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Consider the following alternative paragraphs containing a line of mathematics. The mathematics is in its own line (thus not in line with the text), e.g., for the sake of emphasis.

This paragraph contains a mathematical expression $$f(x)\to g(c)$$ After the mathematical statement I have not added punctuation.

This paragraph also contains a mathematical expression $$f(x)\to g(x).$$ However, I closed the mathematical statement with punctuation.

Which one is correct? Are there better alternatives? I think the second is correct, though I find the punctuation somehow inappropriate in the mathematical line (one might for example confuse it for a mathematical symbol).

pele
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  • I would write $x\mapsto f(x).$ There are worse situations for confusing dots than this one. If your argument would go on like $f(x)\rightarrow g(x). h(x)\rightarrow i(x)$, then perhaps it is confusing. – Dietrich Burde Mar 30 '23 at 19:26
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    My point is that the mathematics is on its own line. Would you put the . there or not? – pele Mar 30 '23 at 19:37
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    Consider the difference if you write the statements inline:

    This paragraph contains a mathematical expression: $f(x)\to g(x)$ After the mathematical statement I have not added punctuation.

    This paragraph also contains a mathematical expression: $f(x)\to g(x)$. However, I closed the mathematical statement with punctuation.

    The flow is broken in the first sentence. Given that we typically place math on its own line because it does not fit inline, I tend to think the punctuation rules should carry over from the inline conventions.

     – csch2 Mar 30 '23 at 19:52
  • Previous discussions of this issue on this site include Should I put interpunction after formulas and the last paragraph of https://math.stackexchange.com/a/2321350. – ryang Jul 22 '23 at 02:05
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    I consider the missing punctuation as one of the biggest sins in mathematical writing. Thankfully it is rarely seen. – Kurt G. Jul 22 '23 at 05:32
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    A forgivable (but still a) sin is it when someone omits the tiny space using \, before the punctuation and after the mathematical symbol. To be precise: $$a=b.\quad\text{bad!}$$ $$a=b,.\quad\text{good!}$$ – Kurt G. Jul 22 '23 at 05:55

2 Answers2

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There are two different styles: one with punctuation following displayed formulas, one without. Both are used. Find the one you like, and be consistent. When you are publishing in a journal, there may be a format recommended by that journal.

Do include punctuation after in-line formulas if the grammar suggests it. But (in most cases) do not begin a sentence with a formula.

Advice on writing mathematics:

Halmos, P. R., How to write mathematics, Enseign. Math., II. Sér. 16, 123-152 (1970). ZBL0205.00101.

Halmos prefers displays with punctuation.

GEdgar
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(This answer is similar to one I posted in response to a similar question on Academia SE.)

The AMS Style Guide (p 100) reads

Each mathematics equation reads as a clause or sentence and is punctuated accordingly. Authors, however, sometimes leave displayed math unpunctuated. Insert commas and periods as needed so that the equation(s), the preceding text, and the following text together read grammatically.

So, per that style guide,

The Pythagorean theorem asserts that if $a$ and $b$ are the lengths of the legs of a right triangle and $c$ is the length of the hypotenuse, then $$ a^2 + b^2 = c^2.$$

is correct for AMS publications (note the period at the end of the displayed equation).

As noted in other answers to the linked Academia question, other style guides have different advice (in particular, this answer indicates that the American Chemical Society does not punctuate displayed math). Hence it is wise to consult the relevant style guide when preparing a paper for submission to a journal.

Xander Henderson
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