# Wikipedia talk:Naming conventions (theorems)

... see also Wikipedia:WikiProject Mathematics

## from Pythagoras...[edit]

Why is Pythagorean theorem correct and Pythagorean Theorem incorrect?
This is not an article about the general concept of a Pythagorean theorem (any theorem proved by Pythagoras?) but about a specific theorem, *the* Pythagorean Theorem.
"Pythagorean Theorem" is a proper noun, and I've always seen it capitalised as such in mathematics texts.
The same, of course, goes for Poincaré's Conjecture, Zorn's Lemma, and all the rest.
Where would it be best to bring this up for discussion in general?
— Toby 22:55 Sep 13, 2002 (UTC)

- Interesting point. Somewhere in the maze of Naming Conventions pages, maybe. While we're at it, it's Pythagoras' Theorem. ;-) -- Tarquin 23:10 Sep 13, 2002 (UTC)

I think it could be argued both ways, but the trend these days in books and journals is toward using more lowercase. They are sort-of proper nouns, but they aren't really *titles*; they're still just "Person's thing", even if they do bring a particular one to mind. For example, you would still use an article in front of the ones without the possessive (i.e., "the Poincaré conjecture", "the Pythagorean theorem", "a Bessel function", etc.), indicating that they are used more like a noun than a title (a title would stand by itself: "'Sophie's Choice' was the best movie..."), and I'm not sure uniqueness is enough to qualify a phrasal noun as "proper", for example "Michaelangelo's Sistine chapel ceiling" or "Einstein's theory of general relativity" are unique, but you wouldn't capitalize "ceiling" or "theory" in those. At any rate, I think we have a strong precedent *here* in Wikipedia for using lowercase as much as possible, and I generally agree with that. --LDC

- Hmm... I hadn't thought of "Bessel function". That seems right in lower case. Quick check through a maths book I have to hand: "Fourier integral", "Laplace transform". Even "theorem" doesn't get special consideration: "Green's theorem". After consideration, I'm with LDC on this. -- Tarquin

I don't think that it's actually about naming conventions at all.
It's more along the lines of the Manual of Style.The naming conventions say to name articles with the same capitalisation that is used in ordinary running text; that's perfectly clear.
The problem is, what is the capitalisation to use in ordinary running text?
(Indeed, I shouldn't have mentioned the article title at all, but should talk about what appears in the text.)
I don't particularly care one way or another, but my experience is that the names of theorems, lemmas, and the like (not other things like functions or integrals, however) are capitalised in most (but not all) math books.
If my perceptions are wrong, fine, but that's the only issue, not Wikipedia's "strong precedent ... for using lowercase".
We *don't* have a strong precedent for using lowercase in running text; what we have is a strong precedent for matching the capitalisation of running text with the capitalisation of article titles, and that is agreed on all around.
— Toby 04:10 Sep 17, 2002 (UTC)

- I sometimes wonder if people actually read a word I write... I wrote above that one of my mathsbooks uses lowercase for "Green's theorem". I've just checked four more, and they are all the same: lowercase for "theorem". -- Tarquin 07:39 Sep 17, 2002 (UTC)

- I read it. I'm not sure what you expected to happen because I read it. After all, I was quite aware that not every book capitalised the names of theorems, lemmas, and the like; but it was still my impression that
*most*did. I hope to make a survey of math books next week, when I'll have several to look at; then we'll know for sure not only what is being done but also what the trend is towards. - I hope, however, that we can all agree that:
- The capitalisation that we use should be written up in the Manual of Style;
- We should follow the modern trend, what is likely to be used in most English language math books in the future;
- Names of articles should follow the same capitalisation as we use in running text, as per longstanding Wikipedia policy;
- Redirects should be made between both capitalisations, since both are in use and both are likely to appear in running text, Manual of Style or no.

- Is this much true? — Toby 05:24 Sep 18, 2002 (UTC)

- I read it. I'm not sure what you expected to happen because I read it. After all, I was quite aware that not every book capitalised the names of theorems, lemmas, and the like; but it was still my impression that

## from maths topics ...[edit]

It is OK to write Matiyasevich's theorem but not Dirichlet's theorem. Why is that so? Can you please decide how to name theorems? --XJam 09:50 Oct 14, 2002 (UTC)

To help deciding, here is a Murphy's law like *Grammar bug Wikipedia theorem*: there are exactly *27* wrongly named mathematical theorems here (2002-10-16). **Proof:** see list below:

- Baire category theorem
- Bezouts theorem
- Borsuk-Ulam Theorem
- Brouwer fixed-point theorem
- Cauchy integral theorem
- Cayley's Theorem
- Dirichlet theorem
- Goedels completeness theorem
- Hahn-Banach theorem
- Hilberts basis theorem
- Laurent expansion theorem
- Lowenheim-Skolem theorem
- Metrization theorems
- Nash embedding theorem
- Peter-Weyl theorem
- Ramsey theorem
- Riemann mapping theorem
- Riesz representation theorem
- Stone-Weierstrass theorem
- Sylow theorem
- Taylors theorem
- Theorem of Bolzano-Weierstrass
- Theorem of Heine-Borel
- Theorem of Lagrange
- Tietze extension theorem
- Weierstrass-Casorati theorem
- Wilsons theorem

Q.E.D. The same thing is with other terms (lemma, group, number, ...) :) --XJamRastafire 20:44 Oct 16, 2002 (UTC)

There is no general rule for naming theorems; we should follow the most common usage and then provide redirects. Of course, all the ones with a missing apostrophe, like Taylors theorem, should be moved to the proper version Taylor's theorem. Then the entries in the list of math topics need to be changed as well. AxelBoldt 00:30 Oct 17, 2002 (UTC)

OK, how about this issue: are names of theorem, lemmas, and the like capitalised? Although I find the practice distasteful personally, textbooks seem to prefer "Pythagorean Theorem" over "Pythagorean theorem" to me. As in "There were many Pythagoren theorems — theorems proved by the Pythagoreans — but the most famous of these is the Pythagorean Theorem — although it was actually known long before their time.". — Toby 06:48 Oct 29, 2002 (UTC)

This discussion came up on Talk:Pythagorean theorem -- maybe we should refactor both there and here to Wikipedia talk:Naming conventions (capitalization) -- or we could create Wikipedia talk:Naming conventions (theorems), since there's the issue of "Theorem of X" / "X's theorem" (resolved but worth mentioning somewhere central). Most of my textbooks use "theorem", small T. -- Tarquin

The apostrophe issue is almost solved now; the articles have been moved to the proper titles. I guess we just have to live with the fact that some theorems traditionally have apostrophes (Goedel's incompleteness theorem) and other's don't (Tietze extension theorem); it doesn't make sense to have a general rule of style there. That leaves the capitalization issue. I don't have a strong opinion, and since math books seem to be divided on the issue as well, we may as well be lazy and stick with the current convention of using lower case. And add redirects if needed. AxelBoldt 17:57 Oct 30, 2002 (UTC)

Well, I've completed my survey of math texts, and I don't think that capitalisation is as wide spread as I previously thought. It seems to be confined to a few, however prolific and influential, authors, such as Conway. So I hereby declare my opinion to be that we use lowercase (except for individuals' names, of course) in running text, and hence in article titles. Unless some new dissenter shows up, that probably settles it .... — Toby 14:54 Oct 31, 2002 (UTC)

Can I be a new dissenter? Since Euler had lots of theorems, then they are all Euler's theorems, but only one of them is Euler's Theorem, isn't it? It's a proper noun, sort of, because it's only refering to one specific theorem. I think it makes sense to make the distinction clear by using capitalisation. -- Oliver P. 17:32 19 Jun 2003 (UTC)

Maybe it's high time we started naming functions and theorems after what they prove instead of who thought them up, or maybe include both thinker and proof in the names of the theorems. Example: Pythagorea's Theorem, Showing Long Side of Right Triangle to be Square Root of Sum of Squares of Short Sides, or Pythagorea's Rule of the Hypotenuse for short. Rickyrab 17:38 19 Jun 2003 (UTC)

- Well, we're not in the business of
*changing*usage. We shouldn't just make up our own names for things... We should use the names that people commonly use in real life, where possible. -- Oliver P. 18:26 19 Jun 2003 (UTC)

In calculus, it is **the** **P**roduct **R**ule; not, **a** product rule. Pizza Puzzle

Pizza Puzzle is correct. Re the issue of capitalisation in general, the "growing trend" to use lower case has *nothing* to do with academia or accuracy. In the 1990s the book trade was de-controlled. One result was that a lot of large US publishers bought up many small and not so small publishers in Europe, or set up their own imprints in Europe. To save money, they decided that rather than have to prepare two forms of textbooks (one using capitalisation in British english for places outside America, another lowercasing practically everything in American english) it would be cheaper to produce just one, and surprise, surprise, they went for American english. This has been greeted with fury by many academics, writers and ordinary people outside the US who see it, to use a term I have heard used a lot to describe it, as "linguistic imperialism", or "bucking our language".

The result has been capitalisation wars between these publishers and some academics and colleges. One college banned an entire book from its courses when a publisher launched an American english new edition of a book traditionally written in British english. Another threatened to remove every book from every college reading list that had been published by one British publisher that had recently bought out by a US giant, if they as planned produced new textbooks that followed US "downcasing" of letters. I personally know two major writers who in their contracts *required* that British english not American english be used in the area of capitalisation for the UK imprint of their books. A *very major* British author whose textbooks are widely used in the US and UK threatened to refuse to produce a new edition of his top-selling economics textbook unless *British english* capitalisation was used in the *American* print run, saying, "you think you can use your financial muscle to buy our english in England, and force us to write like you. Well, guess what? You need me and I'm going to force Americans to read my books in British english." (His publishers went beserck. In fact he was winding them up, but they actually thought he was serious!)

So for wiki to have a policy of "downcasing" is simply to adopt US-style capitalisation rules that are bitterly resented among many writers and academics outside America and which are beginning to experience a backlash. (A lecturer colleague now operates what he calls a "three downs and you are out" policy in essays. Use the names of three political terms in American english-style lowercase rather than British english-style upper case and your essay automatically gets an 'F' grade. And others give students a bollicking for using downcase spellings of the sort that wiki (or some on wiki) seems determined to push. Wiki if it has any sense should on AE vs BE capitalisation should be following the same policy it follows on AE versus BE in general. Leave it to the original author to decide which version of english to use in any article. If AE users don't stop downcasing everything they find (they have already made a dog's dinner of the political science pages!) then BE (and Hiberno english) users might very well decide to take a stand and start applying BE capitalisation rules to everything on wiki. And AE users might *then* begin to understand how annoyed BE users are beginning to feel about the way they are been treated with the attempted universal application of AE capitalisation rules for reasons that have nothing to do with grammar or linguistic accuracy and everything to do with dominant American publishing houses making more money for themselves to the fury of the natives. FearÉIREANN 01:51 20 Jun 2003 (UTC)

- Well said FearÉIREANN!! I find it incredibly annoying too. The other strange thing is that the Wikipedia doesn't appear to be sticking to it's own conventions, just take a look at the headings on the main page, they all appear to be in "Title Case" i.e most of the words are capitalised.Steeev 12:41, 10 Dec 2003 (UTC)

I don't even think its a question of "american" vs "british" - its simply a case of wrong vs right. Im American and my American literature uses capitalization. Pizza Puzzle

This discussion is peppered with references to "english" rather than "English". I thought that convention, at least, was not open to debate. akame