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OpenAI Says AI Solved One of Mathematics’ Hardest Problems in 88 Hours

From The Punch · () English

Translated from English and summarized by DistantNews. Read the original for the full story.

At a glance

Press release Official statement New plan
  • OpenAI says an internal AI system produced a solution to the Navier-Stokes existence and smoothness problem in about 88 hours.
  • The system used roughly 10,000 concurrent AI agents and produced both an analytical proof and a formalization in Lean, according to the company.
  • The problem is one of seven Millennium Prize Problems, each carrying a $1 million prize for a valid solution.

OpenAI says an internal artificial intelligence system has produced a solution to the Navier-Stokes existence and smoothness problem in about 88 hours, using roughly 10,000 concurrent AI agents. The company announced the result in a research release published on Tuesday.

The Navier-Stokes problem is one of seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000. The problems highlight some of mathematics’ most difficult unanswered questions, and the institute set aside a $7 million prize fund, with $1 million allocated to each solution.

A solution to the Navier, Stokes existence and smoothness problem, one of the Millennium Prize Problems.

· OpenAIThe company’s research release describes the result it says its internal AI system produced.

OpenAI said its agents reached the Navier-Stokes resolution on September 5, about 88 hours after the first agents were launched. The company said the proof was produced by an internal system and showed that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. OpenAI said it was sharing both a written proof and a formalization in Lean.

We’re sharing both a writeup of the proof and a formalization in Lean.

· OpenAIOpenAI said it was publishing both a written proof and a machine-checked formalization.

The equations apply Newton’s second law of motion to fluid movement and are used in fields including aircraft design, weather forecasting and the study of blood flow. The central question is whether fluid motion that begins smoothly can break down. OpenAI defined a singularity as a situation in which fluid speeds grow without bound within a finite period.

The company said its system produced an analytical proof and a Lean formalization showing that an initially smooth fluid at rest can develop a singularity in finite time, while its energy remains finite throughout the process. OpenAI said the effort also aimed to demonstrate the pace of AI development. It said the model used was significantly more capable than GPT-6 Astra and that informing the public about AI progress was important.

A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity.

· OpenAIThe company described the broader purpose of its AI research.
About this summary

Originally published by The Punch in English. Translated, summarized, and contextualized automatically by DistantNews, with a note on how the source frames the story. Not individually reviewed before publishing. How this works.

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