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Don't set out to "learn math", do things that require math to get them done. Run your own stats and summaries of Census data or something. Program your own gravity simulator, use any graphics or game engine you like, but do all the physics sims in your own code. Things like that.

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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.

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