First of all, let me be clear: I LOVE being on sabbatical (one semester plus a summer). And this time, I did something different: I started my paper at the beginning of the sabbatical rather than doing the “relearning stuff I once knew but forgot or never learned that well to begin with” stuff.
And yes, the idea for the paper formed quickly and started writing….and have now entered the rabbit hole.
It works something like this: “wow, I know how to prove Theorem X for a class of objects Y” and you start to write the proof. As you go you realize “oh wait, I really don’t need this hypothesis, and if I use this other technique, that I only “sort of” understand, I’ll be able to prove something much stronger. There is a temptation to just put the idea off, but no one wants a referee’s report that says that the author of the submitted paper is, well, a lazy idiot. So there I go…making sure “does this REALLY follow? It seems counter intuitive”…and I disappear.
I’ve got to give myself a time limit though.