- Will CMI declare the Navier-Stokes problem solved by December 31, 2026?4¢4%
- Will CMI declare the Navier-Stokes problem solved by December 31, 2027?14¢14%
- Will CMI declare the Navier-Stokes problem solved by December 31, 2028?38¢38%
OpenAI’s September 2026 announcement that an internal multi-agent AI system produced a Lean-formalized proof of finite-time singularity in the forced three-dimensional Navier-Stokes equations has driven recent trader sentiment, though CMI immediately described the problem as only “apparently settled.” The institute’s rules require peer-reviewed publication in a qualifying journal, broad community acceptance, and a two-year waiting period before any declaration, leaving the problem officially active as of late October. Parallel human-AI results on related forced Euler and Boussinesq equations by Buckmaster and Alpöge have added context but do not resolve the unforced case central to the prize formulation. Ongoing scrutiny, including an October arXiv note questioning semantic fidelity of the Lean formalization, and the absence of an accepted journal paper keep resolution timelines uncertain despite the computational milestone.
Rules
This market will resolve to "Yes" if the Clay Mathematics Institute (CMI) awards a Millennium Prize for the Navier-Stokes existence and smoothness problem, or otherwise officially declares the Navier-Stokes existence and smoothness problem solved on its website or in an official communication, by 11:59 PM ET of the listed date. Otherwise, this market will resolve to "No". A Millennium Prize award will qualify as an official declaration, but is not required; an official CMI statement that the Navier-Stokes existence and smoothness problem has been solved is sufficient on its own. Whether the solution was produced in whole or in part by artificial intelligence, and whether any recipient accepts or declines a prize, will not be considered. A published or publicly posted proof will not qualify on its own, regardless of its acceptance by the mathematical community. The primary resolution source will be official information from the Clay Mathematics Institute (e.g., https://www.claymath.org); however, a consensus of credible reporting may be used to confirm that a qualifying CMI declaration or award has occurred.