If you find this interesting, you should look into Solomonoff induction. It combines Kolmogorov complexity with Bayes rule to provide a general framework for inductive inference, and naturally formalizes Occam's razor.

I wouldn't say so about Occam's Razor which is a heuristic.

The relationship between compression and intelligence, while not equal is definitely there. It looks like 3Blue1Brown is going to be doing some videos on this aspect.