>>82080194Read the book How to Prove It for a great into into first-order logic and set theory. Also read Logic for Philosophers to get a more in-depth look at the scope for logic. From there you can graduate to learning non-classical logics, such as modal logic, intuitionistic logic, etc. There's even quantum logic if you really want to find something esoteric. Also even before that learn the basics of a syllogism, going back to Aristotle. You may even be able to understand some high level math theorems once you learn all this, like in model theory and stuff from Godel, depending on how high and how in-depth you want to actually go.