* I find it quite unusual in practice for genuinely new symbolic notation to be used by an author. Maybe that just reflects the fields I read about most (information theory, Bayesian modelling, harmonic analysis).

* Usually you don't come across a journal article or even blog post with a single isolated equation. So any new or unusual notation can be explained once and reused many times.

* Even if you did have an isolated equation with unusual notation, I still think it's more clear to define the notation and then show the equation rather than spelling it out it words! (I'm sure you could find terrible counterexamples!) The visual benefit seems so great to me that it would be worth splitting it into two parts. A bit like a diagram or a graph can make things clearer even if it needs a bit of explanation.

It doesn't need to be genuinely new to be confusing. It just needs to be unfamiliar to the reader. At the very least, one should point the reader to a resource where they can read about the notation.

> * I find it quite unusual in practice for genuinely new symbolic notation to be introduced by an author.

This sentence seems to contradict the rest of your comment; did you mean "I find it quite unusual in practice for genuinely new symbolic notation to NOT be introduced by an author."?

Thanks, that was ambiguous and the way you read it wasn't what I intended. I meant it was unusual for an author to use a new symbolic notation at all, without saying anything about whether they define it in those cases where they do use something new. I've edited "introduced" to "used".