The difficulty of visualization comes from 3-ness which gives rise, as Lao Tzu said, to everything-ness.

More depth of understanding of math could come from breadth of sources.

Problem solving is about mental checklists:
1. Getting the "groceries";
2. Not getting munchies.

In divine revelation, two explanations go together if they are on the same subject.
If not, they usually are counters of each other in my heart, unifying only in wisdom.
Or, they can never morph their qualities into different ones.
Same for linear algebra.

In Plato's pedagogy of music, philosophy, then physics, math progresses from simple sound differences, to logic, to matter and space, because these mirror denser aspects of reflection requiring greater precision.

Like reading among other things, problem solving starts from a child, so not until every small problem is solved on the way to the big one, will there be a real answer.
That's why some children keep asking "why?"

Pick a cause,
Any cause
Then traduce it
Down to flaws
Not justified
To drive its message
Sloganeering
Its progressive
True intention
Buried in
The factory wreckage
Manufactured
Discontent,
Last vestige of
The dissident

The child thinks the simplest, and therefore is the object of the simplest questions.
It also gets the most heat from those sure of themselves.
The child is the source of the deepest learning and is therefore the Source of enlightenment.

All the ways of math are so hard to memorize, its study is more about the (not) mere study than the completion of pedagogy.
That is the difference between the genius and the degree.
Study, reflect, wrestle, struggle.
That is the very definition of genius, not an A on every course.
Moreover, although it would seem that one could complete the pedagogy, it is never complete unless the whole is memorized and one is capable of using any part of it at the drop of a hat.
I don't even know if I've met someone like this, although some professors on YouTube seem to exemplify this.

I have to stop thinking about math symbology as a part of a hierarchy, but rather an ad hoc system where everyone must be familiar with everyone else.