Wikipedia talk:Naming conventions (theorems)

... see also Wikipedia:WikiProject Mathematics

from Pythagoras...

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 Cistene 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:

1. The capitalisation that we use should be written up in the Manual of Style;
2. We should follow the modern trend, what is likely to be used in most English language math books in the future;
3. Names of articles should follow the same capitalisation as we use in running text, as per longstanding Wikipedia policy;
4. 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)

from maths topics ...

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:

1. Baire category theorem
2. Bezouts theorem
3. Borsuk-Ulam Theorem
4. Brouwer fixed-point theorem
5. Cauchy integral theorem
6. Cayley's Theorem
7. Dirichlet theorem
8. Goedels completeness theorem
9. Hahn-Banach theorem
10. Hilberts basis theorem
11. Laurent expansion theorem
12. Lowenheim-Skolem theorem
13. Metrization theorems
14. Nash embedding theorem
15. Peter-Weyl theorem
16. Ramsey theorem
17. Riemann mapping theorem
18. Riesz representation theorem
19. Stone-Weierstrass theorem
20. Sylow theorem
21. Taylors theorem
22. Theorem of Bolzano-Weierstrass
23. Theorem of Heine-Borel
24. Theorem of Lagrange
25. Tietze extension theorem
26. Weierstrass-Casorati theorem
27. 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

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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)