> Why should a finite carbon brain be able to map out a coherent and finite model of something much, much bigger than itself.

Have asked that and have a guess: Darwin-style selection rewarded getting some rational understanding of the most important parts of nature -- fire, rock tools, clean water, agriculture, staying warm in winter, basic geometry, bows and arrows, the Pythagorean theorem, levers, wheels, boats, etc. -- we encountered. Well, it so happens that in this universe such "rational understanding" is enough to understand basic math, physics, chemistry, biology, ... back to the Big Bang, the 3 K background radiation, cells, reproduction, nutrition, diseases and immunity, ....

I gave up on the US education physics community when my teachers couldn't give a valid proof of Stokes' theorem, explanation of Young's double slit, or the beginnings of quantum mechanics.

So, now I have several polished treatments of each of Stokes' theorem, Maxwell's equations, and special relativity. Got a good background in probability (Neveu, Poincaré recurrence, martingales, etc.), enough to get a good path through thermodynamics. From Rudin, etc., got enough solid Fourier theory to check carefully the uncertainty principle in physics (doubt that what physics does there is fully justified) -- also carefully treated in a great course in "Analysis and Probability". For differential geometry, an Andrew Gleason student gave me some lectures and explained that the keys are the inverse and implicit function theorems, proved in a book by W. Fleming and just exercises in a Rudin book -- local nonlinear versions of what is easy in linear algebra. So, now I attack physics as a curious amateur!

I do remember a remark from a good mathematician: "Physics abuses its students." Well, they can abuse me no longer, and I can still do high quality study of physics.