So I would like to know how it found the proof. Because it’s much more likely to have been plucked from an obscure record where the author didn’t realize this was special than to have been estimated on the fly.

This makes LLMs incredibly powerful research tools, which can create the illusion of emergent capabilities.

Here's the PDF: https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cyc...

It wasn't Knuth who used Claude, but his friend. Nevertheless, Knuth was quite impressed.