What is good english grammar and punctuation with mathematics statements?

Question

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).

Answer 1

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.

Answer 2

(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.