[sebastiennight]

I think you're strawmanning my math point from "if you're made of math and can make a trivial improvement in the math, you get a smarter n+1 program that can likely make another trivial improvement to n+2"... to "AI can solve all math" (which is not my point at all).

You seem to be generalizing item #3 from "there are limits to what AI can do with math", to "therefore, AI can't improve any math, and definitely not the very specific kind of math that is relevant to improving AI". That is a huge unjustified logical jump.

Has it ever happened on the path from Enigma to Claude Opus 4.6, that the necessary next step was to figure out a new nth Busy Beaver? Is Opus 4.6 a better Busy Beaver than Sonnet 3.5?

Or is that a mostly unrelated piece of math that is mostly irrelevant to making a "smarter" AI program from where we are today?