The idea of &quot;notation as intelligence augmentation&quot; is the reason (or one of them) that Haskell programmers are so enthusiastic about things like functors and monads; type theory is its own branch of mathematics that could be appended in the list of things like calculus and vector analysis [1], and might bring in the same kind of new levels of thought and abstraction.<p>[1] Disclaimer; I am not a mathematician.