> This approach breaks down when you go into higher math.

It doesn't have to be literally visualization. Just some "feeling" for the objects. Some conception of them as actors, actees, things interacting, or having emotions or whatever. Again, whatever works. Maybe some people can work with concepts just based on strictly memorizing the definitions and drilling through proofs, but others need to conceptualize it all into a narrative. I don't mean dumbing it down, but making it easier to "grab" mentally. Hard to describe.