No answer I give will be satisfying to you until I could come up with a rigorous mathematical definition of understanding, which is de-facto solving the hard AI

No answer I give will be satisfying to you until I could come up with a rigorous mathematical definition of understanding, which is de-facto solving the hard AI problem. So there's not really point in talking about it is there? If you're interested in why compression is like understanding in many ways, I'd suggest reading through the wikipedia article on Kolmogorov complexity. https://en.wikipedia.org/wiki/Kolmogorov_complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity