What is the 90-year-old Navier-Stokes problem that OpenAI says AI has solved? | Technology News

Decoding Navier-Stokes equations

Imagine trying to predict exactly how water in a river will move over time.

This is what the Navier-Stokes equations do; they are essentially a set of mathematical rules that explain how any fluid (water, honey, air, etc.,) flows based on two simple physics ideas, such as fluid mass and force equals mass times acceleration.

AI generated explainer

These equations can help in forecasting weather, designing aeroplanes and cars, and predicting ocean currents.

The catch here is nobody has proven whether the equations always produce sensible answers.

Since fluid flow is chaotic, the difficulty comes from turbulence. This means tiny changes in starting conditions could lead to wildly different outcomes, which is also why weather cannot be predicted more than a week ahead.

What has OpenAI found?

The Sam Altman-led AI startup claimed that its internal AI system generated a proof showing that such a breakdown can indeed happen. The company said that the solution involves a vortex — essentially a spinning swirl of fluid – that spirals inward while being increasingly stretched. As the central region shrinks, the fluid’s speed increases considerably until the mathematical singularity forms.

Most importantly, OpenAI said the fluid still has finite energy. Hence, the singularity does not come from simply applying an infinite force from outside. Instead, it develops from the dynamics as described by the equations.

OpenAI also said that the proof has been formally verified using Lean, which is a computer system used to check mathematical proofs step-by-step.

OpenAI said that around 10,000 AI agents worked on the problem simultaneously. The system generated about 2.7 million messages and used about 130 billion output tokens while working on the Navier-Stokes problem.

The AI agents reportedly explored different approaches, shared useful discoveries with other groups, and eventually came together for the solution. According to the company, the agents found the result in about 88 hours, and the formal verification took 17 more.

OpenAI also said that the AI model used to produce the proof is significantly more capable than the newly launched GPT-6 Astra.

Is the problem officially solved?

However, when it comes to the actual solution to the decades-old mathematical problem, some caution is needed.

OpenAI claimed its work resolves the problem and released the proof for mathematicians to examine.

It needs to be noted that the broader mathematical community still needs to examine the result. The AI start-up itself claimed that it does not intend to claim the $1 million Millennium Prize.

OpenAI’s announcement also triggered a dispute involving mathematicians Tristan Buckmaster of New York University and Levent Alpöge of Anthropic, who had been working on related mathematical problems.

They have essentially raised questions about how OpenAI’s research was conducted and whether their unpublished work could have influenced the result. “I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything,” Buckmaster said in a statement.

In turn, OpenAI denied accessing their work and said its proof is ‘substantially different’.

The best way to describe this development is that OpenAI has introduced an AI-generated solution to the Navier-Stokes problem which is yet to be scrutinised by mathematicians. If the proof withstands scrutiny, this would be a major milestone for mathematics and AI, as it would mean an AI system helped resolve a math problem humans have been grappling with for nearly 100 years.