I don't think you're being an idiot. There are some connections in mathematics that are quite "magical", where you get something like a correspondence between

I don't think you're being an idiot. There are some connections in mathematics that are quite "magical", where you get something like a correspondence between a family of curved surfaces and a family of integer-valued equations, and it's not at all obvious why that might be until you study it deeply. And sometimes articles about the Curry-Howard Isomorphism suggest that it's an example of that sort (I think this article does, to some extent). But (as I understand it), that isn't the case: here we have a simple directly-constructed correspondence. It's valuable, but not the sort of thing that mathematicians think of as a wonderful result.