DeepMind points Gemini 4 Argon at the Busy Beaver problem
From the AI digest for 2026-10-21
What happened: Google DeepMind retweeted researcher Tom Zahavy's writeup (~11:00 AM ET, October 21, 2026 — https://x.com/GoogleDeepMind/status/2112924036791734645) of a year-long project by the DeepMind Discovery team, led by student researcher Marco Santos, applying Gemini 4 Argon to the hunt for the 6th Busy Beaver number, BB(6) — the search for the simplest Turing machines that run longest before halting, a problem whose resolution is provably beyond any universal algorithm. Rather than solving human-set problems, the pipeline mines the search itself for new conjectures: it simulates raw Turing-machine traces to compress recurring patterns, conjectures transition rules and runs synthetic experiments on edge cases, then proves the equivalences formally in Lean 4. The team reports 20 new potential "Cryptids" — tiny programs whose halting behavior is governed by deep unsolved number-theory questions, akin to Collatz or Goldbach — and verification of 33 more machines previously studied by the community, with proofs open-sourced and halting/non-halting proofs contributed to the community repository; an arXiv paper is linked (https://arxiv.org/abs/2610.22603).
What's genuinely new: A debut — there is no existing thread on AI pipelines generating new mathematical conjectures; the Busy Beaver work, its Cryptids, the 20/33 counts, and the Argon-powered pipeline all arrive here first. As with OpenAI's science claims in this record, the results are the team's own: a paper link accompanies them, but no independent reading of the proofs is in the capture.
Watch: the arXiv paper and how the Busy Beaver community receives the 20 new Cryptids; third-party formal verification of the Lean 4 proofs; whether the trace-simulation-plus-conjecture pipeline repeats outside theoretical computer science.
Links: Google DeepMind on X