I get the sense that there's two levels of understanding for most mathematics: a superficial level where you just have to manipulate symbols and be comfortable

I get the sense that there's two levels of understanding for most mathematics: a superficial level where you just have to manipulate symbols and be comfortable applying rules, and a deeper level where you grasp the underlying relationships and some fundamental 'why' of the problem. I used to think that if you were bad at the first, then the second would be an even tougher challenge. But I'm starting to suspect that actually people who are good at the first often just don't care about the second. And in fact it might be the very need for things to 'make sense' to you on a deeper level that is causing discomfort and difficulty at the superficial level. Some people lack curiosity about the deeper relationships, and perversely this might actually help them get along at the superficial level. For instance in finance, why is Macaulay duration(1) approximately equal to effective duration? One measures time in years, the other measures sensitivity in percentage form. How the heck do they come out at the same number approximately? For some reason i can't find any literature that's in a rush to explain this relationship... even though the two measures share the name 'duration' so presumably there's some intuitive understanding to be reached. (1) when the yield is expressed continuously compounding, at least