OpenAI holds a narrow 57% market edge in the race to solve the next Millennium Prize Problem because its internal models have already delivered a verified Navier-Stokes solution in September 2026 and followed up in early October with hundreds of additional proofs across open mathematical conjectures, including reported progress on at least one other Millennium problem. The company deployed thousands of coordinated AI agents on compute-intensive runs, produced Lean formalizations, and publicly released results that mathematicians are now scrutinizing. Anthropic’s involvement remains limited to a researcher’s personal collaboration on a related Euler-equation disproof, with no comparable company-scale math announcements or verified Millennium-level claims since then. Traders appear to view OpenAI’s demonstrated scaling of agent swarms and rapid iteration on frontier problems as the stronger near-term catalyst, though verification delays and potential credit disputes introduce ongoing uncertainty.