[evouga]

There is not really any new insight in the post, though cellular automata are indeed a good way to explain entropy, coarse-graining, etc.

The breakthrough (if it exists) must be in his computational irreducibility theorem, which he alludes to in many places. Unfortunately the link is to a book chapter which doesn't render properly on mobile and seems more of a long ramble than a formal proof, so I didn't dig into it.

An effective principle along the lines of, "if the output of a sufficiently simple program 'seems random,' then it is indistinguishable from random by all other programs," would be extraordinarily powerful and would immediately close many famous open problems, such as the normality of pi (and other numbers like sqrt(2)), infinitude of primes of the form x^2+1, the twin prime conjecture (and Dickson's conjecture), etc. It's somewhat telling that these are still open problems.

[ianai]

Kind of wonder whether he could help the math world by starting a math college. Could be a stripped down program with basically one or two degree outputs.

There is a LOT of math. It is unreasonably powerful at describing the world. But it’s also hard to cram into one single brain in a more rounded 4 year program. I’m also sure those same degrees would be economically viable as programmers and other professions with minimal added input.