NYU mathematics professor Tristan Buckmaster, a Melbourne native, accused OpenAI of unfair play over the company's claim to have solved the Navier-Stokes existence and smoothness problem—one of the seven Millennium Prize Problems for which the Clay Mathematics Institute offers a $1 million prize. According to him, information about the "quiet" research he had been conducting for nearly a year with Anthropic mathematician Levent Alpöge leaked to OpenAI days before the September 8 announcement, which stated that the unreleased Astra model found a solution in approximately 88 hours using a swarm of about 10,000 parallel agents. The Clay Mathematics Institute has not yet certified either of the two works, so the formal status of the $1 million problem has not changed.
What happened
On September 11, 2026, the Australian Financial Review published an extensive interview with Buckmaster, in which he described the chronology of the conflict. OpenAI's swarm of approximately 10,000 parallel agents was launched on September 1 and ran for about 88 hours, producing approximately 300 billion output tokens, estimated at about $22.5 million in compute; the company announced the result on September 8, and CNBC reported on it on September 9. According to Buckmaster, days before this announcement, information about his joint work with Alpöge, which had been ongoing for about a year and relied on Codex and Claude, "leaked" to OpenAI. At this point, both solution candidates are public: OpenAI's full proof and the results of Buckmaster and Alpöge on so-called "smooth force," verified in the Lean theorem prover. Meanwhile, OpenAI acknowledged that the contribution of anonymized usage data from Codex and other company products to model training is "impossible to exclude."
Context
The Navier-Stokes equations describe fluid behavior, and their "Millennium" problem—the question of the existence and smoothness of solutions—is one of the seven problems for which the Clay Mathematics Institute awards $1 million for a solution; the institute itself decides whose result to count. In the dispute, NYU mathematician Buckmaster and Anthropic's Alpöge are on one side, and OpenAI on the other, with both mathematicians using competitors' agentic tools: OpenAI's Codex and Anthropic's Claude. The competitive dynamics are also telling: the swarm launch began on September 1, days after rumors of others' progress on this problem. Formal verification in Lean here serves as the working standard for checking machine-made mathematical claims, while the final word belongs to the Clay Institute.
Why this matters for the industry
This is the first high-profile public dispute over priority and data around solving a "Millennium" problem using AI agents, and it touches the very model of frontier research. The case recorded a new economics of mathematical breakthroughs: ~300 billion output tokens, ~88 hours, and ~$22.5 million in compute mean that the cost of such an attack on a problem has become a question of budget, not just algorithm. A second specific risk mechanism is OpenAI's acknowledgment that anonymized Codex usage data is "impossible to exclude" from model contribution: the origin of the "solution" data is entangled with other researchers' work, and opting out of training on session data becomes a competitive security issue. There are no product consequences yet: Astra is not on the market, API, pricing, and latency are not published, and the "swarm of thousands of agents plus formal verification" pattern remains unvalidated until independent verification of both proofs.
Why this matters for users
If you use Codex, Claude, or other LLM agents in your own research or code, this case is a live example of the question of whose foreign knowledge and your own ends up in model training. A practical step this week is to audit what you input into commercial agents' context: separate sensitive and public tasks, check and, if possible, enable opt-out from using your session data. A second practical takeaway is not to build solutions on announcements: until the Clay Mathematics Institute issues a verdict, the phrase "AI solved Navier-Stokes" should be treated as marketing, not an established fact, and to follow independent analysis of both published proofs.
What is still unknown / limitations
OpenAI's statement is a single non-reproducible instance (n=1): the agent system architecture is not disclosed, there are no ablations, no independent reproduction, and the methodology of the ~10,000-agent swarm is not described. OpenAI's full proof is published but has not undergone independent peer review and has not been certified by the Clay Mathematics Institute, which has not yet recognized either of the two candidates. The leak claim is Buckmaster's version, presented in the AFR interview; there is no independent confirmation of the leak mechanism in available materials. Finally, Astra has not been released, so its API, pricing, and latency remain unknown.
Sources
- 'Not selling my soul': Why this Aussie maths professor took on OpenAI — AFR
- OpenAI claims to have solved Navier-Stokes math problem — CNBC
- OpenAI fought dirty on career-making math problem, says NYU mathematician — TechCrunch
Author
Look at AI, editorial team