When shall one write a mathematical expression as a separate line in a paper/Ph.D. thesis?

I believe that the answer is the same for researching papers and Ph.D. theses, or maybe even textbooks; but please correct me if I am wrong.

Here I am referring to a paper/thesis on mathematics. When one writes a mathematical paper, sometimes one uses (in LaTeX) the double dollar sign to write a mathematical expression in a separate line such as in the following example:

We know that the identity $$a^2+b^2=c^2$$ holds ture if ....

While sometimes one does not write a mathematical expression in a seperate line, such as in the following example:

Let $f:X\to Y$ be a one-to-one map, ...

My question: When do we write an expression in a separate line?

My impression is the longer the expression is, the more likely it is written in a separate line. But is there any (possibly unwritten) rule for it?