I think we have wildly different conclusions about what happened here. You see the machine as instructing Terrence Tao, as if it were Plato teaching Socrates about the theory of forms; I see Terrence Tao using the machine to teach himself, like an intelligent student uses a book. In this case, it's just a book that fools us into believing it can think and reason like we do, because it generates language in much the same way we do when we think and reason.