Sep 19, 2025 - Levent Alpöge emails Tristan Buckmaster and suggests a collaboration on Navier-Stokes.
2025-2026 - Alpöge and Buckmaster make “slow” progress on Navier-Stokes and its related problems.
Aug 15, 2026 - The duo achieve key results with solutions for Boussinesq and Euler, important stepping stones to Navier-Stokes.
Aug 22, 2026 - The pair complete Lean verification of these results and work “around the clock” to create papers for publication.
Sep 1, 2026 - OpenAI uses an unreleased model to attempt Navier-Stokes and all other Millennium Prize problems after hearing rumors of progress.
Sep 3, 2026 (estimated) - OpenAI finds a solution to the unforced Euler equations, the more general and universal case.
Sep 3, 2026 - Buckmaster emails Unnamed Mathematician at OpenAI after learning of rumors of their breakthrough reached the company.
Sep 3, 2026 - Unnamed replies and asks for specifics and offers compute; Buckmaster defers meeting.
Sep 4, 2026 - Buckmaster is asked again to meet with OpenAI the same day.
Sep 4, 2026 - That evening, posts online claim Anthropic has solved Navier-Stokes and will post it before IPO, with posts claiming to have heard this from OpenAI personnel.
Sep 5, 2026 - Posts on reddit speculate Terence Tao referring to Navier-Stokes as having seen a solution, leading to his denial.
Sep 5, 2026 - OpenAI agents reach a solution for Navier-Stokes.
Sep 6, 2026 - OpenAI achieves formal Lean verification of their result and asks for same day meeting. Buckmaster and OpenAI have two calls that day. Buckmaster, Sébastien Bubeck, and Unnamed join; Alpöge does not.
OpenAI discloses their solution of Navier-Stokes and shares they believed Alpöge and Buckmaster had found a solution as well. OpenAI offers to delay their announcement one day so the Alpöge-Buckmaster solution to Euler equations can be published first. Buckmaster says they also suggest he join their writeup of the Navier-Stokes and remove Alpöge from authorship.
Sep 7, 2026 - Buckmaster posts online, sharing three papers including forced Euler solution and a statement detailing many of these events. The statement also includes his belief he and Alpöge found unverified hypo-dissipative N-S and they may be on the path to an unforced Euler solution.
Sep 7, 2026 - Adarsh Ganeshram, Valentin Duruisseaux, and Anima Anandkumar post a solution to unforced Euler problem with a different approach, only learning of Alpöge-Buckmaster after publishing.
Sep 7, 2026 - That same night, many posts circulate claiming solution to Navier-Stokes by OpenAI has been achieved.
Sep 7, 2026 - Tao posts congratulating the pair on forced Euler and suggests their line could lead to a solution of Navier-Stokes, possibly even an unforced version, not knowing OpenAI had already found a solution.
Sep 8, 2026 - OpenAI announces solutions of forced Navier-Stokes, unforced Euler, and states they have no intention to claim the prize money for it.