OpenAI says its latest artificial intelligence (AI) models and thousands of autonomous AI agents have made significant progress on decades-old advanced mathematics problems.
The ChatGPT developer said on Tuesday, external that approximately 10,000 AI agents—software systems capable of completing tasks with some degree of autonomy—worked together to investigate the problem in just 88 hours.
The research focused on the Navier-Stokes equations, external, which describe how fluids move. For nearly 90 years, key aspects of the problem have remained unresolved because mathematicians lacked the formal proofs needed to establish whether the equations always produce smooth, well-behaved solutions.
OpenAI described the result as a major milestone and said it demonstrates how quickly AI systems are improving at complex mathematical reasoning.
However, OpenAI’s proposed solution has not yet been independently verified or formally accepted by the Clay Mathematics Institute, the US-based organization responsible for the Millennium Prize Problems. The institute offers substantial awards for solving some of mathematics’ most difficult challenges.
OpenAI said it began training the new model at the end of August and quickly found that it performed exceptionally well on advanced mathematics. AI models are computer programs trained on large datasets to identify patterns and generate predictions, text, code, or other outputs.
Although the new OpenAI model is still an internal research tool, company scientists used it to examine high-level mathematical problems because they said it was significantly more capable than the company’s most recent publicly released model.
On September 1, OpenAI said it had heard reports that two Millennium Prize Problems might have been solved. The company then assigned thousands of AI agents powered by its new internal model to investigate several of the remaining challenges.
By September 5, approximately 88 hours after deploying 10,000 AI agents, OpenAI said it had developed a solution addressing the existence and smoothness problem associated with the Navier-Stokes equations.
The problem is closely linked to turbulence, a physical phenomenon that remains only partially understood by scientists.
Although the result appeared to emerge quickly, OpenAI said the AI agents exchanged nearly 3 million messages. Work on the Navier-Stokes problem alone reportedly generated approximately 130 billion output tokens, including lines of text and computer code produced by the models.
Based on OpenAI’s estimates, the project would have cost approximately $10 million (£7.3 million). Its calculations were based on published AI model pricing, external for generating outputs with advanced systems.
According to OpenAI, its work on the Navier-Stokes existence and smoothness problem addresses two of the four statements required for a complete proof of the Millennium Prize challenge. A fully verified solution would qualify for a $1 million prize.
“The purpose of announcing this result is to report significant progress in AI models,” OpenAI said on Tuesday. “We will not claim the Millennium Prize for this result.”
OpenAI’s claims have already prompted debate among mathematicians and AI researchers.
Tristan Buckmaster, a professor of mathematics at New York University, said on Tuesday, external that he and Levent Alpöge, a mathematician at OpenAI rival Anthropic, had also been working on the problem.
Both researchers used OpenAI’s Codex tool in their work. Buckmaster said he learned on September 3 that “information about our progress was being passed to OpenAI.”
Buckmaster released his statement on the same day, several hours before OpenAI published its findings on the Navier-Stokes problem. He alleged that OpenAI began researching the equations only after information about his work had reached the company. His statement included email exchanges with OpenAI, along with questions about the company’s timeline and research methods.
Buckmaster said that although he had not yet reviewed OpenAI’s complete evidence, he felt “compelled to publish what I was told, when and what was suggested to me,” because he did not want later announcements to contain claims he believed were inaccurate.
OpenAI praised the “concurrent accomplishments” of Buckmaster and Alpöge as “remarkable.”
The company said it “had no visibility of their work through any means prior to public release” and did not access user data while conducting its research into the Navier-Stokes problem.
“Although unlikely, we cannot exclude the possibility that anonymized data obtained from the use of our products could have helped improve our models,” OpenAI added. “But our proofs are very different, and even the exact results proven are different.”
Source: www.bbc.co.uk