# Capital letters in "Theorem", "Conjecture" etc [duplicate]

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

• 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". Commented Aug 7, 2014 at 14:03
• 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
Commented Aug 7, 2014 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
Commented Aug 7, 2014 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". Commented Aug 7, 2014 at 15:06

## 2 Answers

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.)

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.

• 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
Commented Aug 7, 2014 at 14:11
• @Mark Updated my answer to answer that question. Commented Aug 7, 2014 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
Commented Aug 7, 2014 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. Commented Aug 7, 2014 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
Commented Aug 7, 2014 at 14:41