This final paragraph is just editorializing. A computer will never care about anything (including games like Go and domination of other beings) that it is not programmed to imitate care about, and will thus remain perennially unmotivated.
Also, my intuition says that gradient descent is an ugly hack and that there HAS to be some better way (like a direct way) to get at the inverse of a matrix (not just in specific cases but in the general case!), but I digress, and not being a mathematician, perhaps someone has already proved somehow that a general method to directly and efficiently invert all possible matrices is impossible