At the Limits of Computability: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier

arXiv:2610.22603v1 Announce Type: new Abstract: 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 Beave

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