OpenAI’s announcement that its agents solved the Navier–Stokes existence and smoothness problem—one of seven Millennium Prize Problems from the Clay Mathematics Institute—has been overshadowed by controversy. The company claims its internal model dramatically outperformed the recently released Astra model to prove that the full equations can break down under certain conditions. However, accusations have emerged that OpenAI built upon work by NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge without proper credit. Buckmaster posted a proof on Mastodon on Monday showing that a simplified version of the Navier–Stokes equations can break down, following nearly a year of research using publicly available models from both OpenAI and Anthropic. Sébastien Bubeck, a member of OpenAI’s technical staff, acknowledged in a press briefing that the team was inspired to pursue the problem after hearing rumors about Buckmaster and Alpöge’s efforts. OpenAI has denied using their work directly and stated it does not plan to claim the one million dollar prize. The episode highlights growing tensions around AI-driven mathematical discovery and raises questions about how human mathematicians will fit into a future dominated by frontier AI companies.

Buckmaster detailed his interactions with OpenAI employees in a public document, alleging that they presented two options: either he and Alpöge post their work and OpenAI follows with their solution the next day, or Buckmaster collaborates on an OpenAI paper excluding Alpöge due to his Anthropic affiliation. Buckmaster also reported asking whether OpenAI’s agents accessed transcripts of his and Alpöge’s research, which they denied, and whether their models were trained on those transcripts, to which they offered no response. MIT Technology Review reached out to Buckmaster for comment but did not receive a response before publication.

This controversy underscores shifting dynamics in mathematical research, where AI models are increasingly essential for solving problems once thought beyond reach. If only a handful of well-resourced AI companies can drive progress on the most important mathematical challenges, it may fundamentally alter the collaborative norms that have long defined academic mathematics. The Navier–Stokes problem, involving equations describing fluid flow used widely in physics and engineering, remained unsolved until now despite its significance in understanding phenomena like infinite fluid velocity under certain conditions.