Wikipedia talk:Manual of Style/Mathematics/Archive 1

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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)

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)

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)

(I know this is old, but...) the point is that this is not precise. Although functions from R to R are characterised by this property, this is only because the reals are connected. Indeed, I think a lot of people have difficulties when starting in topology because they need to make the switch from the connectedness idea of continuity to the "true" preserving-closeness continuity. --Taejo|대조 23:47, 17 July 2008 (UTC)

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)

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. --C S (Talk) 05:47, 14 May 2006 (UTC)

I think we might be missing some subtleties. And that's not the editorial "we", nor the Royal "we", it's the first person plural "we". We in a math paper does not refer to the author (speaking of himself with editorial plural) but to the cooperation of the author with the reader; that is, we assume... means that you and I have to assume this; it's not about my assumptions (as in a scientist conducting an experiment), but about our common assumptions, which we pointedly recognize as critical in the process of deductive reasoning (as in, the defintions of "definition" and "set" are not in logic texts, we assume them). Also, consider refers to Subsequent statements shall refer to the hypotheses formulated here e.g. "consider a group G with multiplicatively denoted identity e and..."; if you remove the word "consider" there is no sentence. But we are hypothesizing something to which we shall refer in subsequent text. "Consider" is a short and simple way of encapsulating that. There's nothing conversational in most technical mathematics papers, really. It's much more formal language than in this encyclopedia. In fact I wish we permitted ourselves more explanatory prose, more often. Pete St.John (talk) 21:01, 12 February 2008 (UTC)

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

$\ T\in B(X)$.

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" (⋅) 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 ⋅, 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)

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)

oleg's rearrangement

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

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)

"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)

It's a common joke that "from which easily follows that" and similar phrases are mathspeak for "I don't know the proof, but I think it's true". Seriously though, I really hate it when books do that. If it's so easily shown, then show it. Shinobu 01:01, 21 December 2006 (UTC)

A good place find examples of this type of thing is On Numbers and Games. In my copy (2nd ed.) I counted 7 identities whose "easy 1-line proofs" were omitted in Chapter 1 alone. Even in the theorems were Conway writes out the proof they're usually full of ellipses signifying "and a bunch of similar expressions" or the like. In this case it made sense; filling in those proofs and writing out everything that the ellipses represent would turn the chapter into an impenetrable forest of symbols which would, if anything, be more intimidating than the text as is. 'Easy' in this case is used in a relative sense, not necessarily easy for anyone who might pick up the book, but easy when compared to the other proofs in the chapter. The problem arises when authors abuse this kind of editorial discretion. In the corresponding Wikipedia article, Surreal number (this is a snapshot), I counted three statements that are described as easy to show or clear. In two cases the statements are easy to show from the rule x^L<x<x^R, the catch is that this rule is never stated anywhere in the article (that I could find, correct me it I'm wrong). The third statement (G + -G = 0) is one where Conway writes out the proof. In this case it might have been instructive to write out the meaning of the theorem and proof in English (which amounts to giving a winning strategy for the second player to move to win the game G + -G). There are two lessons from this little example, I think. First, if an author does use a phrase like "It's clear that ..." they must take extreme care that it really is clear from just the facts presented in the article and not using author's outside knowledge. Articles are in a constant state of flux so the facts needed for the "easy" proof may disappear tomorrow, making the proof difficult. At least the author should put a specific indication of what facts would be used in the "easy" proof, e.g. "From the principle stated above that all men are mortal, and the fact stated in the previous paragraph at Socrates was a man, it's easy to see that Socrates was mortal." Second, if the proof of a statement is mathematically trivial then it may be a good idea to translate it into plain language so that people who are not familiar with the subject can understand it and thus understand the subject better. The upshot of all this (imo) is that a certain amount of "it's easy to show... " may be useful in some cases, but for Wikipedia it will probably require such case and thought to do it appropriately that you may as well just give the proof anyway.--RDBury (talk) 00:54, 24 March 2008 (UTC)

I agree with that, and the assessment linas gives above. In most cases, if you we mention the principle from which a claim follows, it's no longer necessary to use the "easy" or "clear" phrase. Compare:

"From the principle stated above that all men are mortal, and the fact stated in the previous paragraph at Socrates was a man, it's easy to see that Socrates was mortal."

"It follows from modus ponens that, if all men are mortal and Socrates was a man (as discussed above), then Socrates was mortal."

People may (and should) consult our articles to remember why something is obvious, and expect us to tell them directly. In a textbook, by comparison, the author often wants to make the reader think through everything rather than simply telling the reader what's going on. We don't need that sort of indirect (but pedagogical) exposition. — Carl (CBM · talk) 02:01, 24 March 2008 (UTC)

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)

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)

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. $f_{\mathrm {approx} }(\cdot )$, 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)

BTW, the argument of an elementary function should be preceded by a reduced space, such as sin x.

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)

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)

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)

Colour in latex now possible

I thought that people may like to know that colour mathematics is now possible, like this: ${\color {Blue}x^{2}}+{\color {Brown}2x}-{\color {OliveGreen}1}$. —Preceding unsigned comment 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)

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)

I always use the root sign when there's a mathematical reason that the exponent is 1/integer. But I prefer not to use non-integer values that way... unless it makes the equation more readable (which is rare). Shinobu 00:53, 21 December 2006 (UTC)

Definitions: use := or \equiv?

I didn't see anything about which infix to use for definitions. Some use $\equiv$, 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)

Square and cube

Are we allowed to use ² and ³? (They're much easier to type than the alternatives.) Shinobu 18:41, 20 December 2006 (UTC)

I would use ², as it ensures universal readability. —Preceding unsigned comment added by Mets501 (talk • contribs)

I think browsers that don't get ² and ³ are just as rare as those that don't get sup. Shinobu 00:49, 21 December 2006 (UTC)

The problem is that ² and ³ look horrible in many fonts (they are usually far too small). Compare

• 1.0 g/cm³
• 1.0 g/cm³ (1.0 g/cm³)
• $1.0{\text{ g/cm}}^{3}$ (<math>1.0 \text{ g/cm}^3)

With my browser and setttings, the ^... sample is easiest to read, and the ³ by far the hardest. I don't think ¹, ², and ³ should be used at all for superscripts. It also doesn't play well with others: n² and n²ⁿ would look bad on the same page. 165.189.91.148 21:24, 26 December 2006 (UTC)

Even worse is R²ⁿ, where the superscript font sizes, weights, and baselines are different (for my viewing setup). And although superscript 1, 2, and 3 glyphs are available in common fonts, superscripts 4 through 9 and 0, and all subscript digits, are not. For me, the size of the glyphs for these Unicode characters is something like this: R²ⁿ. With such a tiny size, I have great difficulty distinguishing a 2 from a 3.

Perhaps we can help with the typing ease. The typical way to type the superscript-2 character is to use an entity name, ². One way to type a generic superscript is to manually type the tags, ². However, in both cases we have an "insert" button for the edit window, and the latter is bigger and more convenient; Fitts' law predicts it will be faster. The button that inserts the tag version is clever. If text is selected, that gets the tags wrapped around it. Otherwise, place-holder text is used, but preselected so typing replaces it. While editing, look immediately above the region containing the text for a button that looks like this: .

Incidentally, we can use the superscript and subscript tags for simple built-up fractions, like ³⁵⁵⁄₁₁₃. --KSmrq^T 07:37, 28 December 2006 (UTC)

I agree that ² etc. should not be mixed with sups. As for the ² being too small, I can't confirm that, here it looks okay. Unlike sup it doesn't interfere with the line height. So stylistically it depends on the particular situation, I'd say.

@The typical way to type the superscript-2 character is to use an entity name: no. The typical way to enter them is AltGr-2 etc. Fitts' law predicts I'll probably use ² when I'm feeling lazy. Shinobu 22:45, 28 December 2006 (UTC)

If you use ² that's fine, but be prepared for others to correct it to ² or <math>^2</math> for the reasons explained above. 24.177.112.146 05:45, 29 December 2006 (UTC)

Section on notational style

I feel that we should have some section on respect for different notational styles in mathematics articles. Something along the lines of Wikipedia:Manual_of_Style#Disputes_over_style_issues. As long as two notations are acceptable it is inappropriate for an editor to change from one style to another. There have been extremely long-winded debates over such issues (e.g. roman i vs. italic i or := vs. ≡) which always end up going nowhere and draining huge amounts of time. It would be nice to point to this article to end such debates before they get out of hand. -- Fropuff 18:33, 21 December 2006 (UTC)

Fropuff's suggestion seems important to me right now because of a current debate about notation for probabilities and common probability operators. While I have read quite a lot of stuff about probability and statistics, I honestly have never run across some of the notations people are describing in that debate, so it might be good to clarify some of that notation in this manual. I'm not saying we ought to pick one set of symbols and make it the only one, but it would be good to create a reference list of the acceptable notations for quantities like Probability, Expected value of a random variable, Variance, Covariance, etc. DavidCBryant 20:03, 22 February 2007 (UTC)

Well, I suggest using $\mathrm {P,E,Var}$. Var is especially controversial because (as it is rarely used) everyone writes it as he wants, and probably we should leave it to the editor. P and E are sometimes staight sometimes italic (e.g. Probability by Shiryaev vs Brownian Motion by Revus and Yor). I prefer straight because they are operators, I mean in TeX (ideally) they should be written as \E and \P as \sin and \sum. Please, cite some modern books on probability theory to support your opinion. Amir Aliev 21:45, 22 February 2007 (UTC)

I like $\Pr \,$, coded in TeX as \Pr, because sometimes a capital P is used for a particular probability measure, as when one writes

$E(X)=\int _{\Omega }X(\omega )\,P(d\omega ),$

etc. Michael Hardy 22:07, 24 February 2007 (UTC)

Follow-up guideline

I am working on a follow-up guideline: Wikipedia: Writing about math. It is more focused on the body rather than notation and has differences. If it passes, I would like it meged with this guideline. --Ineffable3000 23:47, 25 December 2006 (UTC)

The additions you propose run counter to the current guidelines, and are ill-advised. I would strongly object to inclusion. --KSmrq^T 06:34, 26 December 2006 (UTC)

Categories

Is there any consensus how to format categories? Sometime one sees $\mathbf {A}$ (mathbf) or A, sometimes ${\mathcal {A}}$ (mathcal). Jakob.scholbach 22:42, 12 March 2007 (UTC)

You can ask at Wikipedia talk:WikiProject Mathematics. More people watch those pages. Oleg Alexandrov (talk) 08:59, 13 March 2007 (UTC)

ISO 31 style guide

It might be a good idea to reference some of the style guidance given in international standard ISO 31, in particular ISO 31-0 and ISO 31-11. In particular the following come to mind:

• Typeset variables (including function variables) in italics (e.g., x, y, f), but all constants (e.g., 2×cos x = e^2iπx + e^−2iπx) and units of measurement (e.g., kg, m) in upright font:
• Use the multiplication sign × instead of the center dot · whenever it is adjacent to a digit (to avoid confusion with the decimal dot)
• In order to refer to the numeric value of a quantity in a given unit (e.g., "mass in milligrams"), simply divide the (unit-independent) quantity variable m by the desired unit mg: m/mg (several good examples appear the moment magnitude scale article)

Markus Kuhn 17:44, 5 May 2007 (UTC)

Partial derivatives

I always write

${\frac {\partial ^{2}f}{\partial y\,\partial x}}$

rather than

${\frac {\partial ^{2}f}{\partial y\partial x}}$

Should we have a norm prescribing this usage? Michael Hardy 18:45, 23 June 2007 (UTC)

I say yes. The first form is more legible. hajhouse 15:24, 14 November 2007 (UTC)

Font size

Hi, could anyone exlain why these two expressions are so different in size of font? Is there an easy way to make the font size larger in the second expression?

$(4/3)\pi p_{f}^{3}(r)$

$R(r)=Ar^{l}e^{-\alpha r}$

sbandrews (t) 09:08, 26 June 2007 (UTC)

Answering my own question - its because the top one has a superscript and a subscript - so:

$R(r)=Ar^{l}e_{a}^{-\alpha r}$

works although its obviously the wrong equation,

$R(r)=Ar^{l}e_{}^{-\alpha r}$

does the same with an empty subscript bracket - there must be an easier way! sbandrews (t) 14:54, 14 July 2007 (UTC)

There is! use a \ after the math tag :<math>\ R(r) = A r^l e^{-\alpha r}</math> sbandrews (t) 15:02, 14 July 2007 (UTC)

That will put extra white space at the start of the equation. I do this instead by starting the equation with \displaystyle, the standard TeX command for forcing an equation to be set using large symbols etc. \scriptstyle is sometimes also useful to make a too-large equation smaller. —David Eppstein 16:57, 23 October 2007 (UTC)

Divisions involving terms with subscripts

I'm trying to figure out how to make a legible division equation with terms that have subscripts in them (like a_beta, etc.) 204.52.215.107 16:40, 23 October 2007 (UTC)

Is Something Wrong?

In section 5.1 of this article, when the LaTeX formula is shown on its own line, it is not formatted as LaTeX. Can this be explained?

JIMOTHY46_ct 00:20, 21 November 2007 (UTC)

Never mind, I figured out the problem and corrected it myself.

JIMOTHY46_ct 00:33, 21 November 2007 (UTC)

Add links to aid contributors

It seems useful to have links to how-to-articles on forming equations for articles that otherwise are hard to find. Brews ohare (talk) 19:30, 29 November 2007 (UTC)

See Help:Displaying a formula. The link should be on the main page though, imo.--RDBury (talk) 19:29, 23 March 2008 (UTC)

Proposal to formalise the relationship between MOS and its sub-pages

Dear fellow editors—The idea is to centralise debate and consensus-gathering when there are inconsistencies between the pages.

The most straightforward way is to have MOS-central prevail, and to involve expertise from sub-pages on the talk page there, rather than the fragmentary discourse—more usually the absence of discourse and the continuing inconsistency—that characterises WP's style guideline resources now. If consensus has it that MOS-central should bend to the wording of a sub-page, so be it. But until that occurs in each case that might occasionally arise, there needs to be certainty for WPians, especially in the Featured Article process, where nominators and reviewers are sometimes confused by a left- and right-hand that say different things.

Of course, no one owns MOS-central, and we're all just as important to its running as other editors. I ask for your support and feedback HERE. Tony (talk) 12:20, 5 February 2008 (UTC)

Upper vs. lower case

Is there, and if not should there be, a convention on which types of objects are denoted with upper case letters and which with lower case? My understanding is that the current de facto standard is variables, functions and elements of sets are denoted with lower case, and sets and more complicated objects are denoted with upper case. For example, one might have "Let x be an element of the group G," rather than "Let X be an element of the group g." The standard seems to change over time, e.g. a group theory book from 50 years ago might well use X for an element of a group, so it wouldn't do to carve such a convention in stone. But it would make articles look neater if a standard matching current usage was followed. The reason I'm bringing it up is that the constant of integration in Lists of integrals is denoted C rather than c. I'm more used to seeing c and that's what I used on a different page (before I saw the first article). --RDBury (talk) 19:03, 23 March 2008 (UTC)

Any such convention would have to be specific to the subject area within mathematics. For instance, in triangle geometry (e.g. see Heron's formula) the standard convention is that vertices or other points associated with a triangle are given capital letters; edges or other lengths associated with a triangle are given lower case letters. —David Eppstein (talk) 19:25, 23 March 2008 (UTC)

Introducing notation

The Article body section has the following sentence, 'If you need to use non-standard notations, or if you introduce new notations, define them in your article.' It seems to me that, given OR guidelines, non-standard notation should rarely be used and new notations should hardly ever be used. Non-standard might be used if there doesn't seem to be any standard notation or if the the existing standard is so unwieldy that it can't be used in the article while preserving clarity. In that case the notation itself should have reference, such as 'Using the notation appearing in ...' or 'As defined in ...' If there are competing standards then the article should mention all of them and discuss the differences. A new notation might conceivably be used if there are very few sources for the topic and none of them has notation that is suitable for an article. In this case, perhaps an explanation of the situation on the talk page of the article would be appropriate. Standard notation as well should be either defined or have link to a page defining it, if it might not be familiar to someone at the level that the article is targeting.--RDBury (talk) 17:17, 27 April 2008 (UTC)

Notation can mean something as simple as a variable name. It would be pointless to go through the literature and say that this article uses x, y, and z, this other uses α, β, and γ, while a third uses P, Q, and R. Nevertheless we need to choose a variable name convention within each article and we need to say what each variable means. It would hardly count as original research, in this context, to use a different set of variable names (say i, j, and k) than any of your sources. So your comment doesn't really address this aspect of notation and of introducing new notations. —David Eppstein (talk) 18:04, 27 April 2008 (UTC)

I didn't think variable names came under the heading of notation since nobody would expect the same variables to be used outside the paragraph or section of text where they are introduced. I admit this could be a fuzzy distinction though. For example, if you wrote 'Let O be the center of circle C,' nobody would expect O to always be the center of a circle. But if you wrote 'Let O[C] mean the center of a circle C,' it would be natural to assume that this defines the expression O[X] in any context where X is a circle. My comment was intended to address only the second situation. However, variable names usually do have a standard case, typeface etc., see the previous thread. --RDBury (talk) 19:59, 27 April 2008 (UTC)

Examples revisited

It would be nice if the MOSMATH could address the issue of what sort of examples might be appropriate in a mathematical article. At present, the is the Wikipedia policy WP:NOT#TEXTBOOK seems rather firm about the inappropriateness of certain types of examples:

It is not appropriate to create or edit articles which read as textbooks, with leading questions and step-by-step problem solutions as examples.

To my mind, this clearly does not exclude the "good" examples from mathematics articles. However, I think some further stylistic advice on what kinds of examples are "good" might be helpful. I know for a fact that there have been lengthy discussions about this in the past, but now the MOS does not give much guidance on which examples are desirable, and which are undesirable.

To that end, I suggest explicitly mentioning that the purpose of an encyclopedia is to inform rather than instruct. (See this edit.) It may or may not be appropriate to do this in a separate section of the MOS so that it can receive a more comprehensive discussion. silly rabbit (talk) 12:38, 9 May 2008 (UTC)

Yes, I think many of our best math editors agree with this. We are somewhere between a CRC manual and a textbook in the amount of detail and the amount of pedagogy in our articles, and we don't want to err too far to either side. — Carl (CBM · talk) 15:27, 9 May 2008 (UTC)

Scriptstyle?

I have recently discovered the command \scriptstyle, which causes inline PNG formulas to be smaller, often aligning better with the surrounding text. For example, consider

...where $a=\partial u/\partial x=\partial v/\partial y$ and $b=\partial v/\partial x=-\partial u/\partial y$

to

...where $\scriptstyle a=\partial u/\partial x=\partial v/\partial y$ and $\scriptstyle b=\partial v/\partial x=-\partial u/\partial y$

This trick doesn't seem to be discussed here or at the meta:Help:Formula page (although I may have missed something). silly rabbit (talk) 13:36, 19 May 2008 (UTC)

Both align pretty well in my browser. The purpose of \scriptstyle is to reduce the font size for use in superscript and subscript, as well as tighter spacing. How well it aligns in text will depend on the browser font settings. What you are looking for may be \textstyle, which intends to reduce the vertical space for in-text use:

• Textstyle: blah blah blah $\textstyle \sum _{i}x_{i}+\partial y/\partial x$ blah blah blah
• Displaystyle: blah blah blah $\displaystyle \sum _{i}x_{i}+\partial y/\partial x$ blah blah blah (this is for use in stand-alone equations)

(Hmm, I see now that my Wikipedia settings your first example is converted to HTML, whereas the second and my ones are not due to the presence of the \...style commands) Han-Kwang (t) 09:39, 4 August 2008 (UTC)

Punctuation of block-displayed formulae

Lambiam and I have a disagreement on interpretation of the MoS when it comes to punctuation of block-displayed formulae which are parts of sentences. I say that

Jones suggested that the correct formula were

$g=G(t)\cdot {\frac {m_{1}\cdot m_{2}}{r^{2}}}$

is acceptable as a sentence that comes to an end, whereas Lambiam asserts that the MoS requires that this be punctuated with a period

Jones suggested that the correct formula were

$g=G(t)\cdot {\frac {m_{1}\cdot m_{2}}{r^{2}}}$.

In support of his interpretation, Lambiam notes subsection 5.3 (“Punctuation”) which states “Just as in mathematics publications, a sentence which ends with a formula must have a period at the end of the formula.” I interpret this as in reference to in-line formula elements, and support my interpretation by reference to the MoS itself, which in prior sections has multiple block-displayed formula elements that end sentences but are not followed by periods. (Lambiam notes that the MoS is not itself an article in mainspace, and in any event could simply fail to conform to its intended prescriptions while maintaining the intentions.)

We have agreed to move our disagreement here, in the hope that a consensus will support some clarification. —SlamDiego_←T 09:06, 13 June 2008 (UTC)

I believe Lambiam is correct, the formula needs a period even if it is on its own line. This is accepted mathematical practice, and is present in all mathematical books I have ever seen. Enigneering books do skip the period though. Oleg Alexandrov (talk) 14:25, 13 June 2008 (UTC)

I'm willing to accept a uniform style for mathematical expressions across disciplines, if the MoS calls for such. But I would note that, in this case, the article whose editing prompted the question is, properly, one of economic theory. If the MoS adopted a distinct prescription for engineering articles based on what prevailed in engineering articles, then a survey should properly be made of economic articles to determine a style for these. —SlamDiego_←T 19:00, 13 June 2008 (UTC)

I concur with Oleg Alexandrov. Omitting the punctuation in a displayed formula is an error, however minor, and is not done in properly typeset mathematical work. Ozob (talk) 18:16, 14 June 2008 (UTC)

Textstyle vs scriptstyle

Ozob just took out the recommendation to use scriptstyle, and replaced it with in the following:

If an in-line formula needs to be typeset in LaTeX, often better formatting can be achieved with the \textstyle{} LaTeX command. Compare the formulas <math>\sum_{n=0}^\infty 1/n^2 = \pi^2/6</math>, which produces the too tall $\sum _{n=0}^{\infty }1/n^{2}=\pi ^{2}/6$, with <math>\textstyle\sum_{n=0}^\infty 1/n^2 = \pi^2/6</math>, which produces the more compact $\textstyle \sum _{n=0}^{\infty }1/n^{2}=\pi ^{2}/6$.

My experience is that scriptstyle, while semantically wrong, works a lot better for matching typical browser text size. For this example it would be $\scriptstyle \sum _{n=0}^{\infty }1/n^{2}=\pi ^{2}/6$. In my browser, the scriptstyle version is a little smaller than the browser text, but close enough to flow with it, while the textstyle version is so huge that it might as well be a separate displayed equation. Shouldn't we be recommending scriptstyle rather than textstyle? —David Eppstein (talk) 15:57, 9 August 2008 (UTC)

Actually, I just added the scriptstyle recommendation, and Ozob corrected it to textstyle, which seemed reasonable to me. I think sometimes scriptstyle does look better for typical browser settings, but perhaps the manual should be expanded to include some discussion of both possible settings. Personally, I think the style manual should recommend textstyle for formulas displayed inline as part of the guideline, and allow for the possibility of scriptstyle for particularly troublesome cases. siℓℓy rabbit (talk) 16:14, 9 August 2008 (UTC)

I'd rather have textstyle for a few reasons:

• We can't control browser settings. If the default WP font size makes TeX markup look bad, then we should lobby for a change in TeX output.
• There are a few times when you need scriptscriptstyle, and if you start at scriptstyle the result looks bad. For instance, compare $\textstyle \sum _{i=0}^{2^{N}}$, which is textstyled, with the scriptstyled $\scriptstyle \sum _{i=0}^{2^{N}}$. In the former, the 2 is in scriptstyle and the N is in scriptscriptstyle. In the latter, both are in scriptscriptstyle and consequently the N is too big.

I agree that, given the current output of texvc, there are cases when scriptstyle is appropriate for inline equations. But the right thing to do would be to improve texvc, not use scriptstyle everywhere. Ozob (talk) 21:03, 9 August 2008 (UTC)

Agreed. How about a change that supports either textstyle (which should certainly be favored over displaystyle for inline formulas) or scriptstyle (which is good on a few rare occasions)? siℓℓy rabbit (talk) 00:07, 10 August 2008 (UTC)

I agree with Ozob. \textstyle is semantically correct and it should be a fairly trivial change to the TeX rendering engine to change the font size when an equation starts with \textstyle. It would be even better if the rendering engine could recognize automatically whether <math> tags are inlined or displayed, because the problem with both \textstyle and \displaystyle is that it overrides formatting as HTML. Han-Kwang (t) 08:18, 10 August 2008 (UTC)

It's all very well to say it's semantically correct and that it would be a trivial change to fix the rendering. It's a very different thing to actually, you know, change the rendering. If you're going to request people to use textstyle, are you also going to do anything to make their textstyle formulae less ugly? —David Eppstein (talk) 15:25, 10 August 2008 (UTC)

We could file a feature request, but it's more likely that the request wil be honored if there is a clear consensus from us about what needs to be done. The math rendering engine in Wikipedia has improved a lot over the years. It used to typeset html formulas in the default sans serif font (1, /, I, l all looked the same) and it would not recognize quite a few LaTeX commands. I think I filed bug reports for those issues somewhere in 2004 and they have been resolved. So can we build a consensus? So far rabbit, ozob, and I seem to like the idea of getting texvc changed. You? Han-Kwang (t) 16:16, 10 August 2008 (UTC)

I'm certainly in strong support of getting texvc changed in a way that would make textstyle more useful and usable. I don't have much idea how to go about getting it done. —David Eppstein (talk) 17:01, 10 August 2008 (UTC)

So, it seems that we have a problem. Browsing through old MediaWiki TeX feature requests I found [1], where one person makes the very good point that small fonts are illegible for some users. (I should have thought of this myself, as I know someone whose vision is so poor that she can hardly read.) The present situation isn't ideal for these users, but it's better than it would be with a smaller font size.

The right solution, then, would be to modify MediaWiki and texvc so that it allowed users to configure the font size used for TeX output. Then we could choose a good default and let people adjust it as needed. I'm not familiar with the internals of MediaWiki, but I would guess that it would be at least several days of work. We can still try making a request to the developers, but it would be best if we reached some sort of consensus here as to precisely what was wanted.

The first problem that occurs to me is: What exactly do we mean by "choosing a font size"? The font sizes for \textstyle, \scriptstyle, and \scriptscriptstyle are all different, so it's not a matter of choosing a single point size. It seems that we could reasonably allow a user to choose a \magstep or a single factor to multiply all the font sizes by. The available choices should be wide but not unrestricted, or else it may become possible to perform a denial of service attack by asking WP to render so many different equations in so many different sizes at once that it runs out of resources. Also, if font sizes are scaled, the TeX engine would need font metrics for each size; this is another advantage to allowing only a fixed number of choices, because then the metrics would only need to be generated once.

I'm not really an expert on TeX fonts, so I don't know what would be the best choice or even if I've exhausted the possibilities. Does anyone else have any insight? Ozob (talk) 22:16, 10 August 2008 (UTC)

Personally, I think it would be nice if the TeX renderer would make an effort to match the font and size of the existing text. Right now I'm working on some text which says something like "Corresponding to the cardinals 0, 1, 2, 3 … are the ordinals ${\dot {0}},{\dot {1}},{\dot {2}},{\dot {3}}$ …" On my browser at least, the dotted numerals are 50% larger than the other ones and in a completely different style. Also, is /scriptstyle documented anywhere? I couldn't find it in the formula help page. --RDBury (talk) 02:14, 11 August 2008 (UTC)

(Unindent) Wikipedia has, because of browser differences, a complex way of specifying the HTML font size in monobook/main.css, which boils down to 14 pixels for the main text with default 16px browser font settings. What I mean by choosing a font size is to match inline math (in \textstyle) to the default font size, even though I have my browser setup for sligthly smaller fonts. I am pretty sure that the vast majority of users stick with the default font size since it's typically located under "Advanced settings" in the browser.

The problem of small font sizes is of course that, starting from 14-pixel math fonts, subsubscripts and supersuperscripts tend to become too small. This could be dealt with by recommending in the MoS/Math that \textstyle is only used for very simple equations without fractions and nested subscripts. Displayed equations could still be shown in the current, large font sizes. That way, the smallest font that would be displayed in an equation under normal circumstances would be the same in displayed equations and textstyle equations.

Re what \scriptstyle etc. mean: they are documented in the TeXbook by Donald Knuth. \displaystyle is the default for displayed equations; \textstyle for equations in-text. Although the base font size (i.e., used for ordinary letters) is the same, large constructs such as \sum, \int, \frac are typeset differently. Inside a displayed equation, some parts are automatically formatted as \textstyle, for example when they are inside an \array or \frac. Then, \scriptstyle is for subscripts and superscripts, and \scriptscriptstyle for second-order sub- and superscripts, so they are supposed to have different sizes from \textstyle.

Re matching browser fonts: it is very hard to do this automatically. The Wikipedia CSS files only specify that the font is sans serif, which can mean different things on different computers. Math equations should not be typeset in sans serif, or you get problems reading I=l/2 (uppercase i is ell divided by 2).

Han-Kwang (t) 08:42, 11 August 2008 (UTC)

If I understand what you're proposing, you'd like to replace the default textstyle font (which is probably cmr10) with something smaller (say cmr8) and to choose appropriately smaller fonts for scriptstyle and scriptscriptstyle. I would have agreed with you a couple days ago. But since I've realized that it would make the text illegible for some users with poor vision, I have to oppose your proposal (as I understand it). We should not make the default font size any smaller until users have the option of making it larger. In fact, I believe that we should actively avoid using \scriptstyle to make an equation match the surrounding text size, because this will make it more difficult for vision impaired users. Most people with vision impairment only need a little help to be able to read. (For example, my parents are now this way.) The extra size we now have goes a long way towards helping them.

To put it more jokingly: How many mathematicians with glasses do you know? Ozob (talk) 19:25, 11 August 2008 (UTC)

Vertical alignment of formulas

In addition to the above issues with \textstyle, I'd like to propose a lobby for better vertical alignment of in-text formulas. For example the baseline of $\mathbf {E}$ sticks out below the baseline of the surrounding text. Compare with $\textstyle jx$ that is better aligned because there is a j. Currently, in the Wikipedia CSS there is the CSS rule[2]

 img.tex {  vertical-align: middle; }

and the equation is something like <img src="blabla.png" class="tex">. With some effort (requires changes in the database and mediawiki code), it could be replaced by something like <img src="blabla.png" class="tex" style="vertical-align: -5px">, where the database stores the vertical offset (-5px) with every equation, obtained during the TeX rendering process. Han-Kwang (t) 08:42, 11 August 2008 (UTC)

This bug has been open since November 2007: [3]. The correct solution seems to be to remember how many pixels the image has below the baseline and put this into an HTML tag like you propose. You might want to contact User:Random832, who opened the bug originally and who has a page demonstrating what correct output would look like at User:Random832/Math baseline. Ozob (talk) 19:31, 11 August 2008 (UTC)

ONLY since November 2007???? We've been talking about this one since the beginning of 2003. Michael Hardy (talk) 19:31, 23 August 2008 (UTC)

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 "<" 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)

Have you tried DejaVu? --Yecril (talk) 15:09, 23 September 2008 (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)

TeX is not the best, it is just incomparable to HTML. Wikitext is much stronger than HTML. --Yecril (talk) 15:09, 23 September 2008 (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)

While it is a matter of personal taste, I do not find e⁰ = 1 ugly. I admit it looks a bit different but it does not impair my ability to understand the exposition as much as the images do. --Yecril (talk) 15:09, 23 September 2008 (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.

Wikipedia is rendered in sans-serif and so let it be. The {{math}} template renders formulas in serif as required. --Yecril (talk) 15:12, 23 September 2008 (UTC)

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

Actually, Cambria is superior to Times. --Yecril (talk) 15:09, 23 September 2008 (UTC)

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)

Well certainly, albeit I vote for wikitext. --Yecril (talk) 15:09, 23 September 2008 (UTC)

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 ($\int a^{x}$) 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.

Actually, wikitext gives you a^x with a round a. --Yecril (talk) 15:27, 23 September 2008 (UTC)

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

$\cos(\omega t+\varphi _{0})$,

another article uses

$\cos(\omega t+\phi _{0})$

Why is that a problem? Incidentally, both look the same at my place. --Yecril (talk) 15:27, 23 September 2008 (UTC)

Another difference is, for example, ${\vec {x}}$ and $\mathbf {x}$ - two ways for writing vectors. An additional example is $hf=h\nu$. 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 is much harder to read actual symbols in a monospaced font used for editing. --Yecril (talk) 15:27, 23 September 2008 (UTC)

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 α, 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 ${\vec {x}}$ vs $\mathbf {x}$. We should have a guideline. Although ${\vec {x}}$ is semantically superior to $\mathbf {x}$ (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)

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:

$0\rightarrow A\rightarrow ^{u}B\rightarrow ^{v}C\rightarrow 0$

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

A →^u B --Yecril (talk) 16:01, 23 September 2008 (UTC)

You could fake it:

$0\rightarrow A\rightarrow ^{\!\!\!\!\!\!u}\ B\rightarrow ^{\!\!\!\!\!\!v}\ C\rightarrow 0$

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).

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)

Having a different font height for embedded formulas is actually a good thing because it makes them visually distinct from the enclosing text. --Yecril (talk) 17:12, 23 September 2008 (UTC)

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

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

New guideline? Explanation of symbols

Maybe there should be a guideline on how symbols are to be explained.

Example 1: The foocity is given by

$F=ba\times r,$

where b and a are the barness vector and coefficient and r is the gnat vector.

and

Example 2:The foocity is given by

$F=ba\times r,$

where

• b is the barness vector,
• a is the barness coefficient,
• r is the gnat vector.

Style 2 is used quite often in Wikipedia articles, especially in physics.[4] [5] [6] [7] (links obtained from random clicking in Category:Fundamental physics concepts; apparently style 2 is used in about 20% of the articles) However, in all professionally typeset academic-level physics and mathematics texts that I have seen, style 1 is used. Style 2 is sometimes used in high school and college level textbooks. Han-Kwang (t) 15:55, 16 July 2008 (UTC)

Any objections if I add a section recommending style 1 to the MOS page? Han-Kwang (t) 06:50, 28 July 2008 (UTC)

I object to recommending one style over another. Although I prefer the first style, presumably there are situations in which the second makes for more readable text. For instance, if the variables require more than one sentence to explain them. (See, for instance, some of the physics formulas in heat equation.) I don't feel strongly one way or the other, and I think that common sense and readability should be a good enough guide for editors to decide between which style is better suited to their needs, and that adding this recommendation to the MoS will just be more instruction creep. siℓℓy rabbit (talk) 12:47, 28 July 2008 (UTC)

I also prefer style 1 but oppose instruction creep. CRGreathouse (t | c) 18:31, 8 August 2008 (UTC)

I'm seeing far too many articles using style 2 even when every definition is just one damn single word, and many even omit the commas. So I think in this case instruction creep isn't the worse evil. --A r m y 1 9 8 7 ! ! ! 23:34, 3 September 2008 (UTC)

WP:JARGON

A couple of items related to WP:JARGON. First, in #Encyclopedic vs conversational tone above, there's a discussion about phrases such as "it should be noted". I think it would be a big help if, when copyeditors remove material, they remove it for the most accurate, least offensive, most persuasive reasons. So: removing something due to core content policy should be at the top of the list, and if that's the reason for the edit, then we shouldn't be sniping about poor word choice. Likewise, I sometimes see "it should be noted" removed with the less-than-helpful edit summary "per WEASEL". I think that's the wrong reason; "it should be noted" is common in academia in general and in math articles in particular, and in many contexts, it's not confusing at all. It means "This is important; now let me list the reasons why I think it's important". That's actually perfectly good expository writing style, in a math article, but IMO it's not appropriate for Wikipedia because it is a kind of WP:JARGON. Your neighbor doesn't say "it should be noted", and you don't read it in the newspaper or hear it on TV (unless you watch Numbers (TV series)!) It's academic-speak. So, would you guys mind if I move it out of WEASEL and WP:WORDS and into WP:JARGON?

Second, WP:JARGON now contains "... as a rule of thumb, if expressing an equation requires LaTeX (as most do), do not assume the reader will understand what it means. It is also considered polite (but not always necessary) to explain how the symbols are read, e.g. "A ⇔ B means A is true if and only if B is true". That seems like too much and not enough at the same time. It's not enough because it really should be on the style page that discusses LaTeX, which is this page. It's too much because something shorter would be less of a turn-off to some people; it would also be useful to promote this (MSM) page by pointing people here instead of trying to cover it there. Any objections to putting something like this at WP:JARGON? "Mathematical symbols can sometimes be jargon, to be avoided, written out in words, or explained and given pronunciation; see [proper section of WP:Manual of Style (mathematics)]." - Dan Dank55 (send/receive) 23:11, 19 September 2008 (UTC)

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''→''Y'' gives f:X→Y
2. Spaces: ''f'' : ''X'' → ''Y'' gives f : X → Y
3. Non-breaking spaces: ''f'' : ''X'' → ''Y'' gives f : X → Y
4. Use a style: <span style="white-space: nowrap;">''f'' : ''X'' → ''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)

Good idea. You can fix everything by adding this your monobook.css, then SHIFT+Refesh in your browser:

span.texhtml {
	white-space: nowrap;
	font-family: serif;
}

+mwtoews 21:32, 8 February 2007 (UTC)

Actually, this begs me to question: why doesn't the default monobook.css have this? Currently, it only specifies the font-family, and that's it. Would it be too much trouble to add it to the default? It doesn't make sense to break up equations using the current markup. Anyone? +mwtoews 21:39, 8 February 2007 (UTC)

I have this thing too. It should be raised at MediaWiki talk:Monobook.css, or rather at BugZilla:10438 since it now belongs to shared.css. --Yecril (talk) 17:20, 23 September 2008 (UTC)

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)

I think this is irrelevant here.

The editor may want to put any information in a box.

except that it does not look like encyclopaedia any more. --Yecril (talk) 17:52, 23 September 2008 (UTC)

Derivatives italicised?

We seem to be using a mixture of typographic styles for derivatives in Wikipedia: using either an italic or roman 'd'.

${\frac {d}{dt}}$

or

${\frac {\mathrm {d} }{\mathrm {d} t}}$

Both styles are used in the literature. The same issue applies to integrals and other uses of differentials. — ras52 (talk) 18:12, 5 December 2007 (UTC)

I looked through some the textbooks I have on my bookshelf; of the four (3 math, 1 physics) all used an italic d. It's a small sample but it convinces me to vote for italic as the standard. Besides Help:Displaying a formula already favors italic.--RDBury (talk) 19:22, 23 March 2008 (UTC)

The differential operator d is not a variable, therefore it should rather remain in roman face. --Yecril (talk) 19:05, 23 September 2008 (UTC)

It seems to me that the prevailing convention in most mathematical publications is that d should be italicized. I suppose I have seen other typesetting conventions used, but they are by far the exception rather than the rule. None of the books currently literally within arm's reach of my present position use a Roman face d. One of these books happens to be the (quite authoritative) G.H. Hardy A course in pure mathematics. Another is Hilbert and Courant's Mathematical methods in physics, Volume 2. Still another is Gaspard Monge's Application de l'analyse à la Géométrie. A number of lesser books in my immediate vicinity confirm that the past and present typographical convention is to use an italic d. siℓℓy rabbit (talk) 19:20, 23 September 2008 (UTC)

International standards for the use of math in physical science (eg. ISO 80000, previously ISO 31, also the AIP, and IUPAC style guides) specify an upright d.

Most of the best academic publishers also either expect/recommend it in their style guides (e.g. Cambridge Pniversity Press, Springer, Princeton University Press). The fact that (lazy/sloppy) authors don't adhere to this (or care much about it) and many publishers don't bother to properly edit the manuscripts they receive is no excuse for not doing the right thing in Wikipedia. Just because a maths book is authoraitative it doesn't follow that it's typsetting is also authoritative. The use of the upright d to for the differential (and upright font for descriptive subscripts/superscripts etc. is standard in well edited science texts and conveys useful information about the quantities in an equation (whether they are variables, constants, operators etc.). All scientific articles in Wikipedia should follow this convention. —Preceding unsigned comment added by 86.43.166.52 (talk • contribs) 23:14, 1 October 2008 (UTC)

Yes, upright d is what I usually use, except that in articles which already consistently use italic d I continue using it for consistency. I think the current guideline ("Both forms are correct; what is most important is to consistency within an article, with deference to previous editors.") is entirely reasonable. -- Army1987!!! 12:59, 2 October 2008 (UTC)

I think the reason for this abomination is aesthetic, not semantic. We can still have dx to preserve semantics if you insist. --Yecril (talk) 19:31, 23 September 2008 (UTC)

I have no idea what you mean. siℓℓy rabbit (talk) 21:51, 23 September 2008 (UTC)

In other words, the majority of your books write dx not because d is a symbol of the same kind as x but because dx looks unpretty. Unlike the typesetters of printed books, we can leverage the richness of HTML markup to properly differentiate between d and x without loosing the semantic difference between the two and without making the formula unpretty. Does that make sense? --Yecril (talk) 15:48, 29 September 2008 (UTC)

In the end, if the d is italiized, then I don't think there's much practical benefit to more complex wiki markup than ''dx''. We're still using PNG images for displayed formulas, after all. If we wanted properly semantic math markup we would have to switch to MathML. There's a benefit to keeping it easy for editors to edit mathematical formulas; I don't see much advantage to switching to code like {{math|<I>d</I><VAR>x</VAR>}}. — Carl (CBM · talk) 16:07, 29 September 2008 (UTC)

Yes, if it were up to me, I'd always use semantic tags wherever possible, but apostrophe-apostrophe is far more common on Wikipedia for a reason, and I'd rather be consistent with that. (The reason is that it is easier for editors not fluent in HTML. This was pointed out in the MoS somewhere, but I can't find it right now.) -- Army1987!!! 12:27, 30 September 2008 (UTC)

There was a furious discussion about this at Wikipedia talk:Manual of Style (text formatting) after an editor changed the MoS to mandate <var> for all variables; that was later reverted. The proper solution to marking semantics is content markup in MathML, but unfortunately it's quite verbose and very hard for humans to write. Ozob (talk) 15:30, 30 September 2008 (UTC)

Correct me if I am wrong. I think '' is common on Wikipedia because it resembles a quote and works like one and it is great for marking external text embedded in the current paragraph; ''' is an extension of that concept. There are other uses of italic variant that should not be quoted in this way, e.g. EM for emphasis. Bold text, where it is required for definition, can be served as a hyperlink to itself; I do not know what other uses of bold are legitimate in running text. All this has nothing to do with entering formulas that are technical by their nature and obviously require more sophisticated mechanisms (preferably templates).

Of course, expert editors that do not want to learn semantic markup should not be forced to do this; otherwise they would have no time for sharing their expert knowledge. However, they should not be encouraged to ditch the post-processing work done by markup editors.

--Yecril (talk) 15:46, 30 September 2008 (UTC)

No, '' is used because it is common typographical practice to put variables in italics. Also, you might want to look at [8] to see just how awkward it is to enter MathML content markup; but as far as I know there's no better solution. Ozob (talk) 23:13, 30 September 2008 (UTC)

There are several ways to put variables in italics, of which '' is the worst and it is not for variables exclusively, not even mainly. Per Wikipedia, Wikitext is a better solution than MathML because it does not require any client-side support.

--Yecril (talk) 09:14, 1 October 2008 (UTC)

Bad style examples

Examples of bad style should be explicitly marked as such, otherwise the readers tend to memorize them along with, or instead of, the examples of good style, especially if they come first. It should be explicit even if the example is taken out of context. I am going to add DEL+red markup to bad examples and INS markup to good examples as in my recent edit. --Yecril (talk) 16:13, 30 September 2008 (UTC)

I'm afraid I find the markup more confusing than helpful, especially the … symbol. If you do want to mark examples of bad style (and that's not a bad idea), I would suggest putting something like "(BAD)" in front of them.

More importantly, I disagree with the rule "Terms in running text should be preceded by a short English word that briefly describes what they mean" that you added. This may be good advice in some circumstances, but not all. -- Jitse Niesen (talk) 17:25, 30 September 2008 (UTC)

This is meant to be a guideline. A guideline by definition is a good advice in some circumstances but not all. In particular, it is much more natural and appropriate to use the English word describing the symbol in order to avoid starting a sentence with a symbol than to invent conjunctions for the purpose as the current text does. How do you recommend differentiating between BAD because missing and BAD because present?

I would appreciate an example where obeying this guideline would be detrimental to the content. --Yecril (talk) 18:07, 30 September 2008 (UTC)

Is this discussion about this text [9]?

• Terms in running text should be preceded by a short English word that briefly describes what they mean:

• Any group G that fulfills the conditions above may be decomposed into cosets as follows.
• Let H be the corresponding subgroup of the group G. Then the group H must be finite.

Doing so will make the text easier to understand when it is being listened to. This recommendation does not apply to embedded statements like x = 0.

That style differs from all published mathematics I am used to, and all mathematical writing style guides I have seen. Of course the first use of a variable has to explain what the variable represents; but uses after that don't need to repeat that. This is the purpose of variables, after all.

More fundamentally, the variables in the terms above aren't needed at all and should be omitted:

• Any group that fulfills the conditions above may be decomposed into cosets as follows.
• Any such subgroup of the original group must be finite.

— Carl (CBM · talk) 02:02, 1 October 2008 (UTC)

Of course, the example was trivial so that it can be short, and no wonder it can be simplified further. I agree it is best to write without any symbols at all; it was meant to demonstrate the recommended style when symbols are necessary.

The purpose of variables is to name objects; the purpose of the introductory word is to explain that the following letter is a name for an object. I agree it is not necessary for names as Peter; however, it is common to write e.g.  the village Tucaneoa. The problem is even more acute with mathematics than with geography because mathematical formulae are generally harder to pronounce.

I am afraid most mathematical books out there are not meant to be read aloud.

--Yecril (talk) 09:25, 1 October 2008 (UTC)

Also when speaking, I think these words are often not necessary (and in fact harmful). For instance, in the example

"Let H be the corresponding subgroup of the group G. Then the group H must be finite."

I think the second "the group" should not be there, regardless of whether the text is written down or spoken. It's an ugly repetition and unnecessary. The first "the group" may be useful to remind the reader what G is, depending on the context. This is assuming that the variables do need to be introduced. And of course, most people read Wikipedia from the screen, so that should guide our writing.

In answer to your earlier comments, a sentence with should in the Wikipedia Manual of Style is supposed to be valid in almost all situations and entertain only the occasional exception.

In reply to "How do you recommend differentiating between BAD because missing and BAD because present?": By putting bad and corrected examples next to each other, it's clear what is bad about the bad example. So, I would write the current examples as something like

(BAD) Suppose that G is a group. G can be decomposed into cosets, as follows.

(GOOD) If G is a group, then G may be decomposed into cosets as follows.

and I would probably add some formatting so that the examples line up and there is some spacing between the tags (BAD) and (GOOD) and the actual text. -- Jitse Niesen (talk) 11:01, 1 October 2008 (UTC)

Is it possible to write down a recommendation that is advisory and not obligatory? Because I still think this style would make things easier for people who cannot read.

Besides, as User:CBM correctly noticed, the example marked as GOOD is still BAD, although in a different way. --Yecril (talk) 21:34, 5 October 2008 (UTC)

templates for established symbols

I am considering the possibility of making a template for π and π to discern the two in formulae. Another option would be π and π. The advantage to the reader would be that she can hover over the symbol do discover its meaning. I am not sure how these templates should be named; perhaps {{math/perim}} and {{math/pcf}}? --Yecril (talk) 21:47, 5 October 2008 (UTC)

It seems to me that consistent use of the latter two templates would lead to overlinking. It's fine the first time, but what about the twentieth? As for the first two, I don't see what benefit they provide, since the <span>s that you insert don't get styled. (And how would you style them, since they're both just a pi?) Ozob (talk) 01:28, 6 October 2008 (UTC)

Hover over the symbol to see the benefit. This agrees with what you do when you see something you do not know: you focus on it, you examine it, and, quite probably, you move the mouse pointer over it. I need your opinion about which way of doing this is fine: a wikilink, which also provides a title but happens to change the colour as well, or a plain title. I am concerned with overlinking as well so it seems having just the title is a bit safer. --Yecril (talk) 13:00, 6 October 2008 (UTC)

Myself, I don't think these are needed, for the general reason that we should used text to explain things. If it isn't clear that π is meant to be the prime counting function, then the article should come out and say it, not hope the reader will hover over the symbol. This improves the prose, is still usable when the article is printed or viewed without a mouse, and is generally better expository style.

In any case, don't start any massive changeover to the new style without getting some agreement first about it. This is true of any massive style change; these are not well received in general. — Carl (CBM · talk) 14:08, 6 October 2008 (UTC)

For example, this is a textbook example of where these templates are not needed. The very same sentence already explains clearly what the symbols represent. — Carl (CBM · talk) 14:40, 6 October 2008 (UTC)

I never opposed using plain text to introduce things, or suggested that special templates could be used instead; I only think it can be a convenient reminder to the reader when it is likely that a formula would make him scratch his head. And you cannot explain things in the middle of the formula so the user has to scroll somewhere else, losing context. In a printed work, you have to look it up in an index of symbols, where you can find the right meaning if you are lucky. An interactive medium such as HTML can do better than that.

I included the templates in new sections in case only one section is selected to be viewed. --Yecril (talk) 14:50, 6 October 2008 (UTC)

A reader in the middle of the article on Skewes' number is unlikely to forget that the π, which just a moment ago represented the prime counting function, still represents it. If they did for get that, readers would just scan around for the definition. The benefit to the templates seems to be mainly hypothetical. — Carl (CBM · talk) 15:56, 6 October 2008 (UTC)

Having links within formulas is seldom a good thing to do. Not only do they look extra-ugly to people who have set "Underline links: Always" in their preference (though I believe that they deserve that! :-) ), but also see the last-but-one point in Wikipedia:Access#Text. I once viewed a Wikipedia article on a cellphone, and I wasn't able to see where links pointed by "hovering" on them. It is much better to explain what symbols means, when it's not obvious from context. (BTW, I think you meant to link pi, not Perimeter.) -- Army1987 (t — c) 15:16, 7 October 2008 (UTC)

Using HTML attributes

$\lim _{h\to 0}{f(x+h)-f(x) \over {h}}.$ So apparently we can treat the math tags like any HTML tag, add style to them, change the border, and even add an alternate description. So my question is how to best give an alternate description to the equation above.

The limit as h approaches zero of the difference between f of (x + h) and f of x over h

Is it understandable? Too wordy? — Dispenser 03:09, 20 October 2008 (UTC)

The alternate text defaults to the contents of the math tags (in this case: \lim_{h \to 0}{f(x+h) - f(x)\over{h}}.) People familiar with LaTeX will find that very clear because that is what they are used to. On the other hand, it will mystify people that do not know LaTeX. The problem with your text is that it is ambiguous; apart from the formula to the right, it can also refer to $\lim _{h\to 0}f(x+h)-{f(x) \over {h}}$ or $\lim _{h\to 0}f(x+h)-f({x \over h})$. -- Jitse Niesen (talk) 12:22, 20 October 2008 (UTC)

The LaTex does not fit well with the "Imagine you're writing for an audio cassette" suggestion for alt text. — Dispenser 13:33, 20 October 2008 (UTC)

At present I don't think <math> allows us to specify alt text; the only choice is raw LaTeX. Ozob (talk) 17:50, 20 October 2008 (UTC)

If you do a view source of this section you see that the alt text of the equation is the text above rather than the latex. My fealing at the moment is that loss of information is marginally worse than not knowing latex. The effort of adding specific alt text probably does not justify the advantage. --Salix (talk): 18:47, 20 October 2008 (UTC)

Too wordy, but "The limit as h → 0 of the ratio between f(x + h) − f(x) and h" would be better (but I understand that was meant to be an example). Army1987 (t — c) 12:13, 21 October 2008 (UTC)

Latex should be preferred over HTML

I would like to raise concerns about the guidelines for the use of HTML-based 'sub' and 'sup' tags for creating simple mathematical formula in Wikipedia. I think that these HTML tags do a rather bad job of separating content from style: I think that all mathematical entities should be surrounded by <math></math> tags,nd we shouldn't have multiple ways of writing such things. Down the track, Mediawiki will surely become better software, and the minor issues of line-alignment, font sizing, etc will be overcome, and with <math></math> tags we will have a much clearer markup that reflects the true meaning of what is being written, eg an italicised 'c' is not a mathematical thing, but $c$ clearly is. User preferences could then be harnessed to highlight mathematical objects in a different color, etc, etc, but this is only possible if users are discouraged from 'hacking' math using HTML. Furthermore it saves people from having to learn two entirely different markup systems (eg HTML entities for the infinity character, versus latex markup for the infinity character).

I think that use of <math></math> tags is the future-proof semantic markup that we should be using, and it really does do the job of separating style from content in a way that HTML does not. Jdpipe (talk) 11:21, 23 October 2008 (UTC)

These "minor" issues of line-alignment, font sizing, etc. have been pointed out a gazillion times for ages, and they were never overcome, so why are you so optimistic for the future? (Not to mention the fact that too many PNG images make pages take longer to load.) -- Army1987 (t — c) 12:54, 23 October 2008 (UTC)

Maybe it is time for a FAQ about why certain controversial guidelines are the way the are. Han-Kwang (t) 14:16, 23 October 2008 (UTC)

Use of unicode characters for exponents in units of measurement

When typing values for measurements that include units of measurement, it is vastly more readable when editing a page if the writer has used unicode characters as in N/m², compared to N/m<sup>2</math> or even worse Nċm^-2. It's not hard to learn how to type these special characters, and they do make editing a much more pleasurable process. Furthermore, these unicode characters render correctly in text-only browsers such as Elinks and Lynx, but superscript characters do not (contrary to what is stated in this Manual of Style page). The argument is made that using these <sup> tags somehow aids separation of style and contents. This is a dud argument, because the superscript location of the '2' in W/m² is part of its meaning -- this is not a '2' in the sense of 'multiplied by', so without its correct position, it means something else.

The argument about using <sup> for mathematical formulae is what I argued against earlier. For units of measurement the case is different however, because exponents greater than 3 in units of measurement are extremely rare. I can only think of the stefan-boltzmann constant as a case where higher exponents are used in units of measurement. Given that digits up to 3 are available in standard fonts in unicode, I think it is best to use them for units, so that values can be easily read by as many users as possible, and without clogging up pages with excessive markup. For particularly complex units of measurement, I think that using HTML markup is appropriate, but this happens only quite rarely.

Units of measurement within mathematical formulae are another case; obviously then latex markup (nonitalics) must be used.

Jdpipe (talk) 11:21, 23 October 2008 (UTC)

As for "separation of style and contents", we use <sup>, not <span style="whatever the CSS for superscript is">, so what do you mean exactly? -- Army1987 (t — c) 12:57, 23 October 2008 (UTC)

The separation I'm talking about is ² which means 'squared' (note: means) and ², which conveys that a '2' is to be placed in a high place -- this is a typographic style thing, and meaning is not conveyed in the same clean and succinct way (and furthermore is unrenderable in text-only browsers, FWIW). Jdpipe (talk) 12:50, 24 November 2008 (UTC)

No, the unicode character does not mean "squared". It means "high 2". I'm not saying it should or should not be used on units, just that the argument is faulty. — Arthur Rubin (talk) 21:44, 24 November 2008 (UTC)

Long numbers

Consider the value of π in Pi:

We currently have: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 582

Greg L would have us use: 3.14159265358979323846264338327950288419716939937510582

I think this is both ugly to edit and difficult to read, in spite of the international standards for 3-digit spacing. — Arthur Rubin (talk) 22:28, 7 October 2008 (UTC)

How ugly it is to edit can be seen that the last "span style" got mangled when I attempted to copy it from his draft of Pi, causing the last margin to be negative. — Arthur Rubin (talk) 22:37, 7 October 2008 (UTC)

My proposal is that mathematical constants should have 5-digit spacing after the decimal point, especially if there are more than 12 digits after the decimal point. — Arthur Rubin (talk) 22:39, 7 October 2008 (UTC)

• This is absurd. Delimiting every three digits it is done on Wikipedia in accordance to

1. BIMP: 5.3.4 Formatting numbers, and the decimal marker, and per
2. NIST More on Printing and Using Symbols and Numbers in Scientific and Technical Documents: 10.5.3, Grouping digits, and
3. ISO (which follows what the BIPM says)

Greg L (talk) 23:15, 7 October 2008 (UTC)

We don't follow the "international standards" on KiB / MiB, because no one in the real world does. This case isn't as bad, but it would be interesting to compare representations of numbers of more than 20 digits, rather than just normal 7-digit physical quantities. This case isn't as extreme, but the de facto standard in mathematics articles, for numbers of over 12–15 decimal places, is undoubtably 5-digit grouping. To do otherwise requires a consensus for change. — Arthur Rubin (talk) 23:26, 7 October 2008 (UTC)

• Is that the best argument you can make? There was no “international standard” with regard to the IEC’s proposal on the binary prefixes (KiB, etc.). Why? Because it was just that: a “proposal.” And if flew like a wet noodle. After ten years, no computer manufacturer still adopted the proposal when communicating to their end users. Wikipedia wisely decided to follow the way the real world works and use the conventional binary prefixes (megabyte, etc.), notwithstanding their shortcomings.

  Now stop trying to divert us away from the real issue here and get busy and provide some evidence for us to back up your allegation that the mathematics world decided to flout the rule of the SI (and the NIST and the ISO) and standardize on delimiting numbers every five digits to the right of the decimal marker. I think you are wrong about your facts. Greg L (talk) 23:56, 7 October 2008 (UTC)

Dicklyon gives some examples of real-world examples of the five-digit grouping at Talk:Pi#delimiting values every five digits. Apparently a majority of books (based on a Google books search) prefer to split Pi into five digit groups. However, I have no strong opinion either way on the matter. siℓℓy rabbit (talk) 00:17, 8 October 2008 (UTC)

• I think Pi is a special exception to the general rule and will back off on demanding that it conform to the rule of the SI. People are fascinated with counting all those digits, and groups of five helps. Still…

  I think we need to resolve whether there is any truth to the suggestion that mathematics departs from what is clearly spelled out by the BIPM for compliance with the SI (and which is further supported by the NIST and the ISO) with regard to delimiting every three digits on the fractional side of significands.

  If a Ph.D. mathematician who has had a couple of papers published can weigh in here and resolve this issue, that would be much appreciated. If it can be shown that mathematics flouts the rule of the SI and there is a well-established style in the mathematics world, then, please advise. Short of any proof that mathematics marches to the tune of a different drummer, it is too unwieldily to discuss this in two forums. May I suggest we keep this all here on WT:MOSNUM? Greg L (talk) 04:21, 8 October 2008 (UTC)

Abramowitz and Stegun is the canonical book of tables of (and identities for and other information on) special functions for applied mathematicians and physical scientists. It uses groups of five digits throughout. That is the only relevant source that I have to hand, and it may be that it is an unusual exception — but the five digit groupings do seem to add to the readability of A&S's tables. — ras52 (talk) 07:50, 8 October 2008 (UTC)

I do not concur with keeping this at WT:MOSNUM. I was proposing this as a guideline here even if there were a guideline for 3-digit grouping at WP:MOSNUM. (In fact, I thought there was a guideline there, except that, after some research, I discovered that Greg L had recently placed it there without evidence of consensus.)

Also, most mathematicians don't work with numbers, as oxymoronic as that might appear, so number formatting issues are not at the forefront of their thoughts.

Finally, see Arthur Rubin for a few publications, none of which have actual numbers in them. — Arthur Rubin (talk) 18:07, 8 October 2008 (UTC)

I believe the mathematical convention is no spaces at all. This is what's used in the OEIS, for example. It's also used in Ribenboim's The Little book of Bigger Primes. It may seem counterintuitive, but as Arthur Rubin notes, we don't work with numbers, only letters. (I once told a literature person that, and she said with a smile, "Oh! Then we do exactly the same thing!") Ozob (talk) 21:36, 8 October 2008 (UTC)

This should therefore be referred to a chemist or physicist. In lieu thereof, I cite the CRC Handbook, 84th edition. Their Table of Fundamental physical constants, at the beginning of section 1, spaces every three decimal places; almost all the other long decimals do not space. Their mathematical tables used to space every 5 decimal places, but are now published separately.

This is the merely rational way to do things; do what is clearest in each place, without the hobgoblin of a foolish consistency getting in the way. MOSNUM, even more than the rest of MOS, is a waste of time, imposed on us by bot, to satisfy the will to authority of a handful of "editors" who find it easier to invent rules than to actually contribute content or convince others to do what they would like.

When it is unprotected from its latest edit war, it should be considered whether any of it should be a guideline at all. Septentrionalis PMAnderson 05:38, 26 November 2008 (UTC)

Transpose

Please forgive if this is the wrong guideline, but looking through the Linear regression articles, I've noticed a plethora of notations for the transpose of a matrix X.

1. $X'\,$ (X')
2. $X^{T}\,$ (X^T)
3. $X^{\mathrm {T} }\,$ (X^\mathrm T)
4. $X^{\top }\,$ (X^\top)

Number 2 is obviously bad, and I think number 1 is hopeless; if we ever start differentiating, the ambiguities are obvious. I'd like to propose that we standardize on number 4, or with possibly number 3 as an option. — Arthur Rubin (talk) 15:36, 7 November 2008 (UTC)

Writing

$A'\,$

for the transpose of the matrix A is done far more frequently in the statistics literature than is the superscript-T notation for transpose. It's also done in Herstein's Topics in Algebra, but the superscript-T is used in Weisberg's Applied Linear Regression, so I privately jocularly thing of the superscript-T notation as the Weisberg notation and the prime notation as the Herstein notation. Michael Hardy (talk) 17:37, 7 November 2008 (UTC)

Hasn't anyone seen $X'$ as the derivative of X with respect to time a spacial parameter? (In fact, last year, I had occasion to try to describe the derivative of a matrix with respect to time, where the matrix is a function of other time-varying matrices and vectors. I didn't use that notation, because it was specifically forbidden by our style manual, but....) — Arthur Rubin (talk) 18:32, 7 November 2008 (UTC) (changed 16:06, 26 November 2008 (UTC))

I use $X'$ for the derivative of a matrix. I checked seven books in my bookcase and all seven use option 2 so I wouldn't call it obviously bad. As far as I'm concerned, we don't need to standardize this. -- Jitse Niesen (talk) 16:48, 26 November 2008 (UTC)

Lay person's understanding

I know this will probably be considered anathema to many here, but, if possible, shouldn't a mathematics-related article explain the topic in lay language? Currently, the manual of style, suggests that math-related articles be written in simple terms. But, an overwhelming number of articles seem to consider "simple terms" to be paired down definitions that are still, alas, filled with technical nomenclature and jargon. A "simple" intro that still has four or five blue-colored (linked) jargon-words that a lay person would have to look up is not really that simple. The definition may be simple to you and me, but I don't get the sense that it would be for most people. The article, Pell number, is an example of an Wiki entry whose intro ought to be clearer for lay people. Now this isn't always possible, and, often, an introduction will try its best to be intelligible to a wide audience but will inevitably leave some readers scratching their heads. But, if possible, simplification of introductions should be achieved. If others agree, perhaps, this instruction can be added to the Manual of Style for mathematics. In the end, the more people that understand Wikipedia's mathematics articles, the better it is for the math as a whole, no? ask123 (talk) 15:45, 26 November 2008 (UTC)

If possible are the key words here. What is the lay language for non-linear partial differential equation? Septentrionalis PMAnderson 16:44, 26 November 2008 (UTC)

I just read the first three paragraphs of Pell number, and I think reasonable high-school students would understand. (But "lay person" usually means someone who doesn't know high-school math.) Michael Hardy (talk) 23:29, 26 November 2008 (UTC)

It's been considerably rewritten since it was tagged. Septentrionalis PMAnderson 19:07, 28 November 2008 (UTC)

Analogy

I draw an analogy to this page over at WT:Layout#Proposal; if my analogy is wrong, let me know (either there or here, depending on where you want the thread). - Dan Dank55 (send/receive) 18:19, 12 December 2008 (UTC)

C function?

continuous function is...a function from one topological space to another that preserves open sets? That is loosely speaking? That DO is wrong. It is open map.--刻意 21:14, 20 December 2008 (UTC)

Hidden proofs

I've tried to revive the discussion on different styles of proof over at Wikipedia talk:WikiProject Mathematics/Proofs - please come join the discussion! I was torn as whether to put it here or there... SetaLyas (talk) 11:18, 28 December 2008 (UTC)

Redundancy in descriptions

I and another editor disagree over the phrase "square, symmetric, positive definite matrix" in the Matrix decomposition article. I am of the opinion that squareness is implied by symmetric and therefore redundant. He takes the point of view that "some readers may not notice that symmetric implies square, so the redundancy makes it clearer". I disagree with that too but that's not really relevant to my current posting. (It's not really an argument between us as there has only been one revert but it raised for the first time for me an important question about Wikipedia's approach to these type of situations.) Obviously the Wikipedia:Use common sense guideline is always in effect but in this case it's not so clear which makes more sense. Could somebody point more to a section of the MoS that advises on redundancy issues? I skimmed Wikipedia:Manual of Style (mathematics) but did not find a section that addresses this problem specifically. Advice appreciated too. Jason Quinn (talk) 14:00, 20 February 2009 (UTC)

I doubt there is a specific guideline. I take no position on what is most clear in this case—calling the matrix square might help some readers, but it might wrongly suggest to others that there is a definition of a non-square symmetric positive definite matrix. If you and the other editors cannot come to an agreement as to what is most clear, you might try asking on Wikipedia talk:WikiProject Mathematics. Ozob (talk) 21:27, 20 February 2009 (UTC)

The readers who "may not notice that symmetric implies square" are the ones who just don't know what symmetric means in that context, so saying "square, symmetric" isn't going to help them any more than just "symmetric": in order to understand that sentence, they would have to look up "Symmetric matrix" anyway, which starts with "In linear algebra, a symmetric matrix is a square matrix ...". So I would be slightly in favour of omitting square there. --A. di M. (talk) 12:06, 23 February 2009 (UTC)

Using scriptstyle to make in-line symbols "fit"

User:CBM and I are having a discussion (User talk:CBM#MSE) about the use of \scriptstyle to adjust symbol size. Symbols with decorations (hat or tilde, for example) automatically display as PNG, and those without, or with simple super/sub scripts, displayed as HTML. When I was working on the Maximum spacing estimation article, I used \ss to make many of the decorated symbols appear "normalized" (in my opinion) with the in-line HTML, as I had my settings set as per the MoS (HTML if simple, PNG otherwise). CBM believes that they should always be shown as displaystyle, and the simple ones forced to display using \,. I pointed out that this was not in agreement with the Math MoS, and he suggested that we bring this for discussion here, as scriptstyle is too small in his opinion. Here is how the scriptstyle looks on my browser (FF 3.0 under WindowsXP) [10]. Here is a comparison on CBM's browser [11]. The article as it stands now has CBM's changes in it. What is the opinion of the greater WP:MATH community on this? Thank you. -- Avi (talk) 18:57, 6 March 2009 (UTC)

Both look bad. Why not use clean LaTeX source and simply wait for the math rendering to get fixed one day. If Planetmath can do it and commercial publishers can do it why not Wikipedia? Then there will be a lot of kludges to fix. Why add to them? Jmath666 (talk) 04:05, 9 March 2009 (UTC)

Because it has been so badly broken for so long (for many years), with not the smallest step taken towards fixing it, that even the most optimistic person has stopped hoping it will ever be fixed? Ghod, can't even show $-1$ in non-PNG mode without a space between the minus and the one which shouldn't be there... --A. di M. (talk) 07:31, 9 March 2009 (UTC)

I would say that scriptstyle is slightly too small, displaystyle is way too big, so the first is better. But Jmath666 might have a point... And what about the problem that inline math $g$ is very different from displayed $g\,?$ Some people write italic g to avoid this, but then, italic f is disastrous, so some people use ƒ, about which I have no idea where it comes from. A di M (Al di Meola?), what do you suggest for this problem? All of this is ridiculous and hopeless to optimize, I'm afraid. So, arriving at the end of this paragraph, I say that Jmath666 is right, and for the sake of our mental health, we should just write in normal LaTeX, and accept that it looks bad on wikipedia... A question: on WHOM or WHAT does it depend on when this rendering will be fixed? --GaborPete (talk) 08:08, 9 March 2009 (UTC)

Ultimately, the MediaWiki developers. However, they currently depend on a package called texvc. While several people have tried making replacements, so far none of them has displaced texvc. Ozob (talk) 18:20, 9 March 2009 (UTC)

My understanding is that texvc is just a wrapper for LaTeX. It doesn't directly participate in the process of generating PNG images for the Wiki software. That job still belongs to LaTeX. So unless the Wiki development team is currently working on a replacement for LaTeX — which is extremely unlikely at any point in the foreseeable future — I suspect that this is a permanent problem with TeX on Wikipedia. Workarounds should therefore be encouraged, within reasonable limits. Sławomir Biały (talk) 16:23, 17 May 2009 (UTC)

Perhaps you mean replacement of a particular LaTeX rendering package that wikipedia uses and which is not working properly? LaTeX as such is fine. Other sites I mentioned above use LaTeX too and all is well there. Jmath666 (talk) 16:44, 17 May 2009 (UTC)

Layperson's understanding

I agree with the top post in this discussion page. I just came here to say exactly that, and noticed that somebody already had. I'd like to extend the notion a little bit to say that, even if Wikipedia is not *obligated* (ethically, or according to its own policies) to provide layman's explanations, it would really be nice if there were such an encyclopedia mathematica for laymen somewhere, and what better medium than Wikipedia to be that.

The problem with explaining mathematical ideas in jargon terms is that the learning curve for people who aren't already highly educated in mathematics to learn about a concept this way is ridiculously steep, maybe not even practical. Perhaps you might argue that someone not highly educated in mathematics wouldn't need to look up things like, for example, 4-d rotation, or how to make a Bezier spline, but I've found myself in this position *often*. Wikipedia could be a great portal between the layman's and the mathematician's worlds.

I'm sure those who *do* know their maths could argue that they shouldn't have to wade through descriptions put into layman's terms where a more concise terminology would suit them better, but I'm not proposing that the layman's-terms descriptions act as a replacement for the concise definitions - just that writing additional sections where things are thoroughly (or even summarily) explained in simple terms in a guiding way could be encouraged.

Also I'd like to see more algorithms posted for how to arrive at mathematical results. That's usually what I basically need, and having an algorithm there would be 1000x easier for me than trying to understand an abstract mathematical description and then coming up with my own algorithm. And even to people who understand these terms, I would think a formal definition alone doesn't necessarily imply some highly efficient algorithm for arriving at the given result that some mathematician may have come up with.

Maybe not every article can guide a layman to an understanding of the mathematical concept in a self-contained manner without including an entire lecture series in higher maths, but between having links to other articles and striking a good balance between generality and specificity, I think a very informative middle-ground could often be reached.

Inhahe (talk) 19:21, 20 April 2009 (UTC)

This question arises frequently. The consensus as I understand it is that while some mathematical articles are poorly written, much of the underlying content is difficult and cannot be made substantially easier to grasp. I invite you to browse the archives of Wikipedia talk:WikiProject Mathematics, where you'll find more discussion of this. Ozob (talk) 20:41, 20 April 2009 (UTC)

Blackboard bold

Is there a consensus as to when it's appropriate to use blackboard bold and when not? Right now, the MOS has a section, WP:MOSMATH#Common_sets_of_numbers, which, in my opinion, can be read to endorse either bold or blackboard bold for, e.g., the real numbers R, the complex numbers C, or the quaternions H. My own opinion is that blackboard bold is ugly and hard to read in print: The two vertical lines create a sharp, distracting contrast between whitespace and ink. For this reason I prefer to use blackboard bold only on blackboards. But we don't seem to have a policy. This became an issue recently at quaternion when an anonymous user switched boldface to blackboard bold and User:Virginia-American and I disagreed over which we should use. Does anyone have an argument for one or the other? Ozob (talk) 14:44, 2 June 2009 (UTC)

You have already stated the argument for using simply bold: it is typographically superior. On the other hand, many (most?) professionally published mathematics texts nowadays use blackboard bold in print, and the appearance is decent enough. The wikipedia tradition for these sorts of minor issues is to leave each article as it was formatted by the first major editor. — Carl (CBM · talk) 14:48, 2 June 2009 (UTC)

I would suggest the guiding principle should be simple: do what ever the majority of recent sources do. — ras52 (talk) 15:29, 2 June 2009 (UTC)

Angle brackets

Is there a preference with respect to the usage of "proper" Unicode angle brackets versus "faking" them with less than/greater than signs? Apparently, the angle brackets in an expression like 〈v,w〉 (using ⟨ and ⟩) are not displayed properly for many users. Should one write this expression as <v,w> instead? —Tobias Bergemann (talk) 08:50, 10 June 2009 (UTC)

The proper use are the r/l angles. If they don't display correctly, these won't be the only things to not display correctly. This isn't the internet of 1995, and any modern browser uses default fonts which supports them.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 06:49, 25 June 2009 (UTC)

Good advice

can be found at http://www.maths.ox.ac.uk/files/study-guide/index.shtml, esp. part II. I found this info out far too late to be of any use to me, but I felt good knowing that someone made explicit the process of writing theorems (or I was away at the lecture they told everyone else)...

Perhaps this should be basic knowledge for anyone actually writing a maths article on WP. Otherwise a link to it may be helpful. 118.90.74.32 (talk) 02:22, 16 July 2009 (UTC)

Italicization of π / Pi

The Greek letter pi is italicized in some parts of the Pi article, and roman in others. That needs to be fixed, but which is correct?

67.171.43.170 (talk) 02:37, 17 September 2008 (UTC)

Pi should be italicized; π should not be. Septentrionalis PMAnderson 16:58, 20 September 2008 (UTC)

Not exactly consensus, but I agree and boldly made the change throughout (in celebration of this glorious day), but e still appears italicized. Note that, as a constant, this is different from the several variables that appear italicized (d, r, etc.), although I'm not 100% sure what's proper there, either. Out of curiosity, would $\pi$ be an option for the article body? Or $e$? /Ninly (talk) 16:04, 14 March 2009 (UTC)

WRONG. π should always be italic, for the following reasons..

1. The tradition of mathematical typography is to italicize π. There is discussion of whether this is 'correct' but the lower-case italic form $\pi$ is the most widespread in the literature. (π is italic when it denotes the standard meaning of pi in trigonometry, calculus, physics, etc -- but deviant statisticians use π and Π to symbolize other stuff).
2. MathML, LaTeX, and Wikipedia tags {{math}} or <math> all italicize $\pi$.
3. From Edward Tufte's website:
“ These traditions are hundreds of years old. Italics help distinguish between variables and other things like numbers and operators. For instance cosine of x is written "cos $x\,\!$". (This issue comes up in other symbolic systems; programmers need that distinction too, but today almost universally use color coding instead.) But like any centuries-old tradition, there are a lot of quirks, for example vector variables are sometimes bold, non-italic. Also which letters you use for which variables is important. A lot of today's traditions were introduced by Descartes, like using the end of the alphabet for unknowns and the beginning for known quantities. At one point people used vowels vs. consonants, I think, but no longer. ”
4. According to Stephen Wolfram:
“ One of the things that Euler did that is quite famous is to popularize the letter $\pi$ for pi--a notation that had originally been suggested by a character called William Jones, who thought of it as a shorthand for the word perimeter. ”
5. Most fonts are non-mathematical and render π as "π" (non-italic). But mathematical typesetting packages render \pi as "$\pi \,\!$" (italic).
6. The Pi article even shows this italic image of the letter! ---

I believe this article should follow mathematical convention, so I would prefer to italicize the π's. Any objections? ~~ Ropata (talk) 05:38, 17 June 2009 (UTC)

The Wikipedia Manual of Style clearly asks not to italicize π (or any other Greek letters for that matter, except possibly when they are variables). The discussion really belongs to WT:MSM, not here. — Emil J. 11:54, 17 June 2009 (UTC)

The discussion is already here, not at WT:MSM. The Manual of Style does not enforce rules, it merely states a few conventions. Wikipedia ought to follow mathematical convention not reinvent it. ~~ Ropata (talk) 11:00, 20 June 2009 (UTC)

That the discussion already started here does not make the choice any more appropriate. People who are interested in conventions for formatting Greek math symbols are supposed to watch the MoS page, they are not supposed to watch every article which uses the symbols such as this one. — Emil J. 14:25, 23 June 2009 (UTC)

My understanding is that italicizing Greek is redundant because Greek letters are already somewhat slanted (or at least their supposed be even though some computer fonts don't show them that way. For another project Angr wrote:

The Greek alphabet doesn't distinguish between italic and roman types; Greek letters themselves are usually printed slightly inclined to the right, especially in fonts used for Ancient Greek rather than Modern Greek. (Modern Greek fonts are often assimilated to the Latin alphabet, having completely vertical lines and distinguishing between serif and sans-serif fonts.) At any rate, even though the Greek will look slightly italicized to people used to the Latin alphabet, it shouldn't be set as italics.

--RDBury (talk) 05:37, 25 June 2009 (UTC)

π should be italicized in a math context because that matches TeX style, and obviously we do use TeX. If writing words in Greek, then one follows different rules outside of the jurisdiction of the WP:MOSMATH policy page. Clearly "sin θ" looks different from "sin θ".

It is not clear that Angr was writing about mathematical typesetting! (If so, he was wrong because TeX italicizes the lower-case π. If not, then he shouldn't get quoted as an authority in this discussion.) Michael Hardy (talk) 00:10, 29 July 2009 (UTC)

The TeX argument is bogus, TeX italicizes all letters by default. \gamma\pi\rho\mu gives $\gamma \pi \rho \mu$. Pi as a constant is straight, Pi as a variable is italicized. A diameter of 3π but A parity eignenvalue of π = 1. Like wise sin is straight when it means the sine, and italicized when it means s*i*n. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 18:22, 4 August 2009 (UTC)

Not really, constants and variables should both be in italics. Function names and the like should be in simle Roman. ~~ Dr Dec (Talk) ~~ 18:29, 4 August 2009 (UTC)

Inline math notation

(moved from Talk:Torque)

So, apparently inline LaTeX is discouraged, but not prohibited. From the guidelines it is seen that you still can use LaTeX without getting the full size PNG, which keeps the height of the line almost the same as when using text. For example, $\tau$ is obtained using LaTeX but it is not as big as $\tau \,\!$. I think both symbols are better than using the text symbol τ, which is nowhere close to the symbol $\tau \,\!$ from the equation. So, I am asking for people's opinion on this matter. How do you want the article to look like: with inline equations using text or LaTeX? sanpaz (talk) 04:06, 17 July 2009 (UTC)

In a perfect world I'd like to see <math></math> used for everything, but as things currently are, LaTeX PNGs stick out from the rest of the text like a sore thumb. (Too bad the MathML option on Wikipedia is so wimpy—just about the only time it seems to kick in is with simple fractions.) Getting consistency in appearance between the text and the out-of-line equations is definitely a problem, and I can definitely see why so many editors prefer inline PNG rendering. Strad (talk) 18:30, 17 July 2009 (UTC)

Is there some reason you bolded the tau in your text symbol example? Either the regular τ or the italic τ looks better, I think. On my browser, all your TeX-formatted examples are significantly larger than the size of the text. My opinion: text wiki formatting of math is ugly but mis-sized inline bitmap images are even uglier. So I prefer the wiki formatting. —David Eppstein (talk) 00:15, 18 July 2009 (UTC)

I don't think this should be anything individual editors have to worry about. Ideally, editors would simply tell the software that some text is is mathematical, and then the software would display it appropriately. Having editors use different markups just to circumvent the limitations of the software is just a hack. If this view is shared by a majority, then I could enter an enhancement request at bugzilla. (There seems to be none yet ; see https://bugzilla.wikimedia.org/buglist.cgi?query_format=specific&order=relevance+desc&bug_status=__open__&product=MediaWiki&content=math.) — Sebastian 00:21, 18 July 2009 (UTC)

Would you propose to fix this by instituting the mis-sized bitmaps whenever any text is called out as mathematical, or by restricting mathematical formulae to the limited options available in wikiformatting? Neither is satisfactory for all purposes, and until all browsers support MathML they're what we're stuck with. —David Eppstein (talk) 01:02, 18 July 2009 (UTC)

To be honest, I don't know enough about the technical implementation, and maybe I'm misunderstanding something here. What I'm getting out of the conversation so far is that we have two basic ways to enter simple mathematical text: (1) without markup, as in "τ"; (2) with markup, as in <math>\tau</math>. (Each of these can be modified, e.g. by bolding it or by adding "\,\!", but I'm glossing over these subtleties here.)

I only thought about it at the level of how we enter the text. My proposal is on this higher level, not about a specific bug fix. (This is why I think of it as an enhancement.)

Now, let's assume that we have sufficient consensus that the bitmaps are uglier than the inline text. So far, we have been trying to address this through the MOS, by discouraging inline math markup. But if we have that consensus, then there is no reason to even offer the choice. The enhancement I propose would shift that worry onto the software, so that editors only need to decide whether a text is mathematical or not. If an (inline) math text can be displayed as plain text, then the software will do so. If not, it will display as a bitmap. I think this is a more elegant and logical solution. — Sebastian 02:16, 18 July 2009 (UTC)

Besides text and math markup, you can also use html tags which is what the x² and x₂ buttons above the editor window generate. Theoretically, you could also type in the MathML directly as well, but there are a lot of browsers that still don't support it (as mentioned above). In my experience there is no good solution, at least the way things stand. For example, what do you do with something like ${\vec {v}}$? It's impossible (or at least very difficult) to do without math markup but putting a single character in it's own line seems silly. What I try to do to carry on with the established style in the article, even if I disagree with it, on the theory that eventually the situation will improve and it's not worth tweaking formulas until then.--RDBury (talk) 06:11, 18 July 2009 (UTC)

Just some background info: As I understand it (correct me if I'm wrong) the way the server handles math markup is to first try to convert it to either html or MathML, depending on the user's preference settings. Only when the formula is too complicated, which it usually is, is it converted to PNG. In an ideal world, the server would be able to convert any LATEX code to MathML code, but the conversion program to do that is still under development. So the math markup is usually converted to PNG, and that conversion is done by an open source program developed externally. The problem with that program is that it doesn't know what font you're using in your browser so it picks a size that it thinks is reasonably legible. You can see this by bumping up the font size in your browser; all the text gets bigger but the math that gets converted to PNG stays the same size. In fact, you could "fix" the size mismatch problem by fiddling with the font settings in you browser, but then you've got huge text and there are still alignment problems.--RDBury (talk) 06:41, 18 July 2009 (UTC)

Imaginary unit

Some articles (such as Z-transform) needlessly use j instead of i for imaginary unit, which can confuse readers. Can there be any addition in this Manual of Style (or maybe somewhere else) that will encourage the usage of i as imaginary unit? --93.136.201.179 (talk) 13:31, 19 July 2009 (UTC)

That's common in electronics and by extension signal transforms because i might stand for current. Dmcq (talk) 13:40, 19 July 2009 (UTC)

Articles in question don't use electrical currents in their formulas and certainly don't use lowercase i for electrical current, so there is no need to confuse readers by usage of j for imaginary unit in those articles.

Also, electric current is usually written as uppercase I. --93.136.201.179 (talk) 14:03, 19 July 2009 (UTC)

Perhaps the articles don't mention electrical currents, but if I'm not mistaken, the Z-transform is frequently used in electrical engineering. Certainly an article using j for the imaginary unit should say that that's what that notation means. Michael Hardy (talk) 15:25, 19 July 2009 (UTC)

See Wien bridge for a simple example of i and j occurring together. In fact there they have i_in, i_out but people also say I and i to distinguish them. The usual rule in wikipedia for things like this is the first person to write a article sets the style. Dmcq (talk) 16:11, 19 July 2009 (UTC)

Also, it's inappropriate to force one convention across all of Wikipedia when several conventions occur in practice (just as in American vs. British spelling). As long as each article makes clear what i and j stand for, then we're doing as well as we can. Ozob (talk) 21:28, 20 July 2009 (UTC)

Fully agree. Both mathematicians as well as electrical engineers should know these formulae anyway and can figure out what j stands for in this context--Tprosser (talk) 11:18, 21 July 2009 (UTC)

Yes, only electric engineering articles should use j for imaginary unit, preferably with short notice in every such article that states something like "In this article j is used for imaginary unit, because i is used for electric current". All other articles should use i for imaginary unit, as most people use it. --antiXt (talk) 14:31, 23 July 2009 (UTC)

Personally I wouldn't be surprised if there aren't more electrical and electronic engineers, telecommunications engineers, signal processing etc etc than everybody else put together who ever comes in with occasional contact with i. Dmcq (talk) 15:40, 23 July 2009 (UTC)

How come those electrical engineers don't mix up current density j with their imaginary unit j? And why do they have to use lowercase i for electric current while it is standardized to use the uppercase I? --78.0.225.197 (talk) 10:13, 21 August 2009 (UTC)

epiphenomenal spacing characters

Why does this page say one should write

<math>\sin x \,\!</math>

when

<math>\sin x \, </math>

would do the same thing? The purpose of the spacing character is to force png rendering, and one is enough. It does not actually affect the appearance to the reader unless something inside the math tags comes after the spacing characters. It's better to keep things simple when complicating them would do nothing except to complicate them. Michael Hardy (talk) 00:02, 29 July 2009 (UTC)

I don't think most people are aware of this feature, namely that extra whitespace is cropped:

\,\!: $\sin x\,\!$test text.

\, alone: $\sin x\,$test text.

If the whitespace were not cropped, then \,\! would be a better choice, and I'd guess that's why the MoS currently suggests \,\!. Ozob (talk) 14:27, 29 July 2009 (UTC)

The whole point is that \, by itself does not force PNG rendering if math preferences are set to "HTML if possible or else PNG", whereas \,\! always does. — Emil J. 14:40, 29 July 2009 (UTC)

Plural nouns

Shouldn't the plural form of formula be formulae? The article uses formulas. ~~ Dr Dec (Talk) ~~ 19:28, 3 August 2009 (UTC)

Well, to be picky, it would be formulæ. -- Avi (talk) 01:39, 4 August 2009 (UTC)

"æ" is just a ligature for "ae"; linguistically they're identical.

"Formulae" is the Latin plural of formula. This is the English wiki, so we use "formulas". Ozob (talk) 04:07, 4 August 2009 (UTC)

Well, it could also be an ash, which is a full letter in many languages, :) -- Avi (talk) 04:12, 4 August 2009 (UTC)

Ozob, formula itself has a Latin root! If this is English Wikipedia then maybe we should stop using formula too? My dictionary lists eight meanings for formula:

1. A mathematical relationship
2. A chemical formula
3. A fixed form of words
4. A method or procedure
5. (before or after a noun) denoting a rule or style
6. A list of ingredients
7. An infant's liquid food
8. A classification of racing car, e.g. formula 1

Here's the key: my dictionary says that the plural form in senses 1 and 2 is formulae, and the plural form in senses 3 to 8 is formulas. This is backed up by the fact that in every published mathematical article I have ever read the word used is formulae. Also, Avi, "to be picky" it should be formulae and not formulæ, the latter is the exact Latin word, the former is the English language derivative. ~~ Dr Dec (Talk) ~~ 10:32, 4 August 2009 (UTC)

IIRC, and I may be wrong, the word came into English as "formulæ". It was a later evolution that separated the digraph. English is known for its being replete with loanwords. I am not sure that there is a word that may be traced to Old English that carries the meaning of formula :) -- Avi (talk) 14:38, 4 August 2009 (UTC)

Maybe you're right that it came into English as formulæ, but non of the online dictionaries have entries for formulæ. The Oxford English dictionary and Merriam–Webster both list formulas and formulae, but not formulæ. As I said above: The OED explicitly says that formulae applies to mathematical and chemical formulae, where as formulas applies to the other meanings. Merriam–Webster makes no such distinction. It would be interesting to see some publisher's guidelines on the topic. Like I said: I've only ever seen formulae in publish academic works, but that doesn't mean that all journals insist upon that spelling. Maybe some give the author the choice. ~~ Dr Dec (Talk) ~~ 16:08, 4 August 2009 (UTC)

And just to add a little weight to why we should follow the OED: The OED article tells us that it "is used by the United Nations, the World Trade Organization, the International Organization for Standardization, and many British academic publications, such as Nature, the Biochemical Journal, and The Times Literary Supplement." ~~ Dr Dec (Talk) ~~ 16:13, 4 August 2009 (UTC)

And as a dumb American, what does that mean to me? :-P -- Avi (talk) 16:21, 4 August 2009 (UTC)

If you are "dumb" as you claim, then why waste everyone's time making silly comments on what was intended to be a productive discussion thread? ~~ Dr Dec (Talk) ~~ 17:01, 4 August 2009 (UTC)

That was a somewhat humorous attempt to point out the wikiepdia manuals of style are not based specifically on British English; I guess it fell flat. -- Avi (talk) 17:20, 4 August 2009 (UTC)

No, you're right: Wikiepdia manuals of style are not based specifically on British English. Nor is the OED; it simply happens to be published in England! It actually uses the American English endings -ize instead of the British English -ise. I wouldn't call the United Nations, the World Trade Organization or the International Organization for Standardization British establishments either. But if such powerful and respected organisations use the OED as their standard English language reference then who are we to argue? If the OED says that it's formulae and not formulas then who are we to argue? ~~ Dr Dec (Talk) ~~ 17:31, 4 August 2009 (UTC)

Personally, as long is an article is consistent with usage (-as, -ae, -æ) I'm fine with that. Usually, the editor who writes the majority of the article sets the precedent. -- Avi (talk) 17:40, 4 August 2009 (UTC)

I see your point: consistancy is key. But when I read formulas it just feels ameature to me. It feels like the person using the word doesn't have enough understanding of where the word came from. When I read formulæ it feels like the person is trying to be smart, when the oposite is actually true: we don't use the character æ in the English alphabet, we only use it when we quote Latin. I don't know, maybe I'm being a pedant, but if I am, so is the OED, the UN, the WTO, and the IOS. ~~ Dr Dec (Talk) ~~ 17:50, 4 August 2009 (UTC)

I guess I'm one of those people failing to be smart ; I like the digraph, and while it is archaic, it is not improper. The word is still English; just an older form. And, for the record, there is nothing wrong with being a pedant (in the original sense of the word) :) -- Avi (talk) 19:18, 4 August 2009 (UTC)

It's interesting that you also link to pedant. This article links directly to minutiae, the plural form of minutia. Although they mention minutiæ, there is certainly no mention of minutias ~~ Dr Dec (Talk) ~~ 19:47, 4 August 2009 (UTC)

(←) Hmm. I find the objections presented here quite interesting. So, my point about English plurals versus Latin plurals runs, in more detail, like this:

1. "Formula" is (essentially) a Latin word.
2. If we were speaking Latin, we would say "formulae".
3. We are not speaking Latin, therefore it can be grammatically correct to say something other than "formulae".
4. We are speaking English. (At least, I try to speak English. Sometimes it doesn't come out so well.)
5. It is grammatically correct to use the English-language plural "-s" suffix for many foreign loanwords.
6. Therefore, I think that it is at acceptable, though perhaps not necessary, to use "formulas".

There are, of course, several assertions here that can be debated. But even if you were to knock down every one of those assertions, I'd still vote for "formulas", and for reasons that are admittedly subjective and aesthetic. My taste is guided mostly by my own professional experience: I, in my life as a professional mathematician, use "formulas" exclusively, and so does everyone else I know. "Formulae" sounds pretentious to me; you might be able to convince me that it's grammatically correct, but it crashes, discordant, against my ear. Ozob (talk) 23:40, 4 August 2009 (UTC)

Ozob you say that formulae sounds pretentious, for me it's the oposite, hearing formulas is like hearing someone say inexplainable (instead of inexplicable) ~~ Dr Dec (Talk) ~~ 23:45, 5 August 2009 (UTC)

I also commonly read and use "formulas" as a mathematician. I see on google books that Paul Halmos, Stephen Cole Kleene, Donald Knuth, and Nicolas Bourbaki used "formulas" as well; so does the Chicago Manual of Style. This points to the issue being one of style rather than correctness. In such matters, we usually simply stick with the convention first established in each article. — Carl (CBM · talk) 02:40, 5 August 2009 (UTC)

The OED (online reprint of the 2^nd ed.) lists the plural of formula as either formulæ or formulas (and has quotations for formulae too, as well as a quotation—from 1864, no less—for formulas in the mathematical sense). The AHD (4^th ed.) lists the plural as either formulae or formulas. They're all acceptable. Consistency is what's important. Strad (talk) 02:54, 5 August 2009 (UTC)

Above, Declan Davis makes a contrary claim about the OED: "[OED] says that the plural form in senses 1 and 2 is formulae, and the plural form in senses 3 to 8 is formulas". I'd like to see an explicit citation (to edition and a quotation from it), since I'm feeling skeptical about this claim. In addition, while he may never have seen "formulas" used in a math paper, I've seen it plenty of times. For example, one can easily see its usage in well-known journals such as Inventiones Mathematicae, (one easy way to check this is put in the name of the journal into Google scholar plus the term "formulas" and weed out the excerpts that have only the singular form). --C S (talk) 23:16, 5 August 2009 (UTC)

C S, I feel quite hurt by the tone of you post. Do you think that I'm going to lie? If I wanted to go around lying to people I wouldn't chose something that has millions and millions of copies is circulation. My dictionary is "The Oxford Compact English Dictionary", second edition, revised. The ISBN is 0-19-860-713-X. ~~ Dr Dec (Talk) ~~ 23:33, 5 August 2009 (UTC)

I get the feeling that I'm flogging a dead horse here. The majority of editors are Americans, or people used to American English, and the Americans always seem to favour simplification of language, e.g. using color instead of colour and thereby losing any links to the word's French roots, and of course formulas instead of formulae. ~~ Dr Dec (Talk) ~~ 23:45, 5 August 2009 (UTC)

The tone was perhaps too harsh. By the way, did I mention that according to google books, Nicolas Bourbaki used "formulas" (in the English translation, of course), and Dieudonné as well? On the other hand some Americans use "formulae". I think it is more a question of what one is used to and what one's editor requires, and this may vary some by field as well. In a similar example, we tend to use "indices" in recursion theory even though the American standard has sadly become "indexes". — Carl (CBM · talk) 00:22, 6 August 2009 (UTC)

I know what you're saying. But the majority of American authors would use formulas and the majority of British English speaking authors would use formulae. Of course there are exceptions to every rule.

I am not inclined to believe that formulae (or formulæ) is significantly more prevalent that formulas in mathematical writing, but if someone can produce data to the contrary I will gladly support an addition to WP:MSM recommending formulae. Strad (talk) 00:46, 6 August 2009 (UTC)

Such data would be, most probably, impossible to come by: who has the resources to sift through every mathematics article ever written in the English language? Those with such resources will be occupied with the greater good and not out little linguistical discussion. One thing I would try to remeber is that journals change the spellings. In my latest article to be published in Geometriae Dedicata, the Springer editors insisted upon changing all of my spellings to American English. (The link is to an original copy so the British English is still in place. See my user page for details of the paper, then you'll be able to compare the post Americanised version with my originally submitted version). ~~ Dr Dec (Talk) ~~ 18:35, 6 August 2009 (UTC)

Then in lieu of such data we can only assume that formulae, formulæ, and formulas are all acceptable plurals for mathematics articles. Strad (talk) 03:21, 7 August 2009 (UTC)

(<-)In my opinion, for what it is worth, I would like to reiterate that this is wikipedia, not Encyclopædia Mathematicæ; it is written by many, many different people. As long as individual articles are consistent with a correct usage (-as, -ae, -æ), I do not see the need to force uniformity across articles. -- Avi (talk) 01:23, 6 August 2009 (UTC)

I don’t feel very comfortable hearing people say things like “formulae is the Latin plural, we speak English, so we should use formulas.” Well, what exactly is the English language? The indigenous tribes of what is now the British Isles spoke a Gaelic language Brythonic language, a language very like modern day Welsh. The along came the Angles and the Saxons from what is now Germany speaking an ancient Germanic language. Then the Romans came to settle, bringing with them Latin. The Vikings made the British Isles their home bringing with them ancient Scandinavian dialects. Finally the Normans came with a language not dissimilar to modern day French. All of these languages and cultures mixed to give rise to the English language and the British people. To say that “We are speaking English, and that’s not Latin!” is like saying, “We are eating an omelette, and that’s not eggs!” Also, we always use the Latin plural form many words. For example, do you say basises, or bases? The Latin plural of basis is bases. ~~ Dr Dec (Talk) ~~ 13:45, 6 August 2009 (UTC)

I feel like you're missing my point. I agree that languages change and evolve, and that one goes fluidly into the next; all the same, it's been about DCCIX yeres syn Ich laste spoke Middle English. We're not speaking Middle English right now, we're speaking Modern English. We should speak as other Modern English speakers do—which, in my experience, is to say formulas and not formulae.

As far as collecting usage statistics goes, I don't think it would be too hard. The arXiv has a tremendous collection of mathematical and scientific preprints from all over the world. If we could survey their usage—which ought to be possible—then we'd get a more definitive answer. Ozob (talk) 23:09, 6 August 2009 (UTC)

The following is irrelevant to the topic of the discussion, but the areas of Great Britain that were settled by the Angles and the Saxons were previously inhabited not by Gaelic-speaking peoples, but by Brythonic-speaking peoples (our article on Welsh begins, "Welsh [...] is a member of the Brythonic branch of Celtic"). Strad (talk) 03:18, 7 August 2009 (UTC)

Strad, I'm sorry, I don't follow... ~~ Dr Dec (Talk) ~~ 00:44, 9 August 2009 (UTC) Oh now I see. Well you're right: your comment doesn't make much difference to my point. My point was that modern English is a mixture of other languages including, most importantly in this discussion, Latin. Given that I'm a mathematician and not a language expert I would have hoped that you may have taken my comments in good faith and tried to understand the general meaning. I don't see how the subdivision of insular Celtic languages relates very much to the overall meaning of my comment, and it certainly has nothing to do with the formulae/formulas debate. ~~ Dr Dec (Talk) ~~ 10:36, 9 August 2009 (UTC)

Minima or minimums? Media or mediums? Bases or basises? I'm sure you would agree that the latter options are quite ugly and most uncommon; the traditional forms seems to win the day. Then what about formulae or formulas? ~~ Dr Dec (Talk) ~~ 00:15, 9 August 2009 (UTC)

The plurals of minimum, medium, and basis are not relevant. I cannot argue that the preferred plural of eye is eyen simply because the preferred plural of ox is oxen. The only thing that matters is this: What plural(s) of formula are currently used in written Standard English? I have attempted to answer this question by citing two major reference dictionaries, the OED and the AHD, whose editors have determined that formulae/formulæ and formulas are all commonly used plurals of the word formula. If you do not want Wikipedia to use formulas, you need to present similar statistical evidence (either directly, through a corpus search, or indirectly, through a corpus-based dictionary like the OED) showing the formulas is sufficiently uncommon in mathematical (or general) texts. Strad (talk) 17:44, 9 August 2009 (UTC)

Do you own a copy of the OED? Have you read the thread above? The OED seems to say that formulae is used for mathematical and chemical formulae and that formulas is used for thr other meaning. We want consistancy in our language. Lets make a list of mathematical plural:

1. Matrix & matrices (not matrixes)
2. Basis & bases (not basises)
3. Minimum & minima (not minimums)
4. Medium & media (not medias)

These are just some examples. We use the Latin plurals most of the time... why not use it with the plural of formula?! ~~ Dr Dec (Talk) ~~ 18:00, 9 August 2009 (UTC)

As I understand it, the plural of eye really did used to be eyen. But not anymore, of course; fortunately that's not under dispute.

I commonly hear "matrixes" and "vertexes"—in fact, I first learned the plural of "vertex" as "vertexes". And I do hear people say "minimums" and "maximums". I get funny looks if I say "complices" for "complexes" (I've tried it). And people seem to use "simplexes" and "simplices" interchangeably. Now, I have to admit to being a bit of a language snob myself (that's why I tried using "complices" instead of "complexes"). But the trend seems pretty clear to me here: People tend to use an -s suffix to pluralize Latin loanwords. The only real exception I'm aware of are words like "basis" which already end in an "s".

I tried searching the reference desk archives and I came up only with the following unhelpful but slightly amusing result: Wikipedia:Reference_desk/Archives/Mathematics/2006_November_14#help i want to pass in maths exams of mvita school based kenya. So I've asked: Wikipedia:Reference desk/Language#Plural of "formula". Hopefully there will be someone knowledgeable who can solve our problem. Ozob (talk) 19:03, 9 August 2009 (UTC)

Ozob, where exactly have you heared people talking about vertexes, etc? The only time I have ever heared that usage is when a Spanish friend of mine was giving a talk in English. And trust me, I've been to a lot of conferences! See my user page. You really seem to live in a parallel universe. Besides, Ox and Oxen are Old English and not pure Latin, so how does that have anything to do with Latin plurals? Please, for the love of God, stick to the point and stop picking up on side issues! ~~ Dr Dec (Talk) ~~ 19:54, 9 August 2009 (UTC)

The remark on ox, oxen, eye, and eyen was a comment on Strad's remark: He says above, "I cannot argue that the preferred plural of eye is eyen simply because the preferred plural of ox is oxen." Note that according to Middle English#Nouns, the plural of "eye" was "eyen" between about 1066 and 1650. This is relevant to my point: Just because you retain an older plural form in some words does not mean that you must do so for other words. And conversely: Just because you use a more contemporary plural form for some words does not mean that you must do so for other words. I am sure that you would say both "oxen" and "eyes", not "oxes" and "eyen".

Regarding the plural of vertex, I am told that "vertexes" is the standard terminology in the computer graphics community; while I hear it less frequently than "vertices" in my own trade it seems to be gaining popularity. If you Google "vertexes", ignore "Did you mean: vertices", and skip the first two pages of results (which are mostly encyclopedia articles), then you start to see real hits, mostly involving computer graphics (which is consistent with what I've been told). That doesn't make "vertexes" right; I say "vertices" just like you do, and I think it's more correct. "Vertexes" is a minority usage which is incorrect in formal, written English, except within computer graphics.

I believe that the situation is different with "formulas". As an experiment, I went to the arXiv and tried their full text search (at [12]). I got:

• 55870 hits for "formulas".
• 45490 hits for "formulae".

Based on that, I think we can confidently conclude that both "formulas" and "formulae" are acceptable in formal, written mathematical English. Ozob (talk) 23:12, 9 August 2009 (UTC)

I have access to the full, complete, up-to-date OED through my university's online subscription. I assume (since you are a professional mathematician, and therefore most likely have university affiliation) that you do as well. When the UN, the WTO, ISO, Nature, etc say "the OED", they mean the full, complete, up-to-date version, not a condensed print version. Perhaps the usage note in your print version takes advantage of new information since the publication of the formula entry in the full OED (it was effectively written over a century ago, after all), but that is only speculation.

Just to rehash: the language on Wikipedia needs to reflect contemporary, written Standard English, not notions of what should happen based on arguments from etymology or consistency. Having consulted several dictionaries—whose information is drawn from observations about contemporary, written Standard English—I conclude that formulae/formulæ and formulas all appear with reasonable frequency in contemporary, written Standard English, and thus they are all acceptable pluralizations for use in Wikipedia. Unless new information enters the discussion I don't think I have anything more to contribute to this topic. Strad (talk) 21:14, 9 August 2009 (UTC)

Well, yes you do. I was branded a liar by C S for just saying what was in my dictionary. Let's have some quotes, some references, and some links. Get off your high horse ("Unless new information enters the discussion I don't think I have anything more to contribute to this topic." - what an arrogant thing to say!) and let's aproach this topic as people with a common goal; as we all are! ~~ Dr Dec (Talk) ~~ 21:34, 9 August 2009 (UTC)

Someone said above that formulae is BE and formulas is AE. Actually, I am pretty sure it's the other way round in my field (model theory): formulae is AE and formulas is BE. This would also be in accordance with what an older (British) colleague told me about topoi (AE) vs. toposes (BE), and with the general principle that AE is more conservative than BE except for (1) Noah Webster's reforms such as theater, which were not followed in the UK, and (2) some spellings such as -ise, where BE remains closer to French. (Actually (1) can also be seen as a special case of (2).)

Model theory literature is currently dominated by Europeans, and within the field formulas is standard for this technical term (see well-formed formula), outnumbering formulae by at least 2:1 according to my Google Scholar tests. Note that for such tests one needs to put even the single words formula or formulae into quotation marks. I believe Google changed their algorithm recently. Hans Adler 10:50, 21 August 2009 (UTC)

Templates using <math></math> and conditional statements

I am wanting to create a new template for dental formulas, but I keep getting a "Failed to parse (lexing error)" whenever I try it out. The code I'm using is:

<math alt="Upper: {{{upper}}} / Lower: {{{lower}}}{{#if: {{{total|}}} |, Total teeth = {{{total}}}|}}">\tfrac{ {{{upper}}}}{ {{{lower}}}}{{#if: {{{total|}}} | \times 2 = {{{total}}}|}}</math>

Admittedly, this is the first complicated template I've ever written, although I have read Help:Template. If I take the \tfrac part out, and leave <math>...</math>, no errors are generated and the alt text comes out correctly. If I leave the 1 & 2 variables in the \tfrac, but remove the conditional statement, it works fine. For some reason, it objects to the conditional statement, which will allow me to either show a general dental formula or show the formula along with the total number of teeth. Is there something I'm doing wrong, or do I have to create two separate templates? –Visionholder (talk) 16:12, 15 September 2009 (UTC)

Sorry, I should have included examples of what the output should look like. If the user passes the following: {{DentalFormula|upper=2.1.3.3|lower=2.1.3.3}}, then they would get:

${\tfrac {2.1.3.3}{2.1.3.3}}$

If the user passes the following: {{DentalFormula|upper=2.1.3.3|lower=2.1.3.3|total=36}}, then they would get:

${\tfrac {2.1.3.3}{2.1.3.3}}\times 2=36$

Hope that helps. –Visionholder (talk) 16:32, 15 September 2009 (UTC)

Why do you need a template to do this? The resulting wikicode is not much longer than the templated version and easier to read? Plastikspork _―Œ^(talk) 18:20, 15 September 2009 (UTC)

I was mostly doing this to make things easier for WP:MAMMAL. Biology people aren't necessarily math people, and previous attempts at creating dentition templates have resulted in tables that cannot be used inline. For people used to using templates rather than math markup, this might be a lot easier and require a lot less reading. Furthermore, it also ensures that alt text will be used, which cannot be guaranteed if left up to each editor. –Visionholder (talk) 19:17, 15 September 2009 (UTC)

The problem has been fixed, thanks to a suggestion at MediaWiki. For those of you wanting to use <math>...</math> in templates, follow the link to learn more. –Visionholder (talk) 08:45, 16 September 2009 (UTC)

WARNING: Technical problem

Yesterday I edited this page - ok. But today I could not edit this page via IE: "Internet Explorer has encountered a problem and needs to close. We are sorry for the inconvenience." I wrote this message via Konqueror under Linux. At the same time, other pages I had tested is ok.--Tim32 (talk) 11:06, 24 February 2010 (UTC)

Circle vs. Disk issues

Mathematically, a circle is a curve and a disk is the region enclosed by it. The same distinctions hold for sphere vs. ball, torus vs. toroid, and I'm not sure if there are different names for square (interior) vs. square (perimeter). While mathematically accurate, these distinctions fly in the face of common usage, for example the area of a circle is actually 0, it's the area of a disk that's πr². In light of this, I think it would be better to merge corresponding articles together. I've already proposed a merge between Torus and toroid and it occurred to me that this idea could be applied more generally.--RDBury (talk) 17:31, 22 October 2009 (UTC)

Lots of people use circle to mean sphere in common usage. For example "The sun is a circle", is not an unheard of refrain. Likewise, people will use square for cube and indeed cube for square.

This does not mean that we should merge those articles. ObsessiveMathsFreak (talk) 13:17, 18 November 2009 (UTC)

Section "Very simple formulae"

This section seems to be routinely misunderstood to give free license to write mathematics as inline LaTeX, regardless of whether it displays as inline PNG (and thus conflicts with other parts of the guideline). I suggest emphasizing that this is not what is intended by changing the sentence:

"Either form is acceptable, but do not change one form to the other in other people's writing."

to read

"For very simple formulas such as this, either form is acceptable, but do not change one form to the other in other people's writing."

Second of all, the sentence

"Changing to make an entire article consistent is acceptable."

also seems to be very gameable. I think this sentence should be removed, since it is definitely not acceptable to change inline formulas to TeX if that will force them to display as PNG (unless there is an overriding necessity to do so). 173.75.159.210 (talk) 15:05, 1 November 2009 (UTC)

Transpose

I was just told on my talk page that my use of $A^{\top }$ (A^\top) for transpose wasn't kosher; that I should be using $A^{\mathrm {T} }$:

For a matrix transpose, use X^T (not X^T) or $X^{\mathrm {T} }$ (not $X^{T}$ or $X^{\top }$).

From the histories, it looks like this came from rolling in old content from Wikipedia:WikiProject_Mathematics/Conventions. That topic saw only limited discussion on that talk page. While I'm all for consistency, I think I see $^{\top }$ in more textbooks. Personally, I find it clearer that it's an operator rather than just raising something to the T^th power. Finally, typographically it seems more consistent to use a symbol than a letter, to go along with $A^{*}$ for conjugate transpose and $A^{+}$ for the Moore–Penrose pseudoinverse. Orthogonally, is there any way to add a definition of \transpose to the "global preamble" so that it is available in all of Wikipedia's <math>? That would separate the typography from the semantics and would make it involve a lot less ugly curly braces in the source. —Ben FrantzDale (talk) 03:29, 18 November 2009 (UTC)

Well what do you know. Some textbooks do use the top symbol. I say some; most don't.

My opinion is that this symbol is entirely inappropriate. Typographically, it looks awful, with top not having the correct ratios for a capital "T". In addition, the conjugate transpose is also denoted $A^{H}$ for the Hermitian matrix, which matches up with $A^{T}$. Oooo, those lovely serifs! Along these lines, the mathrm "T" is disgusting.

This looks like a fad. A bad fad started by mathematicians who've spent too much time using latex and haven't realised that they're not typographers. There is nothing wrong and everything right with using a standard "T" for the transpose operation. The standard T, not the mathrm one. There is no reason to use a symbol that was never intended for that purpose, and further there is no reason to mix italicized and regular text in the one symbol. ObsessiveMathsFreak (talk) 13:36, 18 November 2009 (UTC)

It was Arthur Rubin. Oh dear ObsessiveMathsFreak (talk) 13:53, 18 November 2009 (UTC)

There is a good reason for using \top , or a roman T, or something other than a standard T: it frees up T to be a variable name. —David Eppstein (talk) 15:44, 18 November 2009 (UTC)

I doubt anyone would confuse the transpose operation with a variable denoted by T and vice verse. I'm pretty sure I've even seen $T^{T}$ somewhere before. In any case, it doens't really free up anything as \top looks similar enough to a T to cause confusion.193.1.104.8 (talk) 16:29, 18 November 2009 (UTC)

Perhaps T (or T) should never be used for transpose. I could live with a convention that only ′ should be used, but it is absurd to recommend an italicised "T" be allowed for anything other than a variable. — Arthur Rubin (talk) 17:00, 18 November 2009 (UTC)

May I add additional hypothetical confusion; in the matrix exponential article, it would make perfectly good sense to write:

$e^{T^{\top }}=\left({e^{T}}\right)^{\top }.$

I would never do that, but if the transpose symbol were a simple unadjusted "T", it would be impossible to parse. — Arthur Rubin (talk) 17:07, 18 November 2009 (UTC)

It's already impossible to parse. Anyone who wouldn't write $T^{T}$ is not going to go about writing $T^{\top }$. They're not going to go about writing it because $\top$ looks too much like $T$. In fact, that is the very reason it is being (mis)used in place of a regular $T$ the transpose operation. Having said that....

You say that an italicised "T" should never be used for anything except a variable. This has not been my mathematical experience. I have seen $A^{T}$ and moreover $A^{H}$ used in a great many publications and $A^{\top }$ used in one very recent one. I suspect this "convention" of requiring $A^{\mathrm {T} }$ to be a recent invention of a rather small group of typographically minded mathematicians, and not something generally agreed upon anywhere. Therefore, I question its imposition by fiat in the style guide.

This conversation began when someone was told they couldn't use $A^{\top }$ because "it conflicted with the style guide" or else "wasn't kosher". As far as I can see, there is no "kosher" way of typesetting mathematics, so I find the imposition of these quite foreign notions on others to be against the spirit of the mathematical community and against the ostensible aims of the site.

I recall a case from some time ago where someone attempted to rewrite all vectors in the Electromagnetism pages so that they used arrow notation and not boldface. Needless to say, this did not go down well. Why the, should essentially the same typeforcing be allowed in the case of the transpose operator for matrices? Because it is in the style guide? This is not good enough.

Having read through it, my opinion is that the mathematics style guide is best left empty. Any attempt to impose the styles, manners or symbols of one field or region onto all others is a bad idea. "Horses for courses" as the saying goes. I think people need to take a serious look at the content and indeed the place of the mathematics style guide. My recommendation is to begin by removing, entirely, conventions for the transpose operation.ObsessiveMathsFreak (talk) 13:25, 20 November 2009 (UTC)

Well the style guide can simpy serve as (useful) information about notations and as a nonbinding suggestion. The problems comes only with strict enforcement then it is likely authors will clash and we may get a lot of bad blood. So the rationale should be to consider the guide mainly as information & suggestion and not as something to be imposed on authors. As long as an author stays within in the general range of mathematical conventions, it should be up to him what to use in (his) article. In the case of heavily collaborated articles it might be useful to enforce some consistence throughout the article though.--Kmhkmh (talk) 06:31, 27 November 2009 (UTC)

As for the second part of my question, can we all agree that it would be nice to have \transpose defined universally to be whatever we agree upon? Is this technically feasible? —Ben FrantzDale (talk) 17:29, 18 November 2009 (UTC)

It would be nice, but I don't think we (as en.Wikipedia) have control over the <math> interface. — Arthur Rubin (talk) 17:42, 18 November 2009 (UTC)

Well, we could petition the developers through Bugzilla, but that's a long run, especially since they are likely to regard it as a low priority issue. — Emil J. 17:51, 18 November 2009 (UTC)

And I should add that for the same reason it's not really a good idea anyway, because any future change of the macro would also need to undergo the same process, so we would essentially lose control of this bit of MoS. — Emil J. 17:57, 18 November 2009 (UTC)

In any case, to answer the original question, there is a Unicode \top ( ⊤ ) so you may use that symbol outside of a PNG (X^⊤) if you like. —Werson (talk) 02:58, 19 November 2009 (UTC)

Does anyone have a published style guide dedicated to mathematics handy? I don't have any at present and I am curious to know what they say on this issue. — Carl (CBM · talk) 13:05, 19 November 2009 (UTC)

What is the best way to number equations?

Is there a favored way to number equations? I would think LaTeX supports putting numbers like "(1)", "(2)", etc., aligned on the right side of the page, but I can't find any documentation for it. I have seen multiple methods in articles here, all of them ugly. It would be nice to document the "right" way here and/or on WP:MATH. Thanks in advance; I would love to know how to do this. CosineKitty (talk) 18:30, 20 February 2010 (UTC)

I don't know of a good way to do it here, either. LaTeX does support it, but texvc, which Wikipedia uses, does not. There are several issues. One is that we never say \begin{equation} or anything like that; there's nothing to distinguish any use of <math> from any other, and in particular no way to distinguish which uses should be numbered. Another issue is that math tags are processed individually, not collectively; there is no way for any tag to know where it is relative to other tags, and hence no way to number. I can't imagine this problem ever going away, either. But it's not all bad; I find that rewriting my prose to avoid equation numbers often makes it better. Ozob (talk) 05:25, 21 February 2010 (UTC)

Hmmm... OK. I would settle for manually numbering the equations if I could just get it to look right. But you do have a good point about rewriting the text to avoid numbers. Thank you for taking the time to reply! CosineKitty (talk) 22:53, 21 February 2010 (UTC)

I just found a way to number equations that looks pretty nice. Take a look at BKL singularity. CosineKitty (talk) 02:00, 23 February 2010 (UTC)

And it lets you put a clickable link to the equation in your text which is nice too. I also much prefer templates if available rather than putting own code into the article pages. Dmcq (talk)

Yep, use {{NumBLK}}, {{EquationRef}}, and {{EquationNote}}. Unfortunately, there seems to be no way to have them automatically number the equations. Sławomir Biały (talk) 20:26, 23 February 2010 (UTC)

Thank you for your help. I used this in Mean anomaly, and it looks a lot better now. I think these templates should be documented (or at least linked) from this page (MOS:MATH) and/or from WP:MATH. Does anyone have an opinion on which (or both) of these is the appropriate place to document equation numbering templates? If so, would they have a problem with me adding it in either place? (I have never edited a MOS page before, and I would think it would require some discussion first.) CosineKitty (talk) 22:47, 23 February 2010 (UTC)

Actually the template should have a greater exposure so that they become known and available (in practical terms) to other authors. However when adding them to MOS:MATH it should be explicitly stated that they are optional, since MOS:MATH is often considered as mandatory and we should keep mandatory regulations to a minimum. Adding to WP:MATH looks like a good idea to me. Do we actually have a project page listing all useful templates for math articles?--Kmhkmh (talk) 13:26, 24 February 2010 (UTC)

Now that you explain it, WP:MATH does sound like a better place. I will move the conversation over there. Thanks! CosineKitty (talk) 18:48, 24 February 2010 (UTC)