AI agent completes Coq proof that Busy Beaver BB(238) halting is independent of Peano Arithmetic
MoonL88537 · x · 2026-10-19
One of Mira's agents, after seeing a single example, quickly completed the proof for the 238th Busy Beaver number — the PR was merged on GitHub.
- The result: BB(238)'s blank-tape halting holds if and only if classical Peano Arithmetic has a finite refutation — i.e., by Gödel's incompleteness, whether this machine halts is undecidable in PA.
- Verified with Coq 8.20.1: includes a literal 238-state, 476-transition Turing machine table, composing finite proof compilation, candidate enumeration, and literal TM execution in both directions.
- The author notes the earlier Metamath approach needed the extra step of embedding the proof in a formal system to invoke Gödel; this route is much easier.
An agent autonomously producing a proof-assistant-verified undecidability result is a landmark moment for AI doing formal mathematics.
More from Fun
- Prototyping with Gemini 4 Argon: WebGL toys, auto-edited reels, procedural C++ music — alexanderchen · 2026-10-20
- Agentic coding triggers the same neurons as a 14-hour Civilization addiction — aniketapanjwani · 2026-10-20
- "0.0 days since last GitHub outage" sign photo goes viral as GitHub fails again — kscottz · 2026-10-20
- Meme: by late 2026 even a glider game ships a true wind solver — MoonL88537 · 2026-10-20
- Google Flow rejects harmless prompts but greenlights a video full of profanity — Frustratedtwice · 2026-10-20
- Chinese humanoid robot shows off pole dancing skills in viral demo — LexiLove · 2026-10-20