OpenAI Claims Resolution of Navier-Stokes, Estimated Cost Up to $40M

OpenAI claims to have found a solution to the Navier-Stokes equations, mobilizing 10,000 AI agents and generating 130 billion tokens of output. LisanBench estimates the total cost between $10 million and $40 million. Two mathematicians contest the use of their data, which OpenAI denies having used directly.

LisanBench estimates the output at $6.5 million and the total at $10–40 million

LisanBench, a benchmark evaluator for language models, estimates that the output tokens alone would have cost around $6.5 million at OpenAI's average public rate. Considering a significantly higher input volume, the total cost could reach between $10 million and $40 million. According to OpenAI, about 10,000 AI agents worked in parallel on the proof, which was obtained after 88 hours, followed by 17 hours of verification. The agents generated 130 billion tokens of output and exchanged 2.7 million messages during the process.

Doubts about training data, OpenAI denies direct access

Mathematicians Tristan Buckmaster and Levent Alpöge have expressed reservations about the use of their research data for training OpenAI's models. The company claims it did not have direct access to their work, while noting that it cannot rule out that de-identified data from the use of its products by these researchers may have contributed to the improvement of its models. Sam Altman, CEO of OpenAI, reacted to the announcement by joking that AI was a bubble.

OpenAI claims a solution and forgoes the $1 million prize

OpenAI announces that it has solved the problem of the Navier-Stokes equations and specifies that it will not seek the $1 million reward associated with a solution. These equations are used to predict the movement of liquids and gases. Their complexity led the Clay Mathematics Institute to offer a $1 million prize for any recognized solution.