The history of mathematics is very complex, and I regret that I will never really study it. What little I know, and am unsure of its accuracy, is that the movement over centuries from a geometric based math to an algebra based math, occurred with considerable conflict.  The transition from an Earth-Centered solar system to a Sun-Centered solar system also occurred at this time.

Ptolemy, around 200 AD composed his Almagest , the second most “published” book for a long time, next to the Bible. He used geometric mathematics to develop a means of computing the retrograde motion of the planets with accuracy. It was purely MATHEMATICAL ASTRONOMY – simply computing planetary positions. His system was a “computer”, using real diagrams of cycles within cycles within cycles – today a version of Fourier Analysis.  This was to be distinguished with PHYSICAL ASTRONOMY, which posited about what was “really out there”. There was no problem between mathematical astronomy and Catholicism, as it was only a technique for prediction.  Later, Galileo ran into difficulty with the church when he claimed physical reality for his Sun Centered system with material planets.

Some propose that with computers, mathematics is making another transition – this time away from algebra to computer generated computations. Computers can “solve” problems, coming to the “correct solution”, but where no one can know the steps taken.  The algebraic mathematical expression – the cornerstone of “mathematical physics”  is no longer the anticipated “holy grail” of theoretical science.