OpenAI Solves Navier–Stokes Equations, One of the World’s Seven Major Mathematical Problems

[Financial News]  

OpenAI announced on the 8th (local time) that it had solved the Navier–Stokes equations problem, one of the world’s seven major mathematical problems and a core equation in fluid dynamics.
Following the Poincaré conjecture, solved by Russian mathematician Grigori Perelman, who is known for living in seclusion and refusing prize money, two of the seven problems have now been solved.
OpenAI announced that its latest unreleased artificial intelligence (AI) model completed a 165-page proof and its verification after carrying out computations with approximately 10,000 AI agents over 88 hours and consuming 130 billion tokens.
However, controversy is growing after OpenAI reportedly rushed to deploy massive computing resources and solve the Millennium Prize Problem itself before making a surprise announcement, amid rumors that rival Anthropic was solving a related fluid-dynamics problem.

According to The Wall Street Journal (WSJ), the Navier–Stokes equations are formulas that describe the movement of liquids and gases. They are used to design aircraft and forecast the weather.
In reality, water and air flow smoothly, but mathematicians have raised a different question. When numbers are inserted into the formulas and calculations are performed, is there a moment when a mathematical error—a singularity—causes the formulas themselves to stop or break down? This was one of the Millennium Prize Problems.
OpenAI’s AI model identified specific conditions that cause the formulas to break down.
First, a small vortex can form in previously calm water. As it rotates, its speed could rise to “infinity” within a short period. In mathematics, a result becoming infinite means that the calculation is impossible and the formula breaks down.
The AI proved that although water flows normally in the real world, the fluid-dynamics formulas we use contain a “mathematical hole” that makes calculations impossible under certain conditions.

According to reports, OpenAI contacted New York University (NYU) mathematics professor Tristan Backmaster and Anthropic researcher Levent Alfoege over the weekend after rumors circulated that they were conducting research related to fluid dynamics and that the problem had been solved. The parties reportedly discussed announcing their achievements simultaneously.
However, after a tense standoff, Professor Backmaster published the research findings online before OpenAI’s official announcement, and OpenAI released its paper several hours later in a surprise move.
Backmaster said he had also used OpenAI’s AI model during the research process and raised the possibility that the OpenAI model had learned from the questions and ideas he entered into the system and used them to solve the problem.
OpenAI emphasized that its 10,000 AI agents had independently found the clues. However, it left open the possibility that it could not guarantee with 100% certainty that Backmaster’s ideas had not been used, given the ordinary process through which users’ data is incorporated into model improvements.
Anthropic had been working on a fluid-dynamics problem related to the Navier–Stokes equations, while OpenAI claims to have solved the Millennium Prize Problem represented by the equations themselves. The controversy, however, has left a difficult question for the AI era: who owns ideas and data provided through user prompts, and where should the boundaries of intellectual property be drawn?

[email protected] Song Kyung-jae Reporter