How does geometry influence the philosophy of Descartes

Specifically, his notion of mind/body dualism?

the actions of a nasty person

Geometry like almost all math holds as a fundamental principle the concept of equality. The dichotomy that results from a concept like equality, (2 equal things), represents the duality of the categorical mind. That’s what they have in common. An assumption of some duality. Now in math there can be real identity because we’re only dealing with symbols. The mind body problem though is real, (at least on the body end), and some try and give functional explanations of this problem that are founded in identity theory. My question is whether or not we can be satisfied by that sort of solution outside the context of science or math? I’m dead serious. Would a big enough equation make you believe that there is or isn’t a soul?