities. In particular, a web browser can announce that it supports MathML, in which case the server can generate and send MathML. Clearly, this needs to be explored, and enabled, on WP. For markup, TeX would be best, as it can be converted to HTML, png or MathML, and is also easy to edit. linas 18:14, 21 August 2005 (UTC)

• Do we have a general "which browsers support what from the WP math standpoint, and how do we configure the danged thing?" type page anywhere? We should, shouldn't we? linas 18:14, 21 August 2005 (UTC)

• In the meanwhile, the most future-compatible thing to do would be to not change markup on existing pages from inline math tags to HTML, as this seems like a step back from the stated direction. linas 18:14, 21 August 2005 (UTC)

I agree with the manual, and even recommend stronger wording, stating that in-line formulas should be entered as HTML if possible. I further would recommend stronger wording stating that even non-in-line simple formulas should be entered as HTML whenever possible. Why should an image (i.e., bloat) be added whenever an efficient ASCII or highly-portable HTML character is acceptable? As stated above, conversion from LaTeX doesn't work correctly; and it might be far in the future before it works well across all browsers and operating systems worldwide.

Aside from this, the bloating of web pages with unnecessary images is a very bad design practice and should be discouraged. Wikipedia web pages already have excruciatingly slow load times for many users. Keep in mind, about 80% of home users worldwide have slow connection speeds. Using unnecessary images for simple formulas bloats pages significantly further, putting an even far greater strain on the servers. Of course use LaTeX when there's a real reason, but for simple formulas, HTML is far better, provided it can be understood and has very good portability across browsers worldwide. --Simian, 2005-09-21, 02:21 Z

Except that html is ugly as sin, making the page hard to read and hard to understand. Math is hard enough already, understanding it shouldn't be hobbled by bad typography. linas 22:15, 21 September 2005 (UTC)

My above post addresses simple formulas that can be understood as HTML. I tried to reiterate that in the last sentence of my above post. In regard to one of your earlier points, simple formulas look great as HTML (far better than a bloated image for every quantity) if the user sets their browser or Wikipedia preferences to Times New Roman font. If you're using a sans serif font (or the Wikipedia default is a sans serif font), therein lies a mistake and part of the problem.

Don't try to outguess the end user and force a style just because someone chose an inferior font. Wikipedia pages should emphasize content, not style, keeping the layout as simple and plain as possible, and therefore portable and configurable by the end user. At least one skin, maybe two, specifies no font or Times New Roman. If you're choosing a wrong, poorly-defined font (i.e., a sans serif font) to try to view math quantities, etc., then we shouldn't blame HTML for a bad design choice and/or a bad skin choice. There's a reason why virtually all newspapers and most text books use Times New Roman -- legibility.  --Simian, 2005-09-25, 14:28 Z

Ok, help me get this right. Shouldn't the burder of rendering (in an ideal world) be entirely on the server - based on user preferences, the formula at hand and the browser used? And shouldn't the authors be able to write what they mean in one single format (I vote for TeX) and let the server decide what to do in each case? I'm confused... (thanks) PizzaMargherita 21:01, 1 November 2005 (UTC)

[edit] oleg's rearrangement

Yes I like the "typesetting" part leapfrogged to the end. Dmharvey Talk 02:44, 19 August 2005 (UTC)

[edit] Own toughts

1) I dislike the idea to let MediaWiki decide to render an easy <math></math> Tex command in plain HTML code (called "HTML if very simple or else PNG" in the user's preferences). This sometimes really makes it hard to recognise variables for being the same, for example, the "letter a" looks different in TeX () than the "HTML a", a^x. When registering a new user, I must say it would be better to always activate the option Always render PNG by default. Therefore, I generally prefer to always use <math></math> TeX tags in formulas to have a unified look throughout the article.

2) Right now, many articles in the Wikipedia don't have a unified base for the variables used - one article uses

,

another article uses

cos(ωt + φ₀)

Another difference is, for example, and - two ways for writing vectors. An additional example is hf = hν. It often confuses the reader to have different variables for basically the same thing - more confusingly, sometimes two totally different variables have the same placeholder. I wonder that there doesn't seem to be an ANSI standard / IEC standard or comparable standard that helps to unify placeholders. It'll be great in my eyes if there was an own Manual of Style about that topic.

3) When writing in direct HTML, is it better to use the correct Unicode symbol or the Ampersand+name HTML entity? For example: Unicode α instead of α, λ instead of λ, ≈ instead of ≈? I prefer to use the Unicode encoding, as it is easier to read.

It'll be great if some of you could comment on my thoughts. Thanks, --Abdull 14:06, 19 August 2005 (UTC)

-- I think that <math>\alpha</math> is preferable to &alpha;, even with the math rendering problems, with either preferable to the Unicode. But I've written so many equations in Microsoft Equation Editor/MathType, WordPerfect Equation Editor, TeX ('Tex' is just wrong; 'TeX' is closer, 'TeΧ' is closer yet), and other formats, that I don't have any trouble writing TeX as if it were WYSIWYG, so I may not be the best person to comment -- Arthur Rubin 21:55, 24 September 2005 (UTC)

1) I think the two "a"s are a small price to pay. I quite like the default settings as they are (also see below in the Tex-vs-non-TeX section). I don't understand how using <math></math> would help you in this, as WM would transform in HTML where possible... Mind you I'm quite new to WP so maybe we're not on the same page here.

2.1) phi vs varphi - minor but should be standardised.

2.2) Same for vs . We should have a guideline. Although is semantically superior to (it uses keyword "vec"), it is also more messy-looking IMHO.

3) Again, I agree we should have a guideline. I don't know which is preferable, it depends on browser support I guess. But once again, see below my comment on TeX vs non-TeX. These issues should not waste our time. There should be just one way of writing it (e.g. TeX) and the server should work out what is the correct thing to do in each situation, depending on the formula, user settings and browser used. PizzaMargherita 20:03, 1 November 2005 (UTC)

[edit] Math or Maths?

moved from Talk:American and British English differences

It is often abbreviated maths in Commonwealth English and math in American English. — 203.132.240.221 23:15, 20 August 2005

(I signed your post for you.) In the USA it's not just often, it's pretty much always "math." People will look at you funny if you say "maths." I don't know what advice should be given to authors. Perhaps the shorter terms should be avoided altogether, and people should be advised to write out "mathematics" or "arithmetic" instead. What do the others here think? — mjb 06:05, 21 August 2005 (UTC)

I agree that writing out mathematics is best in an encyclopedia. However, when an abbreviated term is more appropriate for some reason, the preference of the original author should be respected, in accordance with WP:MOS#National varieties of English. —Caesura^(t) 21:10, 11 October 2005 (UTC)

[edit] "It is easily seen that ..."

Recent manual of style edits by User:Crasshopper deprecate this commmon linguistic style. But I wonder if that is the right thing to do; in fact, I think its not. When a mathematician says "its easily shown that", they are not trying to belittle the reader, (and the reader should not feel belittled or stupid), rather, it is a verbal hint about the length of the proof of a theorem. There is many a time that I've been stumped by some formula, while faced by the mocking words "it is easy to show...". This is always followed by a slap to the forehead, "but of course ... its obvious". For that is the very nature of math. So what shall we write instead of the words "its easy to show"? Should we say instead "the proof of this proposition is very short"? Instead of writing "its easy to show", should we start inserting very short proofs that show it? No I think not. linas 04:24, 2 September 2005 (UTC)

I agree, that section of the manual sounds a bit anal IMHO. Some deprecated expressions are just widely used and accepted idioms of writing maths. PizzaMargherita 20:12, 1 November 2005 (UTC)

I disagree. Although the phrase is commonly used between mathematicians, i think it can be problematic on Wikipedia. What can be easily shown by a degree-level student could be extremely difficult for a high-school student: it's all a question of perspective, and the phrase would be discouraging to those high school students. Personally I would prefer the very short proof to be provided - it's frustrating to follow through a proof and then get lost on one step, but I can see that that would be impractical at times. As the current manual suggests, hinting at HOW it can be shown is more useful. Hermajesty 19:17, 14 January 2006 (UTC)

Of course I agree with myself, but I'd like to weigh in again here, in response to Linas' comments. I personally often feel belittled when reading maths documents that use phrases like "clearly" and "obviously", and such words don't seem (to me) to make texts any more readable. Even if they are standard in current textbooks, that doesn't make them good. In fact I see them as a kind of jargon that reflects poorly on mathematicians (thus perpetuating innumeracy, yadda yadda yadda). In the first place these words bristle at the reader, in the second place they are unnecessary (do most readers actually care how easy or difficult a proof is? I know I don't; I just want the result), and in the third place they are frequently untrue (see Linas' comment about being stumped and then afterwards thinking, "but of course ... it's obvious". If it were obvious then one would not be stumped). Whether or not mathematicians intend to insult readers with their language is beside the point. I think we should take care in our verbal exposition to use our words more judiciously and with more purpose. If you mean "It only takes a few lines to prove," say that. If you need to segue from one idea to another, do so - but don't add insulting words needlessly. Crasshopper 18:52, 20 February 2006 (UTC)

I definitely disagree with the second point: it's important to me whether a proof is short or long, and whether it's routine or requires some major idea. Perhaps "clearly" and "obviously" should not be used, though I don't find them belittling (they signal that if it isn't obvious to me, then I need to study it more, not that I'm stupid). Alternatives: Straightforward, or A short proof / routine argument shows that. It might be good to keep in mind that some people find clearly / obviously belittling, but for advanced maths, the readers are probably used to the style and won't mind. -- Jitse Niesen (talk) 20:20, 20 February 2006 (UTC)

To rephrase Jitse,

In mathematics, there is an immense raft of specialized jargon. The phrases "Clearly," "Obviously," and "It's easy to show that ..." are a part of that jargon. Although they resemble the English language, their true meaning is subtle.

Mathematicians often encounter head-scratching claims in the papers they read, claims that make them stop and wonder "what does this mean?", and "how could this possibly be true?", or "how could the author presume such a thing without any justification whatsoever?". These head-scratchers come in two basic varieties: the simple, forehead-slapping, "duhh, of course" kind, and the complicated kind. These two types can be very hard to tell apart, and one can loose hours or days on them. There are some well-known stories of strong mathematicians who spent weeks on problems only to wake up in the middle of the night with a "duhh of course" inspiration. The phrases "Clearly," "Obviously," and "It's easy to show that ..." are used to indicate to the reader that what follows is of the forehead-slapping variety. They do not imply that what follows is somehow "easy"; its usually not -- if it was actually easy, then the author wouldn't need to coach the reader with this "com'on you can do it" pep-talk.

Yes, texts that use these phrases may seem intimidating, but that comes from an unfamiliarity of math jargon. No one expects that the claim following an "Obviously..." will be obvious to anyone without years of preparation. linas 01:32, 21 February 2006 (UTC)

Key words: In mathematics,

This is an encyclopedia; not a mathematics text. I'm sure there's a wording that conveys what you just said in a way that non-mathematicians will understand without knowing mathematician jargon. — Omegatron 01:56, 21 February 2006 (UTC)

I seriously doubt that there are any non-mathematicians reading any of the WP math articles. For starters, you need at least an undergrad degree in math, if not advanced degrees, to understand most of these topics. Heck, I have a PhD and a postdoc under my belt, and I still don't understand most of the articles. Yes, there are some articles that are aimed lower, but I don't think those use this style anyway. linas 05:58, 21 February 2006 (UTC)

When writing a Wikipedia article, you have to decide on the audience. Some topics in mathematics, like Fermat's last theorem, will attract non-mathematicians, and for those jargon should not be used. However, other topics are so advanced that it is not possible to explain them without assuming that the reader has a grounding in maths (e.g., de Rham cohomology). I see no reason why those articles should not be considered as a mathematics text. Mathematicians do not use jargon to keep non-mathematicians out (at least, they ought not), but they use jargon to denote concepts more succintly and precisely than is possible without using jargon. -- Jitse Niesen (talk) 14:11, 21 February 2006 (UTC)

[edit] Italics for points and variable subscripts

I want to add a new section entitled Points, stating, "Points are usually written in uppercase italics, such as point A, P, O." All text books I checked use uppercase italics for point labels.

Secondly, we currently have the following statement under Variables. "Descriptive subscripts should not be in italics, because they are not variables. For example, m_foo is the mass of a foo." The Superscripts and subscripts section also states superscripts and subscripts should have no other formatting. Should we add a sentence or phrase to both sections stating whether or not superscripts or subscripts that are variables should usually be/not be in italics? An example follows.

σ_ij  versus  σ_ij

Although text books usually show variable superscripts/subscripts in italics, I believe it might be acceptable (for HTML formulas) to use unemphasized variable superscripts/subscripts for on-line purposes. Italic subscripts are slightly less legible on-line, whereas italic and upright subscripts are equally legible in text books. --Simian, 2005-10-02, 22:06 Z

That depends on your browser. Italic subscripts look just fine to me. — Omegatron 02:21, 1 November 2005 (UTC)

I vote for italics, because that is the standard typographical convention. Indices are themselves a kind of variable. Once again, browser shortcomings should not affect the way we write. The server-side can take care of that. PizzaMargherita 20:41, 1 November 2005 (UTC)

[edit] Italics vs. bold vs. bold italics

Concerning italics vs. bold vs. bold italics, this manual of style seems to contradict itself and Wikipedia:Technical terms and definitions. From what I can infer, the relevant rules according to that article are

1. In the first sentence, explain the article title, writing it in bold.
2. Throughout the article, for each technical term, do one of the following:

• The first time it is used, define it, rigorously or nonrigorously, writing it in bold italics; each subsequent time it is used, write it in italics.
• The first time it is used, leave it undefined, writing it in italics; each subsequent time, leave it in plain face.
• The first time it is used, link to an article that defines it; each subsequent time, leave it in plain face. (I added that one.)

Actual WP math articles use a variety of conventions, but they often give defined terms in bold, not bold italics, and leave subsequent uses in plain face. On the other hand, this 'Manual of Style (mathematics)' seems to give them in bold sometimes and italics sometimes. (Also, is there a reason why 'Style' is capitalized?) It might be nice to agree on a simple set of conventions. Joshuardavis 17:06, 22 October 2005 (UTC)

[edit] Style for constants

When I learnt (La)TeX, I also learnt that the "mathit" (or italics in the mathematical environment) should be used only for valiables (e.g. x or i as an index in a sum) and generic functions (such as f(x)). This is why, for example, we have special TeX commands for well-known functions, such as "log" or "sin". I also remember vividly (but unfortunately cannot find a reference) that this also applies to any other non-variable and non-function, be it a less-known function, a subscript having a non-variable meaning (e.g. , or a constant. I know it would be a pain now to put "mathrm"s everywhere, but can anybody confirm that is the (if often neglected even in authoritative books) typesetting rule? Thanks. PizzaMargherita 21:10, 1 November 2005 (UTC)

Yeah, I've been adding mathrm's all over the place for non-variables. I don't know of a better solution. — Omegatron 23:54, 18 November 2005 (UTC)

[edit] More WikiTeX macros, please?

Sorry, but I am a bit of a newbie around here. I would like to do something which is easily available in LaTeX, but not easily available in TeX. I need to be able to set characters (or expressions) over other characters (or expressions). For example:

0\rightarrow A\overset{u}{\rightarrow}B\overset{v}{\rightarrow}C\rightarrow 0

(I normally use \mathop, \xrightarrow, or the xypic LaTex package for such things, but these are less intuitive and none of them happen to be supported by TeX.) The only thing I can think of is:

but this clearly looks bad as far as the typesetting goes. Any suggestions or solutions? Silly rabbit 22:57, 18 November 2005 (UTC)

You could fake it:

but yeah, it would be nice if it was supported natively. — Omegatron 23:54, 18 November 2005 (UTC)

Actually, thanks a lot Omegatron. I was only looking for a bandaid in some particular formulas. My solution involved \vspace and \hspace which aren't TeX builtins either. What you suggest ought to work, though. Thanks. Ok, now here's a commutative diagram that I would like to.... no, just kidding.

On a related note, is there an attempt to LaTeX-ify Wikipedia? There may be possible security issues with running LaTeX on a public server. But I suspect that the WikiMedia software already does the rendering in a locked-down sandbox anyway. Does anyone know if they are working on this?

Thanks, Silly rabbit 00:20, 19 November 2005 (UTC).

[edit] Minus vs. Negative

I'm looking at the -40 article, and wondering if there is a rule or guideline about the use of the words minus and negative. My understanding is that negative is a unary operator and so it is correct to speak of the number negative forty but incorrect to speak of minus forty, while minus is a binary operator and so three minus five is correct while three negative five is not. Can someone please confirm or deny this? And if it is the case, should the wording in the article be changed? I would like it to read negative forty personally, but it is much much more common when speaking of temperatures to hear minus forty. Macho Philipovich 15:50, 21 December 2005 (UTC)

This question arose before, I think at Wikipedia talk:WikiProject Mathematics. I'm sorry I can't be more precise than suggesting you look through the archives. I seem to remember that there was no conclusion on what to use. -- Jitse Niesen (talk) 14:51, 23 December 2005 (UTC)

Yeah, I think some people liked minus, and some negative. In US, I think they indeed say "minus forty" for the temperature (when I was in Minnesota :) but I was told that when teaching math one should say "negative forty". So I prefer negative forty myself, but I don't know.

By the way, you can ask again at Wikipedia talk:WikiProject Mathematics if you want, that page is visited more often than this one. Oleg Alexandrov (talk) 21:07, 23 December 2005 (UTC)

[edit] Typesetting of mathematical formulas

I think a large part of the contents can be moved to meta:Help:Formula. That page is currently biased towards TeX. Moving these HTML instructions/guidelines in that (Meta) page would make it self-contained, and would avoid duplication/contradiction with this page.

I think in this (Wikipedia) project should keep referencing that page, and keep only WP-specific guidelines, like colon for indentation and rendering settings. PizzaMargherita 21:59, 14 January 2006 (UTC)

Such a move may open a big can of worms. I am not sure it is worth pursuing. Oleg Alexandrov (talk) 00:23, 15 January 2006 (UTC)

 ? PizzaMargherita 09:40, 15 January 2006 (UTC)

I agree that m:Help:Formula is biased towards TeX. Do have a go at it. But I think you shouldn't delete anything here. Duplication and even contradiction is not a bad thing. m:Help:Formula should only give the facts while this page can mix them with the policy on the English Wikipedia. -- Jitse Niesen (talk) 13:34, 15 January 2006 (UTC)

IMHO:

• Duplication is always a bad thing because it makes maintenance impossible.
• Contradictions can't be right, by definition.

I agree on the rest: meta should expose the hard facts and this page set out guidelines specific to WP. I'll give it a try when I have some time. PizzaMargherita 14:41, 15 January 2006 (UTC)

The example of an in-line formula on line 5 of this section does not show up (on my browser, anyway). Is this a general problem? Hgilbert 21:07, 2 March 2006 (UTC)

[edit] Typesetting Algorithms

I haven't been able to find any official guidelines for typsetting algorithms, particularly mathematical algorithms. I note that Itoh-Tsujii inversion algorithm and Pohlig-Hellman algorithm both use a fairly standard pseudocode style that is common in mathematics. Is there any chance of formalising some guidelines for presenting mathematical algorithms? Leland McInnes 04:50, 29 January 2006 (UTC)

Have you read User:Dcoetzee/Wikicode and surrounding pages? Then you are probably aware that this might be harder to achieve than you think, unless the guidelines are very flexible. Personally, I find that in practice I prefer to write out the algorithm in prose instead of using a semi-formal presentation (my background is in numerical analysis). Nevertheless, I've nothing in principle against adding some suggestions.

Looking at the examples you mention, I think that Itoh-Tsujii inversion algorithm is fine. I don't like Pohlig-Hellman algorithm that much; it mixes explanation of the algorithm with the algorithm itself, and I think it would be better presented as prose, or perhaps as a combination of algorithm plus explanation of prose (is this clear?). -- Jitse Niesen (talk) 13:11, 29 January 2006 (UTC)

I have read the Wikicode debate. I'm not suggesting anything so strong, simply some basic guidelines to provide consistency in formatting mathematical algorithms. That would mean, for example, that when formatting an algorithm as a numbered set of steps it might be reccommended to do

 :'''Inputs''' Description of inputs
 :'''Output''' Description of output
 :# Description of the first step on the algorithm
 :# If the algorithm has substeps due to conditional or looping constructs
 :## Substeps should be nested numbered like so
 :## Etc.
 

With a few other guidelines based on what seems to be common practice (for instance ← is the popular assignment operator for mathematical algorithms, and "return" rather "output" seems to be the preferred way to denote that the algorithm should terminate outputting a specific value). Indeed, that might be the ideal place to add a few suggestions like trying to keep explanation of the algorithm outside of the numbered steps.

This, of course, doesn't preclude someone using Wikicode, their own pseudocode, or an implementation in a specific language - rather I'm suggesting have some basic formatting guidelines for the general style of algorithm description used here. I guess I mean guidelines of the form "If you are formatting your algorithms in this sort of format, here are soem guidelines on conventions, preferred style, and how to use Wiki markup suitably". Leland McInnes 21:43, 29 January 2006 (UTC)

[edit] Colour in latex now possible

I thought that people may like to know that colour mathematics is now possible, like this: . —The preceding unsigned comment was added by Lupin (talk • contribs).

Cool! But I would argue that one should be very conservative when attempting to use colors in formulas, in the same way as avoiding if possible colored html text. Oleg Alexandrov (talk) 01:28, 1 February 2006 (UTC)

I'm reminded of a paper in an obscure Swedish journal which purported to prove the inconsistency of ZF, using a strange notation with red/black formulas where the color was significant. (It was later generalized to a proof of the inconsistency of PA in a Finnish (?) journal.) Arthur Rubin | (talk) 02:48, 1 February 2006 (UTC)

Whoa! — Omegatron 03:54, 1 February 2006 (UTC)

[edit] Small HTML Rendering

Is there any reason that LaTeX codes that render as HTML are smaller than if they were just written as HTML? For example, for me (using MSIE and with "Recommended for modern browsers" selected at the preferences):

ab + cd = f and ab + cd = f (coded ''ab'' + ''cd'' = ''f'' and <math>ab+cd=f</math>, respectively)

both render as HTML but the first one is a larger font thatn the second. Any ideas, or is this just some problem that only I'm having? --mets501 03:52, 12 March 2006 (UTC)

Depends on the browser setting I think. On my current screen LaTeX rendered as html indeed looks a bit smaller than text, but LaTeX rendered as PNG looks much huger. No good answer I guess. Oleg Alexandrov (talk) 04:48, 12 March 2006 (UTC)

Same thing with mine. --mets501 15:10, 12 March 2006 (UTC)

The reason probably is that the default style sheet specifies that mathematics is rendered in a serifed font (see the span.texhtml section), while the normal text is in a sans-serif font. I fixed this by adding

span.texhtml { font-family: sans-serif; }

to User:Jitse Niesen/monobook.css. You might try to do the same. -- Jitse Niesen (talk) 07:49, 13 March 2006 (UTC)

Works for me. Thanks Jitse :-) AdamSmithee 07:55, 13 March 2006 (UTC)

Thanks guys! --mets501 22:26, 13 March 2006 (UTC)

[edit] Use nbsp to keep formulas together?

I've noticed that many inline statements and formulas do not use a non-breaking space or method to keep it from wrapping to the next line. It seems stupid to see "A+" on one line and "B" on another line. There are four possible inline versions that I can imagine:

1. No spaces: ''f'':''X''&rarr;''Y'' gives f:X→Y
2. Spaces: ''f'' : ''X'' &rarr; ''Y'' gives f : X → Y
3. Non-breaking spaces: ''f''&nbsp;:&nbsp;''X''&nbsp;&rarr;&nbsp;''Y'' gives f : X → Y
4. Use a style: <span style="white-space: nowrap;">''f'' : ''X'' &rarr; ''Y''</span> gives the same as #3

In my browser, #1 looks terrible. #2 looks good, except when it breaks the line, but #3 is an ugly HTML mess if you have to edit it. #4 is nice, but a bit lengthy, especially for a series of statements. I think it would be useful to start using some method to control wrapping, and I would like to hear others' opinions. - grubber 00:26, 18 September 2006 (UTC)

[edit] Boxed (display) equations

Action (physics) uses a boxed equation using some ad-hoc markup. For consistency, I think it's better to use a template for this. Is there already such a template? If not, I suggest {{box eq}} as a template name. I also think the big black box is a bit harsh - we could use something more playful like toc colours. Shinobu 04:27, 4 October 2006 (UTC)

[edit] Powers

Any consensus on the policy on fractional powers? We write the squareroot sign for powers of one half, but what about cube roots? Do we put the squareroot with the 3 above, or do we put ^1/3? And the others? yandman 14:26, 10 October 2006 (UTC)

[edit] Definitions: use := or \equiv?

I didn't see anything about which infix to use for definitions. Some use , but I find this very misleading, since it already has two other meanings: equivalence (hence its Latex code) and identity (first use). I would therefore advocate := or the equal sign with "def" underneath. (Sorry, I don't know the Latex code for that.) — Sebastian (talk) 01:43, 19 October 2006 (UTC)

I suggest you ask this question at Wikipedia talk:WikiProject Mathematics where more mathematicians hang around. Oleg Alexandrov (talk) 02:38, 19 October 2006 (UTC)

Note: Discussion has been moved there, but so far no clear decision has been reached about which policy to recommend. Please participate in that discussion. — Sebastian (talk) 23:01, 24 October 2006 (UTC)