On September 9 (local time, Tuesday), OpenAI made a groundbreaking announcement: it has successfully solved one of the renowned Millennium Prize Problems—the challenge concerning the Navier-Stokes equations. These equations serve as a fundamental tool for describing the motion of various fluids, including air, water, and blood.

OpenAI disclosed for the first time that this remarkable achievement was made possible by a cutting-edge internal model. This model not only surpasses the capabilities of GPT-6 Astra but does so by a significant margin. According to test data, when presented with a selection of open mathematical problems, this new model achieved a remarkable pass rate of up to 48%. This figure stands at roughly three times the highest performance previously recorded by Astra.

OpenAI further revealed that this mathematical breakthrough came at a substantial computational cost, amounting to millions of dollars. To reach a solution, the research team deployed approximately 10,000 collaborative AI agents. These agents worked in tandem to arrive at a solution within approximately 88 hours from the project's initiation.

The study also uncovered a fascinating insight: three-dimensional fluid motion has the potential to produce singularities within a finite timeframe. This phenomenon could lead to a breakdown in the equations' ability to accurately describe fluid continua.

Previously, mathematician Tristan Buckmaster from New York University and researcher Levent Alpöge from Anthropic had published AI-assisted research results pertaining to related fluid dynamics equations. Buckmaster raised questions about whether OpenAI embarked on solving the problem only after his research became public knowledge, and whether they adopted a unique research method that he had spent months refining.

In response to these inquiries, OpenAI clarified that its team had no prior contact with any related work before the public release of the other party's research. The company also emphasized that it did not utilize specific user data in its research process. Furthermore, OpenAI highlighted that there were substantial differences in the proof methods employed by the two teams.