Thank you for the interessting material! I have heard a lecture on the geometric and topological applications to solid-state physics. This is one of the things that excites me a lot that whole areas of physics can be "geometrized".
But then I think that we may be so strongly biased toward doing so because there's something fundamentally easy about evolving a brain that comprehends geometry. That information with geometric representations are fundamentally easier to evolve good mental models for than other kinds of information.
"God ever geometrizes."
and
"Geometry existed before the creation."