No, back propagation is just the chain rule from calculus. d(f(g)) = df(g)dg. It is applied to linear algebra, but with linear algebra alone you will never arrive to it.
You can just admit you don't understand calculus (and go and learn it if you care). No reason to go around doing mental gymnastics about it.
I am so glad that we are having an AI revolution within mathematics where hopefully the computability crowd will dethrone Cantorianist view.