Recent advances in AI formal reasoning systems, such as those building on large language models and automated theorem provers, have elevated the Hodge Conjecture to a 28.5% implied probability, nearly tied with Birch and Swinnerton-Dyer at 22.5%. Traders view these problems as more tractable for current machine learning approaches in algebraic geometry and elliptic curve analysis than the abstract or computational intensity of alternatives like Riemann Hypothesis. The leading 29.5% odds for no solution by December 2027 highlight realistic timelines for AI capability scaling, with upcoming model releases and mathematical benchmarks in late 2026 serving as key swing factors in this closely contested market.