The insight is the point of research. Proof isn't the desired product of research, it's simply an apparatus that exists for the purpose of verifying and demonstrating correctness of insight.

Yes, and his point is that finding that algorithm was, to Knuth, the interesting part. Getting from that to a proof was the boring bit.

Yeah, and I'm not sure what the other guy's argument is. It's Knuth, the primary researcher, who is giving the praise here. I don't see a possible motivation he would have to falsely give accolades to a AI for a problem he presented, then cleaned up to solve.

That’s fair. Clearly Knuth himself thought it was impressive, that’s a strong signal.

AFAICT, Claude was not asked to prove its algorithm works for all odd n, but was instead told to move on to even n.