Generally when “math” is brought up, most of us think of arithmetic, which really doesn’t do a whole lot on its own. As often as not, new ideas, symbols, and rules are created because they are needed, as opposed to being found (like the picture above). Algebra (group theory): This is the entirely abstract study of “there’s stuff, and things can happen to that stuff”. To be more rigorous, and to actually get stuff done, it primarily considers “groups“, which have more structure than just “there’s stuff”. Logic: This includes stuff like: “If P, then Q” is equivalent to “If not Q, then not P”.