Trader consensus shows closely matched implied probabilities for Yang-Mills at 34.4% and no solution by December 2027 at 30.5%, reflecting uncertainty over large language model progress on rigorous mathematical proofs. Recent reasoning models have demonstrated stronger performance on algebraic and quantum field theory tasks tied to Yang-Mills, yet persistent gaps in formal verification and long-horizon deduction keep timelines contested. The Hodge Conjecture at 22.5% trails due to slower AI advances in algebraic geometry benchmarks compared with number theory problems. Upcoming model releases and third-party evaluations of AI capabilities on Millennium Prize criteria remain key swing factors that could alter positioning before 2027.