OpenAI says it has found a solution to a decades-old advanced math problem in a matter of hours using a new artificial intelligence (AI) model and thousands of AI robots.
The creator of ChatGPT said on Tuesday, external which by concentrating a group of approximately 10,000 AI agents, or AI robots that perform tasks somewhat autonomously, solved a notoriously difficult mathematical problem in just 88 hours.
The problem was part of the Navier-Stokes equations., externalwhich refer to how fluids move. For 90 years, important aspects of problems have lacked a proof, the argument underlying a correct mathematical equation.
OpenAI called the solution it found a “milestone” and evidence that AI tools are improving rapidly.
OpenAI’s solution has not yet been independently verified or publicly accepted by The Clay Mathematics Institute, a US-based mathematics organization that administers the Millennium Prize that offers large amounts of money to the first to solve certain mathematical puzzles.
The company said that in late August it began training a new model that quickly demonstrated that it was adept at mathematics. AI models are computer programs trained with enormous amounts of data to recognize and predict patterns in information.
While the new OpenAI model remains a tool only used within the company, as it is “significantly more capable” than the company’s most recent AI model, its researchers decided to use it on certain notable advanced mathematical problems.
OpenAI admitted that last week, on September 1, it had “heard rumors that two Millennium Prize problems had been resolved” and so decided to put thousands of AI robots trained on the new internal model to work to try to solve some of the remaining problems.
By September 5, or about 88 hours after assigning the task to 10,000 AI robots, OpenAI had found a solution to what is known as the Navier-Stokes existence-smoothness problem.
The problem lies at the core of turbulence, a phenomenon that is still not well understood.
Although it apparently took little time for the AI robots to come up with a solution, OpenAI said the robots exchanged nearly 3 million messages and used 130 billion output tokens, or the individual lines of text and code that an AI model produces in responses, in Navier-Stokes alone.
Such an effort would have cost approximately $10 million (£7.3 million), based on OpenAI’s own pricing., external for the production of its most advanced models.
The solution that OpenAI claims to have reached for the Navier-Stokes existence and smoothness problem resolved two of the four claims in the proof that the Millennium Prize had required. The prize is worth $1 million to the winner.
“Our goal in publishing this result is to report substantial progress of our AI models,” OpenAI said on Tuesday. “We do not intend to claim the Millennium Prize for this result.”
The company’s claim is already generating some controversy.
Tristan Buckmaster, a mathematics professor at New York University, said Tuesday, external that he and Levent Alpöge, a mathematician who works for OpenAI rival Anthropic, had also been working to find solutions to the problem.
The duo had been using OpenAI’s Codex tool in their work. But Buckmaster said that on September 3 he discovered that “information about our progress had been transmitted to OpenAI.”
Buckmaster’s statement came the same day, but hours before, OpenAI published its Navier-Stokes work. He stated that OpenAI did not start working on the Navier-Stokes equations until “after information about our work reached OpenAI.” It included texts from emails exchanged with OpenAI about the work and their questions about the company’s timing and methods.
Buckmaster added that he had not yet read OpenAI’s full test, but felt compelled to make public “what they told me, when and what they proposed to me… because the alternative is to let an ad sequence say something that I know is false.”
OpenAI on Tuesday congratulated Buckmaster and Alpöge’s “simultaneous work,” calling it “remarkable.”
The company said it had not seen “any of their work in any media until they published it publicly” and that no user data was accessed in their work on the Navier-Stokes problem.
“Although unlikely, we cannot rule out that de-identified data derived from the use of our products may have helped improve our models,” the company added. “However, our tests differ significantly and even the precise results demonstrated are different.”
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