But Einstein Also Said…
“Insofar as the propositions of mathematics refer to reality, they are uncertain; insofar as they as they are certain, they do not apply to reality.”
And
“Books on physics are full of complicated mathematical formulas, but thought and ideas are the beginning of every physical theory.”
And
“But there is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance, and this Einfühlung [literally, empathy or ‘feeling one’s way in’] is developed by experience.”
Remember when “perfect circles” ruled the heavens? Remember when Euclidean geometry was the only sensible geometry?
First and foremost progress requires new conceptual ideas. Then and only then does mathematics come on stage to play its applied role. Sometimes new mathematics must be invented to play this supporting role.