Not all models are mathematical models. When you build a model of the interior of a star, you are using maths all the way up. Financial models are statistics all the way, which is also math, but a model of a brain could rely only in parts on math, as I said above. The point is that so far, we only have biology to base it on. I am not aware that anybody have made a mathematical model of the brain. Are you?I think you are dodging the fact that modeling is a mathematical discipline.
Actually, they are called neural networks because they are based on a crude biological model. They are not capable of doing anything on their own, but have to learn by reward and punishment. When they can do what they were intended to do, nobody knows how they do it.So these neural networks just appeared out of nowhere then? No mathematical modeling required?
Neural networks have also failed completely in achieving anything like consciousness, and modern attempts at achieving artificial consciousness are taking the path of creating an emulation that uses much more detailed simulation of the elements of a brain than before.