At the Limits of Computability: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier
Recent breakthroughs in AI for mathematics---ranging from Olympiad medal performances to resolving long-standing open conjectures---have rapidly expanded what automated systems can achieve. Yet these successes primarily concern predefined, human-formulated problems, leaving open how AI systems can autonomously uncover mathematical structure and formulate new questions. To push beyond static challenges, we explore the Busy Beaver (BB) domain, an uncomputable frontier that is fundamentally open-ended. Because no algorithm can compute the Busy Beaver number $\mathrm{BB}(n)$ for every $n$, this domain provides a natural setting for sustained exploration through mathematical conjecture and pro...
| Authors | Marco Dos Santos, Vivek Veeriah, Alex Havrilla et al. |
|---|---|
| Primary category | cs.AI |
| Published | 15 October 2026 |
| Last updated at source | 19 October 2026 |
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