OpenAI is under sharp criticism after a public dispute with prominent mathematicians over a claimed solution to one of mathematics’ toughest conundrums—the Navier–Stokes existence and smoothness problem, a high-stakes Millennium Prize problem. The row has widened to include accusations of mishandled attribution, potential misuse of proprietary drafts, and a retreat from public engagement by OpenAI.
The Backstory: Proofs, Credit, and Codex
Earlier this month, NYU professor Tristan Buckmaster and researcher Levent Alpöge (affiliated with Anthropic) disclosed that they had arrived at three related proofs toward Navier–Stokes while using AI tools including OpenAI’s Codex and Anthropic’s Claude. What sparked the controversy was their claim that OpenAI then announced a full proof—not yet peer-reviewed—after purportedly learning of Buckmaster and Alpöge’s approach.
Buckmaster asserts that early drafts of their work were fed into Codex for assistance—and that OpenAI’s model may have accessed those sessions. OpenAI has responded by saying that none of their internal work borrowed directly from Buckmaster and Alpöge’s unpublished efforts, and that no specific user data was accessed in developing its proof. However, the company allowed that it cannot completely rule out that derived patterns from past usage of its tools might have unintentionally influenced its models.
Credit attribution soon became contentious. OpenAI allegedly asked Buckmaster to remove Alpöge as a co-author, triggering additional backlash. Buckmaster claims he was warned that publicizing the dispute could damage his career. OpenAI, in its defense, insists that its model’s proof derives from independent internal trial, leveraging its compute resources to beat others to a milestone. They say the timeline started on September 1, inspired by rumor of advances in other labs.
Escalation: Open Letter, Sponsorship Pullback, and Warnings from the Field
A group of 25 Fields Medal–winning mathematicians has now signed a public open letter arguing that AI labs are jeopardizing the norms of mathematical research by racing to score proofs without proper documentation, adequate peer review, or clear credit. These scholars stress that proofs must be transparent, intelligible by peers, and offered with full citation to prior work.
Meanwhile, awareness has grown around the Leiden Declaration on Artificial Intelligence and Mathematics. Released in June 2026, this document—endorsed by leading professional bodies—offers guidelines on how individual researchers, institutions, policymakers, and AI companies should handle AI-generated or aided proofs, warning that credibility, correctness, and the culture of mathematics itself are at stake.
The tension also played out at Caltech: OpenAI withdrew its sponsorship of a student-run event, Mathathon, after widespread criticism from mathematicians concerned about the event’s incentives. Critics argued that such contests could push participants to prioritize speed over rigor, mirroring concerns voiced about AI systems racing toward headline-grabbing results at the cost of depth.
What This Means and What Comes Next
This dispute reveals more than just rivalries—it highlights foundational challenges at the intersection of high-performance AI, scientific discovery, and academic ethics. As AI labs pursue breakthroughs, mathematicians warn that the norms of attribution, peer review, and transparency must not be sacrificed in the rush to beat competitors.
OpenAI’s actions raise pressing questions: When are AI-generated proofs valid? Who owns nascent ideas fed into proprietary systems? How can journals and the wider math community maintain standards when compute power can accelerate some stages of discovery but leave others—like verification—lagging?
What to watch now: whether OpenAI’s proof survives peer review and can be fully verified by the math community; whether governing bodies adopt tougher guidelines based on the Leiden Declaration; and how governments, universities, and publishers regulate or incentivize credit and data usage in AI-assisted research.
