OpenAI published a 165 page proof that it said shows smooth three-dimensional fluid motion can develop a singularity in finite time. The company said an unreleased internal model more capable than GPT-6 Astra produced the result in about 88 hours, with 100 to 10,000 coordinating AI agents sending 2.7M messages and using roughly 130B output tokens.

The claim concerns one of mathematics’ six remaining Millennium Prize Problems, which OpenAI said has remained unresolved for roughly 90 years. OpenAI said the proof has been formalized and computer-verified, but outside mathematicians still need to validate it independently. The announcement also drew a dispute with Tristan Buckmaster and Levent Alpöge over related work; OpenAI said it did not access their unpublished work or specific user data to solve the problem, though it could not rule out de-identified usage data helped improve its models.