That's an interesting observation. It seems that in theory, you could train it to do math if you encoded literally everything in syntax and started at the begin

That's an interesting observation. It seems that in theory, you could train it to do math if you encoded literally everything in syntax and started at the beginning, like Principia Mathematica 50 pages proving 1+1=2 type beginning, and then the rest of known mathematics encoded similarly, and used that as the training data, although the context window limitations might still stop it from doing anything useful, and it might not work.