New York, Sep 09 (V7N)- OpenAI has claimed that a new artificial intelligence (AI) model, working with thousands of AI agents, has found a solution to the long-standing Navier-Stokes Existence and Smoothness problem—one of the most challenging mathematical problems that has remained unresolved for nearly 90 years.

OpenAI, the company behind ChatGPT, announced on Tuesday (September 8) that around 10,000 AI agents worked together on the problem and produced the claimed solution in just 88 hours.

The Navier-Stokes equations are fundamental to fluid dynamics. They are used to describe how liquids and gases move and are particularly important in understanding complex fluid behavior and turbulence. Despite their importance, several fundamental questions surrounding these equations have remained unanswered.

According to OpenAI, the AI agents exchanged approximately 3 million messages while working on the problem and generated around 130 billion output tokens.

Based on standard pricing for advanced AI model outputs, the computational effort could have cost around $10 million, according to estimates cited in reports.

Part of the Millennium Prize Problems

The Navier-Stokes problem is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute. Each problem carries a $1 million prize for a valid solution.

OpenAI said its proposed solution addresses two of the four statements required for a complete proof. However, the company has made clear that it is not claiming the $1 million Millennium Prize.

OpenAI said the purpose of publishing the research was to demonstrate the rapidly advancing mathematical capabilities of AI models rather than claim a formal solution to the Millennium Prize problem.

Mathematician Raises Questions

The announcement has nevertheless triggered controversy.

Tristan Buckmaster, a mathematics professor at New York University, said he and Levent Alpoge, a mathematician at Anthropic, had been working on the same problem using OpenAI's Codex tool.

Buckmaster claimed that he learned on September 3 that information about their research had reached OpenAI. He subsequently questioned the company's timeline for beginning its own work on the Navier-Stokes problem.

Buckmaster has released excerpts of email correspondence with OpenAI regarding the matter. He said he had not yet examined OpenAI's complete proof but argued that greater transparency was needed concerning what information was shared, when it was shared and what research proposals were involved.

OpenAI Rejects Data-Sharing Allegation

OpenAI congratulated Buckmaster and Alpoge on their research and described their simultaneous work as "extraordinary."

However, the company maintains that it did not see data related to the researchers' work before it was publicly released. OpenAI also said it did not use user data while working on its proposed solution.

At the same time, the company acknowledged that it cannot completely rule out the possibility that anonymized information generated through its products may have indirectly contributed to model development.

OpenAI further said that its proof is substantially different from the work of Buckmaster and Alpoge and that the results demonstrated by the two research efforts are distinct.

How the AI Research Began

OpenAI said it began training a new AI model in late August. According to the company, the model quickly demonstrated an unusually strong ability to tackle difficult mathematical problems.

Researchers subsequently began testing the model against major unsolved mathematical challenges.

The model remains restricted to internal use and, according to OpenAI, is significantly more capable than its most recently released model.

After OpenAI learned on September 1 of rumors that two Millennium Prize problems had potentially been solved, the company deployed thousands of AI agents trained on the new model to investigate some of the remaining challenges.

However, OpenAI's claimed solution has not yet been independently verified, and the Clay Mathematics Institute has not formally recognized it as a solution to the Millennium Prize problem.

The development nevertheless highlights the growing ability of AI systems to tackle highly complex mathematical research. Whether OpenAI's work ultimately qualifies as a genuine solution will depend on detailed examination and independent verification by mathematicians.

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