You’re missing the fact that mathematicians develop an intuition for mathematical concepts...
I am aware that humans are not born with an innate intuition about Hilbert spaces. What I was talking about is that intuition is that which allows us humans to recognize structural similarity and transfer that understanding across levels of abstraction to reach a level of generality that allows us to shed light on big chunks of unexplored territory at once.
I (unsupportedly) suspect that something like “recognizing structural similarity” — or rather, a mechanism for finding the structures something has, after which structural similarity is just a graph algorithm — is the foundation for human abstract thought.
I am aware that humans are not born with an innate intuition about Hilbert spaces. What I was talking about is that intuition is that which allows us humans to recognize structural similarity and transfer that understanding across levels of abstraction to reach a level of generality that allows us to shed light on big chunks of unexplored territory at once.
I (unsupportedly) suspect that something like “recognizing structural similarity” — or rather, a mechanism for finding the structures something has, after which structural similarity is just a graph algorithm — is the foundation for human abstract thought.