It’s not a dichotomy, it’s a fact. Lucretius had the idea that the world was comprised of atomos (by way of Epicurus). Without mathematics and science he didn’t

It’s not a dichotomy, it’s a fact. Lucretius had the idea that the world was comprised of atomos (by way of Epicurus). Without mathematics and science he didn’t have a theory. His intuitions got him far and maybe it set the stage for Dalton but Lucretius’, The Nature of Things wouldn’t be the foundation of discoveries that leads to new understanding. In programming you end up with JavaScript Promises instead of proper monads because of similar appeals to intuition. A monad obeys certain laws upon which further abstractions can be built. Promises do not obey those laws and so one cannot benefit from them. A programmer has to learn what a Promise is and how it behaves. You learn what a monad is once and anything that is a monad behaves the same way. The reason why it’s important to use the proper names is so that people can find the original definitions and theorems. You don’t have to be a category theorist to use a monad. You can have a basic understanding, as I do, and get by fine. However when you want to understand the theorems to build your own abstractions it’s great being able to go straight to the source. Simon Peyton-Jones has a good explanation for why Haskell took this route in his talk, Escaping the Ivory Tower.