OpenAI publishes AI proof as credit dispute grows

OpenAI announced that its advanced AI system has purportedly solved the Navier-Stokes existence and smoothness problem, igniting a dispute among mathematicians regarding the proof's independence and utilization of commercial AI tools. The company posited that its sophisticated AI model, considerably more powerful than GPT-6 Astra, generated the solution following extensive efforts involving up to 10,000 AI agents.

OpenAI published a technical write-up and a formal proof in Lean on September 8, positing that the motion of three-dimensional fluids can form a singularity in finite time. However, this claim has yet to be officially acknowledged as a resolution to the Millennium Prize Problem. The Clay Mathematics Institute retains the Navier-Stokes problem among its unsolved Millennium Prize Problems, with its conditions demanding that any proposed solution be disseminated in a respected publication, endure scrutiny for at least two years, and garner widespread acceptance in the global mathematical community before the institute considers awarding the $1 million prize.

OpenAI asserts that the agents achieved their result on September 5, approximately 88 hours after commencing work. The Navier-Stokes endeavor produced about 2.7 million agent messages and around 130 billion output tokens. Verification and formalization in Lean consumed an additional 17 hours, facilitated by GPT-6 Astra. The controversy revolves around concurrent work by New York University mathematician Tristan Buckmaster and Levent Alpöge, an Anthropic employee.

Both have been investigating related fluid dynamics questions and employed models from multiple AI research institutions, including OpenAI, during their investigations. Buckmaster has raised doubts about the independence of OpenAI's system, claiming that the company learned of his and Alpöge's plans to reveal their work and potentially utilized de-identified data from their use of OpenAI products to enhance their models.

OpenAI denies any access to the pair's unpublished work and states that they did not utilize any specific user data for the project. However, the company admits that de-identified data could have contributed to model enhancements. This dispute extends beyond mathematical priority to concerns about the potential indirect benefits of unpublished research conducted with commercial AI platforms.

Academic perspectives on confidentiality, attribution, and the influence of unpublished reasoning on AI systems operated by the same companies also differ. OpenAI claimed to have contacted Buckmaster and Alpöge upon realizing that rumors about their work prompted its own September 1 initiative. The company proposed coordinating the release and acknowledging their priority.

Buckmaster has contested certain aspects of this account, including discussions with OpenAI researcher Sébastien Bubeck about authorship credit. Bubeck has rejected the assertion that he sought to remove Alpöge from authorship of his work. OpenAI's CEO, Sam Altman, stated that the company favored coordination and dismissed allegations that it improperly appropriated the competing research.

The mathematical challenge itself is significant. The Navier-Stokes equations depict the motion of fluids like air and water, but mathematicians have yet to establish a proof confirming that smooth three-dimensional solutions persist. OpenAI claims its proof establishes a scenario where a vortex amplifies without bound in finite time while adhering to the necessary mathematical criteria.

OpenAI revealed it launched agents for all six unsolved Millennium Prize Problems after hearing rumors of progress elsewhere. After roughly 50 hours, researchers allocated more computational resources to Navier-Stokes when the system demonstrated promising advancements. The company declared it has no intention of seeking the $1 million award and presented the work to showcase advancements in AI-assisted scientific research.

Only the Poincaré conjecture has previously been removed from the original list of seven Millennium Prize Problems after a solution gained acceptance.