OpenAI says it solved one of the hardest open problems in mathematics. The same day, an NYU professor says the company raced him after hearing about his approach. That clash is the story TechCrunch and The Verge covered on September 8, 2026, and it matters far beyond pure math.
Here is the short version. NYU mathematics professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge announced three proofs and related progress on fluid equations, including work that moves toward the Navier-Stokes existence and smoothness problem. They used Codex and Claude while building those results. On the same day, OpenAI published what it calls a full proof of the Navier-Stokes Millennium Prize problem, produced by an unreleased next-generation model that OpenAI describes as more capable than GPT-6 Astra.
OpenAI says roughly 10,000 concurrent agents worked the problem in a week-long effort that burned through about 300 billion output tokens. TechCrunch notes that would cost about $22.5 million at Astra rates. The Verge adds that OpenAI started training the internal model on August 28. OpenAI says the latest push on this problem began September 1 after rumors that Anthropic-linked work had cracked a Millennium Prize problem.
Navier-Stokes sits among the seven Clay Millennium Prize problems. Each carries a $1 million bounty for a verified solution. The equations describe how fluids move, and mathematicians have struggled for decades to prove whether smooth solutions always stay smooth. A real proof would be a landmark for mathematical physics. OpenAI says it will not claim the Clay prize.
Buckmaster’s complaint is about timing and method. He says he and Alpöge had quietly chosen an uncommon route through a smooth force, the options labeled c and d in Fefferman’s statement of the problem. Almost nobody else was working that path, he wrote. Then OpenAI showed up on the same uncommon route after word of their progress reached the company. Buckmaster also raised Codex training-data concerns, because the pair had put drafts into Codex sessions.
OpenAI’s reply is careful. The company says researchers and agents did not see Buckmaster and Alpöge’s work until it was public, and that no specific user data was accessed to solve the problem. It also says, quote from the company via TechCrunch: while unlikely, we cannot rule out that de-identified data derived from their usage helped improve models. OpenAI staffer Sébastien Bubeck told The Verge the proofs differ significantly, and even the precise results differ in the Euler case.
The personal side of the dispute is ugly. Buckmaster alleges Bubeck asked him to remove Alpöge’s credit as part of a proposed compromise, then said, “Why would you ruin your career?” OpenAI has not treated those private exchanges as settled history in its public posts. Readers should treat that claim as Buckmaster’s account, not a court finding.
I work with AI tools every week, and this fight hits a nerve for anyone who drafts research inside a vendor’s product. If your private sessions can help train the same vendor’s next model, credit and consent stop being academic questions. They become product design questions.
Still, the upside is real. AI systems are now useful enough that serious mathematicians use them on career-defining problems, and labs can swarm thousands of agents at a Clay-level target in days. Independent verification will decide whether OpenAI’s Lean formalization holds. If it does, students, researchers, and engineers get a clearer map of fluid math than we had last week. The healthiest next step is open scrutiny, clear training-data rules, and credit that matches who did what. That combination helps regular people trust the breakthroughs they keep hearing about.
