What is Navier-Stokes problem? OpenAI claims AI solved 90

OpenAI on Tuesday said its new internal AI system has solved the 90-year-old Navier–Stokes existence and smoothness problem, one of the most difficult questions in modern mathematics. The system yielded an analytical proof that a smooth three-dimensional fluid could generate a singularity, a situation in which the fluid's velocity becomes infinite in a finite time, the company said. The Clay Mathematics Institute announced a list of Millennium Prize problems in 2000, of which the Navier–Stokes problem is one. Each carries a $1 million prize for a valid solution. OpenAI states that it will not attempt to win the prize, but its victory must still be validated by the broader math world community. The Navier-Stokes equations describe the motion of fluids such as water and air. They are based on Newton’s laws of motion and treat fluids as continuous substances rather than tracking individual molecules. They are applied throughout the range, from weather forecasting to aircraft design, from ocean research to blood-flow studies. The main mathematical problem is whether the fluid's smoothness can be preserved over time or whether it can abruptly develop a singularity. A singularity would occur if the fluid had an infinitely large velocity in a finite time. This would make it very difficult to determine if the equations are still accurately describing the fluid. Viscosity is a fluid’s resistance to motion. For instance, honey is much thicker than water. In general, viscosity dampens irregularities in fluid flow. A longstanding issue has been predicting whether this smoothing effect is sufficiently strong to prevent the formation of a singularity in 3D flow. The existence of solutions has been known since 1934, thanks to the work of the mathematician Jean Leray. But proving that those solutions always remain smooth has remained unresolved. OpenAI's AI system discovered a counterexample to its non-singular fluid assumption, showing that a smooth fluid can form a singularity in finite time. The proposed solution is a vortex that spirals towards a centre point and extends along the axis. The flow speeds up, and the total energy remains finite as the vortex decreases in size. The acceleration, pressure, momentum transfer and viscosity terms get very large but cancel exactly, says OpenAI. This allows the flow velocity to be continuous, while the external force is a smooth function. The company's result confirms statements “C” and “D” in the Clay Institute's formulation of the problem, the company states. It also created a formal version of that proof in Lean, a computer system that verifies mathematical arguments. The project started on 28 August and has continued since then, according to OpenAI, after receiving word on 1 September that the Millennium Prize problems may be solved. The company experimented with multiple teams of AI agents to see what strategies they could develop. Around 10,000 concurrent agents were involved in the group working on the Navier–Stokes equations. According to OpenAI, the agents brainstormed ideas, executed code and utilized pre-stored online information. The system reportedly converged to its Navier–Stokes solution on 5 September, 88 hours after the process started. Lean formalization and verification took an additional 17 hours, according to OpenAI. The claim is important but still requires a careful examination from independent mathematicians to confirm a computer-generated proof. Whether OpenAI's result is up to the decadal challenge will be judged by the wider math community. Pragya is a Technology reporter with over four years of experience in digital media and content writing. She holds a Master’s degree in Journalism and has covered a wide range of stories spanning space, smartphones, gadgets, artificial intelligence, emerging technologies and the ways technology is transforming everyday life. She focuses on breaking down complex technology and science developments into clear, engaging, and reader-friendly stories, with a keen interest in emerging trends and their real-world impact. Before joining her current newsroom, Pragya worked with News9Live, where she covered the technology beat extensively, reporting on smartphones, consumer technology, AI, space and science, while also contributing to video and visual content. Her experience includes breaking news, explainers, SEO-driven stories, product coverage, interviews, unboxing videos and live event reporting. She has also covered major technology and AI events, giving her experience in both newsroom and on-ground reporting. Beyond journalism, Pragya is an avid gamer and a passionate reader of fiction. She enjoys exploring immersive worlds through games and books, with a particular interest in stories that offer new perspectives, ideas, and experiences. Catch all the Business News, Market News, Breaking News Events and Latest News Updates on Live Mint. Download The Mint News App to get Daily Market Updates. MoreOops! Looks like you have exceeded the limit to bookmark the image. Remove some to bookmark this image.