Should I put interpunction after formulas?

Question

I am presently doing my first substantial piece of mathematical writing, hence this, probably somewhat silly, question.

How does display-style mathematics interact with punctuation?

More precisely, suppose I have an sentence like

From the above considerations, it follows that $a^2 + b^2 = c^2$.

As long as the equation is in one line, it is clear that a dot (".") follows. What happens if the equation is in a separate line? Does the dot remain, as in:

From the above considerations, it follows that $$a^2 + b^2 = c^2.$$

or should it disappear? Also, should I separate the sentence from the equation by some punctuation mark? (e.g. a colon or a comma after "that" in the above sentence)

I would also appreciate it if someone could point me to a good and reliable reference for proper mathematical writing.

Answer 1

It is a matter of convention. There are two "references", both of which I found through this question on TeX.se:

• The book Mathematical Writing by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts, which says to include it, and also not to have any punctuation (like a colon) before the displayed equation, and

• Extensive discussion among actual professional mathematicans at this question on MathOverflow, where the top two answers recommend retaining the punctuation, the third is one of throwing up one's hand in frustration, and the next says the opposite, etc.

My personal preference is to treat it as text (e.g. the way you would do if it was an inline equation) and retain punctuation after the displayed as appropriate, though I probably don't consistently follow this.

Answer 2

It should definitely not disappear. No need for a punctuation mark either. Just pretend like the separate line is not separate.

Answer 3

Personally, I'd try to organize the text to that the displayed equation is a "sentence by itself" (or close enough, anyway) that the puntuation afterwards is can be omited. A displayed equation with extraneous puuctuation at the end is jarring to me, and might even confuse the reader or change the meaning. Say you want to emphasize this sentence $$ a = n! $$ Quick, is that $n!$ or emphasis?