OpenAI Faces Controversy After AI Math Proof Dispute With NYU Researcher

A controversy has emerged in the mathematics and artificial intelligence communities after NYU mathematics professor Tristan Buckmaster raised concerns about OpenAI’s efforts to solve the Navier-Stokes existence and smoothness problem, one of the most famous unsolved problems in modern mathematics.

In a statement published after announcing research with Anthropic mathematician Levent Alpöge, Buckmaster said the pair had developed three proofs that represented progress toward the problem. He also described concerns about a parallel OpenAI effort that appeared to follow a similar research direction.

Buckmaster said information about his team’s work had reached OpenAI while the researchers were finalising their results. He questioned the timing of OpenAI’s subsequent announcement and how the company’s research process unfolded.

OpenAI Publishes Navier-Stokes Proof

Shortly after Buckmaster’s statement, OpenAI published a claimed solution to the Navier-Stokes existence and smoothness problem. The company said the proof was produced with help from an unreleased next-generation AI model.

OpenAI said its research system discovered the proof after a concentrated effort that used significant computing resources. The company reported that the project consumed about 300 billion output tokens during a week-long research process.

OpenAI’s published API pricing information provides current token pricing details, although the actual cost of internal research workloads can vary depending on infrastructure and usage arrangements.

A Millennium Prize Mathematics Challenge

The Navier-Stokes existence and smoothness problem is one of the seven Millennium Prize problems identified by the Clay Mathematics Institute. Each problem carries a $1 million prize for a verified solution.

The Navier-Stokes equations are fundamental to fluid mechanics, but mathematicians have not yet proven whether solutions always exist and remain smooth under the conditions defined by the challenge.

Questions Around Research Access and AI Training

Buckmaster also raised concerns about whether information from his work could have influenced OpenAI’s research through interactions with AI tools. He noted that his team used OpenAI’s Codex extensively while developing its work.

OpenAI said its researchers and AI systems did not access Buckmaster and Alpöge’s unpublished work. The company said it could not rule out that de-identified product usage data may have contributed to model improvement.

OpenAI’s data usage policy explains how user data may be used to improve model performance, including options available to users regarding data controls.

The company also provides additional details about data practices in its official data usage policy.

AI’s Growing Role in Mathematical Research

The dispute highlights broader questions about how AI systems will be used in advanced research, particularly when multiple teams use similar models to explore difficult scientific problems.

For mathematicians and AI researchers, the case raises questions about attribution, research transparency and how discoveries made with artificial intelligence should be credited.