A high-profile Navier–Stokes breakthrough is unveiled, with Buckmaster and Alpöge announcing AI-assisted progress toward solving a Millennium Prize problem, aided by OpenAI and Anthropic models.

The claim centers on a forcing method that targets the equations to induce blow-up, a path advanced by Córdoba and Martínez-Zoroa and extended by Buckmaster and Alpöge using large language models.

The announcement marks a potential landmark in mathematics, described as a breakthrough involving AI-assisted work toward one of the field’s most prestigious prizes.

The duo say they used OpenAI’s Codex and Anthropic’s Claude, highlighting a collaboration with major AI players in achieving the result.

Buckmaster asserts that he does not know whether their data or chats were used to train the AI models, amid questions about data provenance.

OpenAI maintains it did not access specific user data to solve the problem but concedes de-identified interactions could have informed models, raising concerns about training data and attribution.

Buckmaster questions whether OpenAI’s models could have learned from his Codex sessions, underscoring debate over data ethics and credit for AI-assisted discoveries.

OpenAI published its own full proof shortly after, produced by a next-generation AI system after a lengthy, intensive run of AI agents and massive compute costs.

The broader implication is that the Clay Institute’s prize may be effectively settled, though debates linger about whether the forcing component is essential and whether the result extends to the full problem without it.

The story raises questions about scientific credit, data privacy, and the evolving role of AI in mathematical discovery, including how to attribute contributions when AI tools participate.

The episode has sparked ongoing debate in online math and AI communities about collaboration, claims, and how future AI-assisted breakthroughs should be recognized and published.

Amid the drama, the piece highlights potential paradigm shifts in both mathematics and AI, emphasizing reproducibility and the future role of AI in foundational scientific work.