I’m sorry to inform you that even mathematicians don’t excel in mathematical thinking when dealing outside their math domain.
Is it due to malice or due to the fact that all of us are mere human, I don’t know, but you can find mathematicians that were orthodox Marxists and orthodox anti-Marxists, you can find Anatoly Fomenko with his “history” and you can find Noam Chomsky with his strange conspiracy theories.
I also want to advice you to study Ptolemy astronomy, and the way he built the cycles of the planets and stars. It is very similar to approximation with series, so your claim that you can decide that Earth is not the center of the universe based on “critical” or “math” thinking is wrong. All you can say is that using Earth as a center of the universe make math model of planets motion too complicated.