Agree. I wonder if aphantasia forces you to construct a richer and more abstract “internal grammar” when you can’t rely on visual imagery.

For mathematicians that aren’t aphantasic I wonder what goes on in your mind when you imagine a “compact set.”

To me I have a distinct object that presents “compactness” in the mathematical sense in my brain. It’s not associated with any other sense (words, hearing) it just “is” the concept of compactness. It’s not even related to the formal definition of a compact set. It’s more like a “feeling” of convergence in the limit (if that makes sense).

For folks heavily reliant on visual imagery would they have instead a visual representation of “compactness” that’s constructed in the visual sense rather than an abstract idea.

Same here! I think whatever compensatory mechanisms I've come up with turn out to be real advantages in some ways.

One interesting thing that I've found is that my approach to physics and math problems is often extremely geometric. Even if I don't visually look at things, I'm constantly constructing objects in my head (e.g., graphs of functions) and playing with them, although it's in more of a tactile way. I'll immediately start thinking "what does this function look like?" when my peers are more likely to start by pushing symbols around.