Navier-Stokes problem: The questions raised by OpenAI’s latest maths ‘breakthrough’

OpenAI's latest AI breakthrough has sparked a fresh debate in the mathematical community: What happens when researchers' work is fed into AI systems and later used to enhance those models? While OpenAI maintains no user data was accessed to solve the Navier-Stokes problem, they admit de-identified data could have contributed to model improvements.

De-identification removes personal identifiers, but crucial information may still be present. Mathematicians like Tristan Buckmaster and Levent Alpöge, who worked on related research using AI tools, including OpenAI's Codex, express worries about de-identified data use. Similarly, Andreas Thom questions whether his private ChatGPT conversations influenced an earlier OpenAI mathematical result, though OpenAI denies this.

The controversy exposes the blurred line between assisting researchers and using their ideas without proper acknowledgment or consent. For Vijay Keswani, this issue extends beyond data privacy to "epistemic ownership." De-identifying conversations does not guarantee that underlying ideas or content are not utilized. OpenAI's de-identification process remains unclear, adding to the sensitivity of the matter in mathematics, where researchers often rely on AI for developing and testing unfinished ideas.

OpenAI asserts no specific user data was used for the Navier-Stokes solution, but this claim is narrower than ruling out de-identified data's potential impact. Keswani emphasizes the power imbalance between AI companies and individual researchers, questioning fairness in this context. The $1 million Navier-Stokes Millennium Prize Problem, a Millennium Prize Problem of the Clay Mathematics Institute, remains unsolved.

OpenAI claims its 10,000 AI agents solved the problem in 88 hours, formalizing the solution in Lean, a proof assistant.