As long as I'm here, I'd like to add that the proofs (in the vernacular sense : ) supporting the geocentric model prior to Ptolemy were common-sense notions, such as, "If the earth moved, there would be great winds sweeping everyone off their feet"; "If the earth moved, then when someone jumped up, he would land in a different spot"; etc.
He actually shook his head toward the end of the lecture, seemingly disappointed that all that artistic math was for naught.