I appreciate this methodology for getting stuff done, It's how I do my programming work, but I really do want to just "learn math" for the fun of it, like a puzzle, not make work. I was reading Descartes and he was writing about how the practice of math structured his thinking and I'd like to try to recreate that in myself. Maybe creating a project would be the best way to do it, but that seems like work rather than play to me.

This is a good technique for the engineering/physics side of the coin. For the more academic and "pure" math it might not be such a great goal. That said there's enough nice libraries and IDEs that one could use videos games to explore other mathematical contexts. But I don't get the impression that OP is a game programming enthusiast. Also that's a lot of overhead.