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I am writing a master thesis in maths and I use lots of enumerations in theorems. I am not sure, how I use a comma and period correctly. As I was told, there has to be a comma after an item, except the last, which has to be ended by a period. Like in the following example: enter image description here

But now I have a more difficult enumeration: enter image description here

The items itself contain a period at the end. So I would

  1. not end the first item with a comma

and

  1. not end the second item with a period.

But then I have the impression, that I do not use a certain style continuous.

What do you say?

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    Actually, the structure and meaning are clear without any "end" punctuation at all. Seems pretty inconsequential.
    – Buffy
    Commented Jan 10 at 15:56
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    Keep in mind that most people here will be used to producing academic texts in English, and their answers will reflect that. I'm not sure you can safely assume the same conventions apply across languages. I suspect you'd be better off asking your supervisor.
    – Chris H
    Commented Jan 11 at 14:01
  • For what it's worth, I generally used sentence punctuation in my PhD thesis (submitted in English at a German institution), but did not use punctuation after conditions like those in your second example (for example). I don't remember if I was following any particular style guide or just doing what felt right to me, but there certainly wasn't any criticism of the formatting.
    – Chris H
    Commented Jan 11 at 14:13
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    I've read a lot of math, and I'd say that the commas after the 1 and -1 do not usually appear there. As for the others, I might change the first period to a semicolon, but wouldn't worry too much about it.
    – Mike
    Commented Jan 11 at 16:29
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    @AndrewMorton in this case, this is acting like an itemized list (like bullet points), so it should be on the left
    – David Raveh
    Commented Jan 12 at 20:06

4 Answers 4

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The problem with punctuation marks in mathematical formulae is that they can appear to be parts of the notation. I personally would not use them.

The way you decide this for yourself is to look at a copy of a classic mathematical text in your field and then copy their style.

If your thesis supervisor has told you to use a certain style, use that style.

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    (+1) Your first sentence is something that, over the years, I've felt more and more strongly about, at least in my personal writing when I don't have to conform to styles in place by others (e.g. in my day-job writing and editing work).
    – Dave L Renfro
    Commented Jan 10 at 17:53
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    To me, it's really irritating when someone adds punctuation after a URL, and in copying it, the URL doesn't work. A similar paradigm would be part of math. Also, separately, different regions of the world would interpret ',' and '.' differently.
    – JosephDoggie
    Commented Jan 10 at 18:11
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    "The problem with punctuation marks in mathematical formulae is that they can appear to be parts of the notation" would you mind providing an example? (And not the exclamation mark/factorial example, as it is pretty rare for an exclamation mark to appear in mathematics.)
    – David Raveh
    Commented Jan 11 at 13:07
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    Besides the factorial symbol, the question mark symbol is (now) standard for this function. Also, a colon : (sometimes a semicolon ; is used) and a vertical bar | are often used for "such that" in describing a set, and =: is often used for "equality by definition". There is even a double factorial symbol! Although I've never had to deal with a factorial symbol followed by an exclamation symbol, I often deal (my day job) with factorial symbols followed by a question mark.
    – Dave L Renfro
    Commented Jan 11 at 14:58
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    @Stef It is not contempt nor disdain. What you write on your own time (i.e. for yourself, not for publication or dissemination) is entirely your own business. When you are writing for no one but yourself, you can write however you like. No one else should care what you do with your own notes. With respect to drawing a line between formal and informal, this is how all writing is done---when you are writing in a formal voice, you are following a narrow set of rules (e.g. as set out by a style guide)---that is what it means to write in a formal style.
    – Xander Henderson
    Commented Jan 11 at 15:13
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I have to disagree with Thomas Schwart's advice (particularly the first sentence—as a matter of opinion, I don't think that properly punctuated mathematics is ambiguous). Mathematical sentences, including sentences which contain notation, should be punctuated in accordance with the normal writing standards of the language being written in.

For further details, I would recommend having a style guide handy. The standard guide for writing mathematics in English is the AMS [American Mathematical Society] Style Guide. The relevant material for punctuation is in Section 12.7. Quoting directly from the introduction to that section:

Mathematical expressions, including displayed equations, are treated as phrases or sentences and are punctuated accordingly (see section 13.4).

There is quite a lot of discussion on lists in Chapter 6, and Section 13.11 is relevant with respect to the punctuation of things in the cases environment.

(Of course, if you are writing for a particular advisor or journal or organization or whatever, and that advisor, journal, organization, or whatever tells you to do something different, then do what they ask you to do.)

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Unless you've been given some guidance from the people writing down rules for theses at your university, just pick a style you like for enumeration from a respectable journal in your field, and use it.

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Regarding Satz 3.1.8(a), I would already dispute the assertion that the item itself contains a period at the end. In my view, the first three commas are dictated by the case-structure of the specific mathematical expression*; but the period is in a slot for a global punctuation mark that treats the entire mathematical expression as a black box. So the rule for what punctuation to put there is the same as in Lemma 3.1.6—that is, the period should be replaced by a comma.**

*People have different conventions for punctuation in case-structures, but my main point doesn't depend on whether those internal commas are used (personally I prefer using them as given).

**It is always a valid optinon (at least in English) to replace a comma by a semicolon if the comma is separating phrases that themselves contain enough commas that the semicolon would add clarity.

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