Comment by brookst
20 hours ago
My favorite thing about your story is that you wrestled (enjoyably, it sounds) with a known problem for decades, but are finding fulfillment in an open ended problem that is exercising creativity about both problem and solution.
IMO that’s where AI is going: as soon as a problem can be formulated clearly enough, AI will trounce us humans. I have yet to see evidence that it can decide what problems are important at a remotely human level.
I think the next test will be asking an AI to come up with a new branch of mathematics - just letting it rip and telling it to construct a system that doesn't reduce to combinatorics, group theory, graph theory, analysis, etc. Just get wild with it and don't start with any known problem as a jumping off point.
I think something like the Collatz conjecture will be solvable not as number theory or ergodic theory but some other completely wacky environment that humans haven't even sniffed at.