Levent Alpöge, at the center of the Navier–Stokes debate

OpenAI announced on September 8 that an in‑house developed artificial‑intelligence system had produced a solution to the Navier‑Stokes existence and smoothness problem. The company also released the technical paper on the solution and its formal verification prepared with Lean.

The Navier‑Stokes equations mathematically describe the motion of fluids such as water and air. The problem had been designated as one of the seven Millennium Problems by the Clay Mathematics Institute in 2000, carrying a one‑million‑dollar prize.

OpenAI announced that it would not apply for the one‑million‑dollar prize for its own work. The company said the solution was developed through the collaboration of roughly ten thousand AI agents, and that formal verification with Lean followed the process.

Turkish mathematician Levent Alpöge at the center of the debate

Alongside OpenAI's statement, a debate emerged about how the work came about.

NYU mathematics professor Tristan Buckmaster announced that he and Turkish mathematician Levent Alpöge, who works at Anthropic, are conducting research on the Navier‑Stokes equations and related equations.

Buckmaster claimed that shortly after learning about OpenAI's own work, he had reached the same result using a similar method. He also alleged that OpenAI had proposed a joint announcement and that Alpöge's name was requested to be removed because he works at Anthropic.

According to Buckmaster's statement, during discussions with OpenAI manager Sébastien Bubeck, he was told, 'Why ruin your career?' and 'If you don't want me to be polite, I don't have to be polite.' The claim that these words were used belongs to Buckmaster; Bubeck described the accusations as 'false and inflammatory.'

OpenAI: We did not access the researchers' work.

OpenAI said in its statement that it began the work on September 1 after hearing a rumor about the progress of Buckmaster and Alpöge.

The company argued that researchers had not accessed the work before it was made public and that no specific user data was used during the solution. However, OpenAI noted that it cannot entirely rule out the possibility that anonymized data obtained from product usage may have contributed to the development of the models.

Buckmaster and Alpöge question whether the method used by OpenAI aligns with their own research and its timing. At the heart of the debate are questions about how AI systems benefit from user interactions and how priority and academic reputation are preserved in scientific work.