[collinrapp]

Correct me if I’m wrong, but aren’t you simply referring to “applied mathematics” and “pure mathematics”, respectively? I skimmed through the replies to your comment and I don’t believe anyone mentioned these terms, although I did see one reference to “abstract mathematics” (a term used by you, as well).

I thought these were well-known terms and thus that the dichotomy you describe was itself well-known, but I thought I’d add this comment on the chance that you weren’t familiar with them.