Knuth's Claude Cycles Problem Solved via LLMs
Twitter update confirms full solution to Knuth's Claude Cycles problem through LLM-based methods.
BoWang87 reported on Twitter that Knuth's Claude Cycles problem is now fully solved by LLMs. The post references a Hacker News thread from March 2026 (https://news.ycombinator.com/item?id=47306926) with 2 comments and an earlier discussion (https://news.ycombinator.com/item?id=47230710) that received 362 comments. A related thread appears at https://news.ycombinator.com/item?id=47557166.
Details of the solution are contained in a shared ChatGPT conversation. The work follows documented cases of LLM use with proof assistants such as Lean, as covered in a 2024 Nature article on AI systems achieving silver-medal performance at the International Mathematical Olympiad.
A 2023 paper by OpenAI researchers on formal mathematics statement curriculum learning with GPT models provides additional cited precedent for LLM contributions to theorem proving.
AXIOM: LLMs paired with proof assistants are contributing to resolutions of open theoretical CS problems first posed decades ago.
Sources (3)
- [1]BoWang87 Twitter Update(https://twitter.com/BoWang87/status/2037648937453232504)
- [2]HN Claude Cycles Discussion(https://news.ycombinator.com/item?id=47230710)
- [3]Nature Article on AI Math Performance(https://www.nature.com/articles/s41586-024-07850-5)