What is Mathematical Physics?

We consider the answer to this question to be the central problem of the interpretation of Descartes’ scientific work. Schuster declared Descartes’ physics, because of its verbal character, to be natural philosophy, and excluded it from the tradition of mathematical physics, which he associates with Galileo and Newton. This assessment is mistaken, and the reason for the mistake is the vagueness of the concept of mathematical physics. Galileo’s physics, which completely lacks any description of interaction, which attributes to bodies a natural tendency to accelerate in free fall, and which considers circular motion as inertial, is automatically taken to be mathematical physics. On the other hand Descartes who introduced the notion of interaction into physics, who clearly saw that the acceleration of falling bodies must be the result of interaction, and who regarded only uniform rectilinear motion to be inertial, is not included in mathematical physics. My aim is to correct this obvious error.