> For example, I know things like (a^b)^c = a^bc, and that I can solve for x in x/a = b/c by cross multiplying so that xc = ab, but I can’t prove either of tho

> For example, I know things like (a^b)^c = a^bc, and that I can solve for x in x/a = b/c by cross multiplying so that xc = ab, but I can’t prove either of those things. That's actually kind of hard. Not because the proof is hard, surprisingly, but because you need a rigid notion of what exactly you're trying to prove. That's the hard part. The closer you get to the basics, the deeper the rabbit hole goes. You end up with axiomatizing the algebra, mathematical logic, formal proofs and different formal models... So _maybe_ start with something less abstract. Some problems which do not involve either algebra or geometry so you can develop intuition for what is a proof and how to see holes in a one. Afterwards, you can try adding more and more rigidity to the things you're familiar with.