After OpenAI solved the Millennium Prize Problem, Altman's next goal: to conquer room-temperature superconductivity?

OpenAI is pushing AI-driven scientific discovery into broader fields. On September 8, OpenAI announced that its internal AI system has proposed a solution to the existence and smoothness problem of the Navier-Stokes equations and verified it formally through Lean. This is one of the seven Millennium Prize unsolved problems, signifying another step forward for AI in cutting-edge mathematical research.

According to an announcement on OpenAI's official website, the system consists of approximately 10,000 concurrent agents and took about 88 hours from startup to solution formation. OpenAI stated that the internal model used to complete the proof "significantly surpasses GPT-6 Astra" and hopes to demonstrate the speed of evolution of cutting-edge AI capabilities.

More notably, AI futurist observer "Dr_Singularity" recently stated on the X platform that OpenAI CEO Sam Altman indicated the company will employ a collaborative approach involving tens of thousands of intelligent agents, similar to the one used in this mathematical problem, to attempt to find room-temperature superconductors. If this direction proves true, OpenAI's AI research will further extend from mathematics to materials science.

Next goal: Room temperature superconductor

Dr_Singularity stated that Sam Altman said OpenAI will attempt to use tens of thousands of AI agents to find room-temperature superconductors, which is the same multi-agent collaborative approach used to solve the Navier-Stokes problem.

This direction also faces considerable competition. According to a previous post by someone from the X platform, rumors circulated that the Anthropic team might have made progress in room-temperature superconductivity research. OpenAI's increased focus on scientific discovery signifies that leading AI companies are attempting to extend their model capabilities beyond solving known problems to finding answers to unknown questions.

Once room-temperature superconductors are realized and can be scaled up, they could transform multiple fields, including energy delivery, quantum computing, and magnetic levitation. For OpenAI, this also means that the application boundaries of multi-agent systems are beginning to extend into scientific research fields such as materials science and physics.

Sam Altman responded on X, saying, "Let's give it a try."

The proof of a century-old mathematical problem: Singularities in fluid equations form in finite time.

The Navier-Stokes equations are the fundamental set of equations describing fluid motion and are widely used in aircraft design, weather forecasting, and blood flow research. Their core challenge lies in whether a smooth solution for a three-dimensional incompressible fluid will form a "singularity" within a finite time interval, meaning that physical quantities such as velocity become uncontrollable.

OpenAI states that its system's results demonstrate that singularities can form within a finite amount of time. Specifically, an initially stationary smooth fluid, upon the application of a smooth external force, will form an inwardly spiraling and continuously stretching vortex structure; its central region continuously contracts and its velocity continuously increases, but the total energy remains finite. This result corresponds to propositions C and D in the Millennium Prize Problem, providing a negative answer to this problem.

However, OpenAI currently describes it as an AI-generated solution and has publicly released the corresponding proof text and Lean formal proof, rather than announcing that the mathematical community has achieved final confirmation. OpenAI also stated that it does not intend to apply for the $1 million Millennium Prize for this problem.

Image source: OpenAI official website

Technical approach: Collaboration of tens of thousands of intelligent agents, taking 88 hours.

OpenAI disclosed that the search began on September 1st. At that time, the company heard that an external team might have solved a Millennium Prize problem, so it decided to conduct a comprehensive test on its internal model, covering the seven Millennium Prize Problems and other high-impact mathematical problems.

On the technical level, OpenAI deployed a multi-agent coordination system driven by an internal model, enabling agents to access internet cached information and run code. The solver group for the Navier-Stokes problem consists of approximately 10,000 concurrent agents, sending about 4.9 million messages and generating about 300 billion output tokens throughout the process; of which, the Navier-Stokes part sends about 2.7 million messages and consumes about 130 billion output tokens.

Prior to this, the system unexpectedly solved the regularity problem of the Euler equations—which can be understood as the limiting case after removing the viscosity terms of the Navier-Stokes equations. After about 50 hours of collaboration among approximately 100 agents, the system constructed a counterexample with no external force. Subsequently, OpenAI devoted more computing power to the Navier-Stokes problem and used the previous Euler equation results as the basis for further solutions.

The final proof was also formally verified using Lean. According to OpenAI, GPT-6 Astra took approximately 17 hours to complete the formalization process.

Competition and Controversy: A Priority Battle with the Anthropic Team

Behind this breakthrough lies a priority story involving the Anthropic team. OpenAI stated that the immediate impetus for the company to begin its work was hearing that Anthropic employee Levent Alpöge and New York University mathematics professor Tristan Buckmaster might have already solved the problem.

After OpenAI completed its proof and passed Lean verification on September 6, it contacted Alpöge and Buckmaster, hoping to coordinate a joint release and acknowledge any priority the other might have. However, the two parties subsequently discovered that Alpöge and Buckmaster were studying Euler equations with external forces, not the Navier-Stokes equations themselves.

According to a post by someone involved in the coordination, OpenAI had proposed solutions such as allowing the other party to release the data first and inviting Tristan Buckmaster to be the first author of the OpenAI proof rewrite, but the two sides ultimately failed to reach an agreement. OpenAI stated that its team and agents did not obtain the other party's research content in any way, and believed that the possibility of the other party using de-identified data generated by OpenAI products affecting model training was extremely low.

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