10

This is my first post and as you can probably guess I am a mathematician so I have no clue about grammar. I am writing a mathematical document at the moment and I would appreciate some advice on my usage of capital letters. Can somebody please confirm if the following are correct?

1) "We know by T​heorem 4.6.1 that..."

2) "the following c​onjecture, due to..."

3) In order to prove the "Mckay-Stevens $k$-covering C​onjecture, once needs to show that..."

I'm particularly confused about 3).

Many thanks for any help

Ronan
  • 7,330
  • 7
  • 39
  • 61
Mark
  • 101
  • The physics journals I publish in differ regarding the use of capital letters. Some insist on using Equation, Figure, etc. when referring to a numbered equation or figure. However, they would not typically require capital letters when talking about an equation in general, such as in "We solve the equation of motions". – painfulenglish Aug 07 '14 at 14:03
  • 1
    I think the main thing here is whether or not the word is appearing in the name of a theorem or conjecture, in which case it is usually capitalised. That's the difference between 2) and 3), for example. – Rupe Aug 07 '14 at 14:07
  • Many thanks for your input. is 3) correct then? I'm a little confused because maybe the Mckay-Stevens t-covering Conjecture is like a name of a conjecture like Conejcture 4.5.6 as opposed to their conjecture? In which case would the C in covering also be a capital? – Mark Aug 07 '14 at 14:08
  • (3) is certainly correct; proper names can be extended to things created by the person named. For a numbered theorem or diagram or equation, follow the custom of the journal you wish to publish in. BTW, capitalization is not "grammar", just like the choice of Greek-letter versus Latin-letter indices for tensors is not "mathematics". – John Lawler Aug 07 '14 at 15:06

2 Answers2

6

There is no standard used throughout mathematics. Not even throughout English-speaking mathematics. Some recommend "Pythagorean Theorem" and others recommend "Pythagorean theorem".

Find your own comfortable conventions and use them. And when a journal or publisher has a different convention, follow it without objection. (There may be more important things to reserve your objections for.)

GEdgar
  • 25,177
1

Those all look correct, to me. Those are examples of proper nouns.

Capitalization

The reason that you would capitalize your first example is because it refers to a specific theorem, namely 4.6.1. Example number two is referring to a theorem less specifically. The third example is capitalized because it refers, again, to a specific theorem.

Capitalization of Hyphenated Compounds

Capitalization of hyphenated compounds in titles is a question of style. You should almost always capitalize the first part, in titles. The second part would be capitalized if it is a noun, proper adjective, or carries equal or more force than the first part. Don't capitalize the second word if it is a participle that is modifying the first word. [source]

Your example is an example of where the second word is modifying the first. In that case, you would not capitalize the word covering.

Journal Style Guidelines

I also agree with what GEdgar said about following the rules of the paper you are publishing in. If the journal you intend to publish in has a style guide, use it! If there is not a style guide, the best rule of thumb is to maintain uniformity in your style. This advice is taken from a style manual written by the American Mathematical Society.

Alex W
  • 2,027
  • Thanks! So would the c in $k$-covering from 3) also be capital C or would it actually depend on whether the authors Mckay and Stevens used a capital? – Mark Aug 07 '14 at 14:11
  • @Mark Updated my answer to answer that question. – Alex W Aug 07 '14 at 14:25
  • Thanks for all your help. One final question if I may: What if the conjecture was something like the "maths number Hilbert Conjecture"? Is it the case that when I state the theorem eg "Conejcture 1 (Maths number Hilbert Conjecture):" I use a capital on Maths, but when i say later on, "... by the maths number Hilbert Conejcture" I don't capitalize the M? Additionally, if the hyphenated word was not the first word in the title, it would be capital, and again, not capital when referred alter on in the text, or not? – Mark Aug 07 '14 at 14:33
  • I would say that, according to the rules in this answer, you should capitalize the "C" in "k-Covering". In this case, the first word is modifying the second, and not the other way around. (It's a covering. What kind of covering? A k-covering.) However, there are some style books that recommend always lower-casing the word after a hyphen, so both choices are fine. – Peter Shor Aug 07 '14 at 14:37
  • Fair enough, but the last word "Conjecture" is always capital in the title as well as when referred later on in the text? And if the word Mckay wasn't someone's surname it would be a capital M in the title but not a capital M when referenced in the text? – Mark Aug 07 '14 at 14:41
  • @Mark Keep things uniform, later in the text. If you are referring specifically to the McKay Conjecture, later in the text, then you would capitalize it because it is specifically referring to that conjecture which is a proper noun. – Alex W Aug 07 '14 at 14:46
  • I see. So however it is referred to when I originally state it is how I should refer to it from then on? – Mark Aug 07 '14 at 14:53
  • @Mark Absolutely. And I'll note that k-covering would be an example of the very rare exception where you might not capitalize the first part of the hyphenated compound, depending on whether or not the actual mathematical variable it refers to is a lowercase k or not. That is a style decision though. It's not a rule. – Alex W Aug 07 '14 at 15:01
  • If I state the conjecture, say "Conjecture 5: Clique-Stable set separation Conjecture", forever inwards in my document, should I use this exact form? Eg "we know by the Clique-Stable set separation Conjecture that..."? It just looks awfully strange messing around with capitals like that during the rest of my text. Or would I merely be using capital C and capital S because it's the title of a theorem, and in the rest of my document I just write "clique-stable set separation Conjecture"? – Mark Aug 07 '14 at 16:14
  • @Mark Yes. Uniformity is very important, to avoid confusing the reader. However, you would not capitalize separation or conjecture in that particular case because they are not part of the actual name of the conjecture. They are just stating that it is a certain type of conjecture: a separation conjecture. Here's an example of a paper which uses that conjecture with correct capitalization: the Clique-Stable Set separation conjecture – Alex W Aug 07 '14 at 16:28
  • Now I'm really confused. How is my 3) correct? Surely it should beMckay-Stevens $k$-covering conjecture, then? – Mark Aug 07 '14 at 17:18
  • @Mark The capitalization of conjecture is completely dependent on whether or not it is part of the name of the actual conjecture, or whether you are just referring to it in general as a conjecture. So, your third example is correct if that is the full name of the conjecture. Otherwise, you would not capitalize C in conjecture. Capitalization is telling the reader: "I am talking about this specific thing." If it's lowercase they will know that you are just describing it as a conjecture. – Alex W Aug 07 '14 at 17:35
  • Then in the paper you referenced since the conjecture is known as "the clique-stable set separation conjecture" shouldn't everything be capital and certainly the C in conjecture be capital? It's the name of the conjecture I think? – Mark Aug 07 '14 at 17:42
  • @Mark It is dependent on the context where it is being used. If it is part of the name at all, yes it should be capitalized. If you are merely trying to convey that it is a conjecture, after mentioning part of the name, then you can write conjecture in lowercase. – Alex W Aug 07 '14 at 17:49
  • Many thanks for all your help Alex. So as a solution to my problem, I could introduce every conjecture and theorem I state as "Theorem n (The Xxxx Yxxx Aaaaa Theorem): ...." and from then on always write Theoren n as "the Xxxxx Yxxxx Aaaaa Theorem"? – Mark Aug 07 '14 at 22:47