> Yes, you cannot hide the callstack when taught with pencil and paper.

Recursive functions were mathematically defined well before the callstack or the von Neumann architecture was a thing. Godel, Church and Kleene did alot of work on them in the 1930s (and I believe even prior to that infinite series were defined recursively although functional theory had not be worked out), this was before ENIAC (1945) which would be just barely recognizable as a general purpose computer and didn't have anything like CALL instruction.

So I don't understand this notion of "hiding the callstack" comes from. If one cannot understand recursion without invoking the callstack, well thats just them. But I don't see how its absolutely necessary or some universal

I have no complaints about how recursion is taught in mathematics courses.

I'm being quite clear that I take issue with how the concept has been taught in many programming books and courses.

You can see the ignorance and confusion in this very thread.