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.
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.