Knuth updated his 'Claude cycles' note with new spectacular developments. The remaining open problem for even m was completely solved using LLMs, including proofs of correctness. The techniques used are very interesting, including multiple agents working together. See the references of the note for details.

Also note the 'Over and out' section.

The transcript from ChatGPT they shared is interesting [1]. Only a few messages from the user were needed, mostly to present the problem correctly. The most meaningful one was a review on a preliminary report, made by another ChatGPT instance. The problem was solved and a full technical report was written in a total time of 2-3h.

[1] https://chatgpt.com/share/69aaab4b-888c-8003-9a02-d1df80f9c7...