OpenAI’s early October 2026 release of hundreds of AI-generated mathematical results from an internal frontier model, including verified Lean formalizations and partial progress on several Millennium Prize Problems after its September Navier-Stokes claim, has accelerated trader focus on whether similar capabilities will deliver full announced solutions to specific open conjectures by year-end. Competitive pressure from Anthropic’s Claude series, Google DeepMind tools, and smaller players like doubleAI adds momentum, yet low implied probabilities around 20% or below for leading outcomes such as the Hodge Conjecture reflect verification challenges, strict Polymarket criteria requiring explicit full-solution announcements by eligible labs, and historical timelines for rigorous peer validation. Upcoming model updates and community assessments through December could still shift sentiment.