When should an equation be numbered when writing a paper?
The dominant philosophy in most mathematical writing is to only number equations that are referred back to within the paper/article/note/book, or to number particularly important equations.
In general, there are three conflicting trains of thought with respect to numbering of equations in a paper.
- Fisher's Rule: Number every equation, every time.
- Occam's Rule: Number only those equations which are referred back to.
- Fisher-Occam Rule: Number those equations which might be referred back to.
These rules were the subject of the article Writing in the Age of LaTeX appearing in the 1995 Notices of the AMS. But even there, some of the reasons for Fisher's Rule haven't aged particularly well.
I try to do what the other answerers say to do: only number those equations I refer to. But on looking at the OP's sample page, another reason to number equations occurs to me: other future writers might want to refer to some juicy equation of mine, and it would do them a service to set things up so they could write "According to Kimchilover's equation (17), blah blah".
Added, 18 July: For example, in the body of the paper I say,
This and that. Clearly $$A=B$$ and so the set $S$ is bounded, proving the theorem.
The equation I don't number is $A=B$, which is referred to only by the sentence it occurs in. By the standard rule it gets no equation number. If I had foreknowledge of how important my work will be, I might say something like this in the introduction of the paper, where the problem and methods are described:
Theorem 2 then follows from the application of our Lemma 1, the Krein-Milman theorem, and the simple-looking equation (17).
And then give my faux-humble formula its number (17).
You should only number equations that you are going to refer back. Most people are not very consistent. But now there are LaTex packages that do exactly that. See this post.