I honestly don't see anything about this website that is really building intuition.

The "derivative operator" notion that the GP is describing was hugely important for me in intuiting what linalg could do.

Right, and that's a perspective you pick up on in a second course in linear algebra, typically. The key insight really is that the core concept is that of a vector space, rather than vectors per se. The only thing we really ask of vectors is that it be possible to apply linear functions with coefficients from your favorite field to them. Other than that, vectors themselves aren't that interesting: it's more about functions to and from vector spaces, whether it's a linear function V -> V or a morphism V -> W between two different vector spaces.

This is actually a common theme of mathematics, that the individual objects are in some sense less interesting than maps between them. And, of course, the idea that any time you have a bunch of individual mathematical objects of the same type, mathematicians are going to group them together and call it a "space" of some kind.

In fact, my previous paragraph is pretty much the basis for category theory. One almost never looks at individual members of a category other than a few, selected special objects like initial and terminal objects. A lot of algebra works in a similar way. If I could impart one important insight from all the mathematics I've read, done, and seen, it would be this idea of relations being more important than the things themselves.

I agree that learning a subject in mathematics requires going through it several times at increasing levels of sophistication.

That way, one gradually develops a level of mathematical maturity that allows an appreciation of abstraction.

I read about half of this. It’s nearly incomprehensible to me - I’d have to dig to find out what he’s trying to accomplish.

He’s going out of his way to introduce novelty and it appears he will try anything except address the subject directly.

You need mathematics abstract to understand this and when you have it you already know most of this.

Right, my exact sentiment.