I didn't expect such a misleading intro from Knuth. It reads like Claude solved Knuth's math problem. In reality, Claude generated various example solution, and Knuth then manually generalized that to a formal proof. What Claude did is certainly useful, but it would have been nice to be clear about the scope of the contribution in the intro.

While not on the same level as these guys, I've done some similar stuff using Claude. This is a classic synergy example, where the output of human + LLM is far greater than just the human or just the LLM working on a problem. My experience has been that the LLM lacks fine grained judgement when it comes to allocating resources, or choosing a direction to work in. But once a direction is pointed out, it can do a deep exploration of that possibility space. Left alone, it would probably just go off on a tangent. But with someone holding the leash and pointing out areas to explore, it is a very useful partner.

I don't think he's misleading, I think he is valuing Claude's contributions as essentially having cracked the problem open while the humans cleaned it up into something presentable.

My interpretation is that Claude did what Knuth considers to be the "solution". Doing the remaining work and polishing up the proof are not necessary to have a solution from this perspective.

That's true but the capability to go back to an older iteration, reflect and find the correct solution (for odd numbers) is, in my book, a sign of undeniable intelligence.