For formal articles, should a displayed equation be followed by a punctuation to conform to the language grammar ?

Question

For formal articles, should a displayed equation be followed by a punctuation to conform to the language grammar ?

For example:

The most well-known physics formula is

    \[E=mc^2.\] %should I put a period here?

And if you expand

    \[(x+y)^2,\] % should I put a comma here? 

you will ...

Answer 1

For what it's worth, Knuth says that they should be added in Mathematical Writing.

Don’t overdo the use of colons. While the colon in ‘Define it as follows:’ is fine, the one in ‘We have: ⟨formula⟩’ should be omitted since the formula just completes the sentence. Some papers had more colons than periods.

That said, in the TeXbook, he omits the periods in some of his displays, but usually when he's showing TeX input and output. Compare the display on page 127

                                                                   α, β, γ, δ;

to the displays on page 128 (which I won't duplicate since that previous one was enough of a pain).

Answer 2

This has been discussed at great length over at mathoverflow. My personal opinion (which agrees with the two most upvoted answers over there) is that you should always use proper punctuation. (In the example of frabjous, where the period "." has a mathematical meaning, I would make an exception.) I think that if you look at books, you'll mostly find everything with punctuation (of course not in the case when I say that

a+b=b+a

holds for all real numbers a and b).

However; I think that Andy is right, there's no real consensus, and it seems to depend on the community if punctuation is desired or not.

Answer 3

I don't think there is any consensus on the matter. I've gotten into heated debates with co-authors on the matter, and I always fight to include the correct punctuation.

When you publish your paper, the journal will force you to conform to their style guide anyway, so it's not something you have complete control over (but it might be worth noting that many journals [eg, I believe, the Annals] believe in using correct punctuation on math displays).

Answer 4

Personally I think it looks very ugly to have punctuation there. It can also be confusing. Not long ago people used dots on the baseline for multiplication, and the Peanist school of logicians used dots in place of parentheses for grouping, and these could be misconstrued as that.

But take that with a grain of salt. I think you'll find that this this is something people disagree about. I've definitely had publishers of my work try to force this kind of punctuation on me, and I've always insisted that it be removed. Sometimes they do what I ask, and sometimes not, and I definitely have seen both practices in stuff that I read.

Answer 5

My personal view is that mathematical documents (as well as other structured documents) should have a linearized version that complies with a well-accepted and consistent set of punctuation rules. While using some symbols like the period may cause ‘interference’ with a display equation, it seldom seems to bring any real barrier for comprehension. (And if it does, you can always rearrange your sentence.)