Pāṇini Was Illiterate! How Marvelous!

By Bbenzon @bbenzon
I have long known that the first grammarian was a 4th century BCE Indian named Pāṇini. I'd tacitly assumed that he was literate and that, consequently, he produced written texts. I've just learned that that is not so. This is from a Language Log post by Geoff Pullum:
...the finest and most detailed phonological description of any language was done about 3,000 years ago for Sanskrit by an ancient Indian known to us as Panini (sticklers note: the first "n" should have a dot under it to indicate retroflexion). If language was not "prominent" for Panini and his devoted circle of followers, successors, and commentators, I don't know what it would mean for language to be "prominent". But Panini was not literate: his phonological description was cast in the form of a dense oral recitation rather like a kind of epic poem, and designed to be memorized and repeated orally. The wonderful Devanagari writing system had yet to be developed. (When it was, naturally it was beautifully designed for Indic languages, because it had the insight of a phonological genius underpinning it.)
I am astounded. Think about it. How'd they do it – Pāṇini and his students?