If you are looking for other branches of mathematics, I'd recommend topology and group theory; both can be pretty abstract, and work quite differently than the

If you are looking for other branches of mathematics, I'd recommend topology and group theory; both can be pretty abstract, and work quite differently than the math you tend to be taught at school. Otherwise, I recommend learning and using "extreme" programming languages, languages that go very far off your standard language. Examples: * Lisp: everything is a list * TCL: everything is a string * Haskell: everything is pure and strongly types, and you use monads and other crazy stuff * Rust: on the extreme end of safety through zero-cost (at runtime) abstractions * Regexes: Just how much you can do with a powerful regex engine (declarative programming) * Prolog Finally: studying philosophy. Philosophers have honed their abstract thinking skills to the max :-)