Not at all! I fully endorse learning. My point is that physical intuition will only get you so far in mathematics. Eventually you have to make the leap to working abstractly. At some point the band-aid has to come off!

Well, can you visualize vector spaces beyond 3 dimensions?

You just visualize 2 or 3 and say "n" or "infinite" out loud. A lot of the ideas carry over with some tweaks, even in infinite dimensions. Like spectral theorems mostly say that given some assumption, you have something like SVD.

Now module theory, there's something I don't know how to visualize.

Your intuitions can often lead you astray. For example, the curse of dimensionality [1] deceives our intuitions about volume at high dimensions.

[1] https://en.wikipedia.org/wiki/Curse_of_dimensionality