A math paper should follow all the usual rules of grammar, so in particular there should be subjects and verbs and the sort of punctuation you'd expect to find in a piece of nontechnical writing. I would prefer to write the following:
The formula for a circle is $$ x^2+y^2=r^2. $$
If I had to use the wording in the original question, I would write
This is the formula for a circle: $$ x^2+y^2=r^2. $$
Occasionally, the aesthetics of the page make punctuation look awkward. For example, one might write:
Therefore, the following diagram commutes: $$
M×N -> M⊗RN \ xymatrix{M\times N\ar[r]\ar[dr] & M\otimes_R N\ar[d] | \ & | \ | v v A } $$
with no punctuation after the diagram. There isn't any sensible location for a period at the end of a sentence, so I'd leave it out.
