OpenAI’s early October 2026 release of 722 papers from an unreleased internal frontier model, claiming solutions or advances on 372 open problems including partial results tied to the Hodge conjecture, Birch and Swinnerton-Dyer conjecture, and a quasi-Riemann hypothesis variant, has become the dominant catalyst lifting those outcomes to 17–20% implied probability on Polymarket. Large language model performance on FrontierMath and Lean-verifiable benchmarks has accelerated sharply, with systems now tackling research-level problems that previously required expert mathematicians, while competing efforts such as AlphaProof Nexus have resolved multiple long-standing Erdős problems. Market odds remain tempered by the need for independent verification, Clay Institute review of Millennium claims, and the strict resolution rule requiring a full, lab-announced solution by year-end rather than incremental progress.