Gemini助DeepMind发现BB(6)新Cryptid
Google DeepMind 的 Discovery 团队在由学生研究员 dsantosmarco 领导的项目中，报告了忙碌海狸第六问题（BB(6)）的新发现：其流程由 Gemini 4 Argon 驱动，可模拟原始图灵机运行轨迹以压缩重复模式、推测数学转移规则、运行合成实验检验边界情形，并在 Lean 4 中形式化证明等价性。据 Tom Zahavy 的帖子，该流程发现了 20 个新的潜在 Cryptid（其停机行为等价于数论中未解难题的微型程序），并验证了 BB 社区此前研究过的另外 33 台机器。团队称所有证明均已开源，并在社区 Discord 频道分享，相关的停机/非停机证明也已提交至社区 GitHub 仓库；上述数量尚未获得独立验证。
DeepMind 将这项工作定位为让 AI 发现隐藏的问题，而非求解人类提出的定理，并表示开源的 Lean 证明旨在帮助社区推进 BB(6) 的解决。
RT Tom Zahavy Over the past year, the Discovery team at @GoogleDeepMind, in a project led by student researcher @dsantosmarco, has made new discoveries in one of the most beautiful open problems at the edge of computation: Finding the 6th Busy Beaver (BB) number. While most AI math systems solve human-generated problems, like theorems, this work tackles a different aspect of mathematical creativity: Discovering hidden problems. For years, the BB Community has pursued one of theoretical computer science’s most captivating collaborative quests: finding the simplest programs that run the longest before halting. Because determining whether these programs ever stop is uncomputable, no universal algorithm can solve it, meaning new mathematical techniques need to be found and invented to make progress. In this way, the BB challenge serves as an open ended domain for mathematical creativity and, in particular, a generator of hard math problems called Cryptids. These are tiny programs whose halting behavior is governed by and equivalent to deep, unsolved math problems in number theory, similar to the Collatz or Goldbach conjectures.
Historically, the BB community had recognized ~20 Cryptids in BB(6), and the best problems were selected for the Busy Math Olympiad (BMO). Building on their work, Marco built a pipeline powered by Gemini 4 Argon that: 1️⃣ Simulates raw Turing machine traces to compress recurring patterns. 2️⃣ Conjectures mathematical transition rules & runs synthetic experiments to test edge cases. 3️⃣ Proves the equivalence formally in Lean 4. Using this pipeline, Marco and the team discovered 20 new potential Cryptids and verified 33 more machines previously studied in the BB community. All the proofs were open sourced and shared in the community discord channel and we hope that they will help the community to make progress towards resolving BB(6). We also contributed related halting/non-halting proofs directly to the community GitHub repository. Finding these Cryptids shows hidden links between simple programs and number theory, and helps mathematicians map the limits of computation. I'm also excited about Gemini 4 Argon's ability to help researchers both solve hard problems and accelerate scientific discoveries, of which Busy Beaver is just one example.