> I think this is correct, if you consider college level linear algebra and an intuition for applying it to novel problems to be non-trivial knowledge

Yes, in the context of "a self-taught researcher", I think I intuitively meant anything that precisely requires a degree, typical academic knowledge. E.g. you can become a great business person who won't feel hindered by lack of academic knowledge, you definitely can't do that as a surgeon or lawyer.

I guess I was wondering where math fit in this picture for AI research. (which I should explicitely relate to "#2" in user ineedasername's post, i.e. "AI Research as examining the theoretical frameworks & approaches to ML/DL in a way that may itself lead to shifts in the understanding of ML/DL as a whole and/or develop fundamentally new tools for the purpose of #1 [AI Engineering Research]. What might be termed "basic" or "pure" research.")

> I guess I was wondering where math fit in this picture for AI research.

Well you can't do #1 or #2 without having a level of maths proficiency that most college grads do not have.

FWIW, I don't understand the difference between #1 and #2 above. Most academic/industrial research is incremental (i.e. #1), and a tiiiiny % will have any impact in the way something like XGBoost would (the example he gave in another comment). That doesn't mean that the non-impactful research isn't 'basic'. You could alternatively just call #2 "groundbreaking research" and #1 "non groundbreaking research, but you need mathematics knowledge for both imo.

I see what you mean. It seems possible the distinction is perhaps academic at best, a matter of perception. (I certainly don't have a personal opinion, yet! but point taken, and the continuity you speak of seems more realistic tbh).