Just because automatic differentiation is a different technique than numerical differentiation doesn't mean it isn't a numerical method.

(I probably should not say this, but I will anyway: your comments regarding math and science always give me the distinct impression that you know the name of a lot of things without knowing much about the thing. You are frequently breathless about analog quantum computing, Lie algebras, Chu spaces, some universal concept of duality, but then you fail to respond with substantial arguments to people that try to temper the breathlessness. If you want to convince people of things, you should work on this.)