[voidhorse]

Generating problems is fantastic, but I'd caution on overreliance in the other two cases.

Basically all of the cognitive science literature on learning that I am aware of says that the more you do directly and the less hand holding you are given, the better your acquisition and long term retention. In particular, having the LLM elaborate concepts for you is probably one of the worst things you can do when it comes to learning. Struggling through that elaboration process yourself is going to make the learning stick much more strongly, at least if all of the research is to be believed.

[tptacek]

I understand that. The core of the pedagogical approach here is Math Academy, not LLMs. (Math Academy isn't an LLM; it's a spaced-repetition accelerated curriculum centered on graded problem set submissions). But the LLM functions exactly the way a tutor would in a math course, and for that application, LLMs have become extremely effective; arguably more effective than human tutors.