This is one reason why it's helpful to learn bottom-up when possible as opposed to diving straight into the deep end and trying to fill in missing knowledge as you go.
Hm, I've always felt bottom up more difficult to learn. I always found it helpful to first have an overview, a mental map of sorts, of the high-level details, so that when I looked at the details later I could make connections and know where to "put" this knowledge relative to other things.
With bottom up I always feel lost because I don't know what it's useful for, the relationships to other pieces of knowledge, etc.
It can definitely be helpful to take a top-down approach in planning out your overarching learning goals.
However, the learning itself has to occur bottom-up. Especially in math. Math is a skill hierarchy, and if you cannot execute a lower-level skill consistently and accurately, you will not be able to build more advanced skills on top of it.
It's good to have a high level view of what your ultimate goals are, but if you are lacking too much foundational knowledge you can't even conceive of it. Especially in a subject like math, everything builds from the bottom up.
We don't give first graders an overview of differential equations and their applications when we start teaching them addition and subtraction.
I think there are certain circumstances where getting in over your head and digging your way out is a better approach -- but I don't know how to distinguish those cases from the rest.
I don't think there's anything wrong with trying to jump headfirst into things that interest you. I would just recommend that you need to be honest with yourself about whether you're making progress -- and if you're starting to flail (or, more subtly, doubt yourself and lose interest), then it's an indication you need to re-allocate your time into shoring up your foundations.
