Statistics is the basis of science. Probability is one of the axioms of reality. Probability just works and is assumed to work and nobody knows why. It is fundamentally the reason why Entropy always goes up.

It is much more then a small branch of math given it's foundational relation to the real world.

Intuitively AI is much more just a branch of math. We are getting closer and closer to understand theoretically how our own brains work. The philosophical connections are profound and you are using language categories to limit your thinking.