> It seems like, we can at best, claim that we have modeled the human thought process for reasoning/analytic/quantitative through Linear Algebra....I don't understand is what about linear algebra that makes it so special that it creates a fully functioning life or aspects of a life?

Not linear algebra. Artificial neural networks create arbitrarily non-linear functions. That's the point of non-linear activation functions and it's the subject of the universal approximation theorems I mentioned above.