One interesting thing I noticed is when I actually got into math at the university level and engaged with professors there were multiple times where I got the feedback along the lines of "Well yes that is right but kind of weird way to think about or answer the question."
I think for higher dimensional problems it's actually an advantage? Like I have no idea how to visualize something in r^n. Not sure how much people "visualize" functions in r2/r3? To me the difference between r3->r4 is similar to the difference for r2->r3. It's more complex but the way I'd "visualize" something is largely the same.