25 Fields Medal winners warn AI-claimed math breakthroughs threaten the discipline

OpenAI announced on September 8 that an unreleased internal AI model solved the Navier-Stokes existence and smoothness problem — one of seven Millennium Prize Problems in mathematics — by coordinating roughly 10,000 AI agents over 88 hours. The claim, still awaiting independent verification, has ignited a fierce dispute over credit, data privacy, and the role of AI in scientific research.venturebeat+2

The Proof and the Dispute

The Navier-Stokes equations describe the motion of fluids such as water and air and underpin modern science and engineering. OpenAI said its model showed the equations can develop a singularity — a "blow-up" in speed — in finite time, a question that has stumped mathematicians for decades. The company said it launched the effort after hearing rumors that researchers connected to rival Anthropic were close to a solution.galaxy+3

Hours before OpenAI's announcement, NYU mathematician Tristan Buckmaster published a statement revealing that he and Anthropic researcher Levent Alpöge had spent over a year working on the same problem using several large language models, including OpenAI's Codex. Buckmaster said that when he contacted OpenAI about his work, the company's researcher Sebastien Bubeck invited him to collaborate — on the condition that Alpöge's name be removed due to his Anthropic affiliation. When Buckmaster refused, Bubeck allegedly asked, "Why would you ruin your career?" OpenAI has denied the claim.singularityhub+4

OpenAI also acknowledged it could not fully rule out that user data helped train its models. "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models," the company stated.venturebeat+1

Mathematicians Push Back

On September 11, twenty-five Fields Medal winners — including Terence Tao — signed an open letter warning that AI companies' rush to claim mathematical breakthroughs threatens the discipline's foundations. The signatories argued that solutions announced hastily, without proper writeups or attribution of prior work, undermine the collaborative culture that sustains mathematics. "Without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive," the letter stated.techcrunch+1

Tao separately warned that if AI companies "jump on a rumor of promising work and throw millions of dollars at trying to scoop competitors, researchers may end up no longer sharing any promising research with the broader community". OpenAI withdrew its sponsorship of a math event at Caltech this week after criticism from researchers there.singularityhub+1

Broader Implications

The episode has raised questions that extend well beyond mathematics. The Clay Mathematics Institute still lists the Navier-Stokes problem as "active" rather than "solved," and under its rules, any prize cannot be awarded until at least two years after publication. OpenAI has said it will not collect the $1 million prize.theweek+2

The controversy arrives as both OpenAI and Anthropic prepare for planned public offerings, giving both companies incentive to showcase their models' capabilities. As the Fields Medal signatories wrote, "The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face".galaxy+1