The company OpenAI claimed yesterday that one of its artificial intelligence (AI) models solved a mathematical puzzle that has defeated human minds for generations, a claim that sparked a dispute with rival researchers over that merit.
These are the Navier-Stokes equations, which describe how fluids such as air and water move, which are used in aircraft design, weather prediction and the study of blood flow, known as one of the seven Millennium Problems, list of the most difficult open questions in mathematics prepared by the Clay Institute of Mathematics.
However, mathematicians Levent Alpöge – linked to the company Anthropic – and Tristan Buckmaster of New York University, published documents last Monday in which they claimed to have made key advances in this problem. But for its part, OpenAI denies having accessed the duo’s data before its publication; However, it does not rule out that the information from Buckmaster and Alpöge has served to improve their models.
The company OpenAI, creator of ChatGPT, said it took 88 hours and millions of dollars in computing power to figure out the problem and said its work showed that those equations can break down over time, answering the question as posed by the Millennium Prize.
“This is a major milestone for AI research, and the promise to the world is that our toughest questions could eventually be answered,” said Mark Chen, research director at OpenAI.
The problem would have been solved by a model that has not yet been released to the public. OpenAI explained that it began training that new model at the end of August, more capable than any that has been publicly released.
The announcement came just hours after Tristan Buckmaster and Levent Alpöge published their own AI-assisted work on three related equations.
In a statement published alongside his papers, Buckmaster said that OpenAI only became interested in the problem after news of its research spread, and that it had resorted to the same unusual approach that he and Alpöge had set out to develop.
OpenAI researchers denied having had any access to the rival team’s work and said they proposed sharing credit.
Buckmaster maintained that OpenAI learned about his and Alpöge’s work the week before its publication, that it already had a team working on the problem and that they proposed two alternatives after a call with Sebastien Bubeck, in charge of advanced research in artificial intelligence and model reasoning capabilities at OpenAI: publish its result with a parallel OpenAI announcement or have Buckmaster himself write an article recognizing the company’s model as the author of the Navier-Stokes test, but without including the name of Alpöge.
“I want to make it very clear that we recognize the importance of the work of Levent Alpöge and Tristan Buckmaster on unforced Euler equations, and we cannot but congratulate them on this monumental achievement they have achieved. To be clear, we do not use their indication or their demonstration to give instructions to our models or to direct our agents,” Bubeck defended in the blog detailing the work.
The unforced Euler equations describe the flow of an ideal, frictionless fluid when no external force acts on it.
In a social media post, Bubeck rejected the idea that the company had suggested dropping the Alpöge name. OpenAI CEO Sam Altman also weighed in on the controversy and defended the team’s work.
The dispute over who gets the credit for solving one of the biggest problems in mathematics could drag on for some time. As AI takes on more of the work involved in finding demos, these types of disputes could become more common.
Each Millennium Problem awards a prize of one million dollars. OpenAI said it will not claim the money if its finding is confirmed. If the mathematical community validates it, it would be only the second Millennium Problem solved, after the one demonstrated on the Poincaré hypothesis in 2003, solved by the Russian mathematician Grigori Perelmán.
(With information from AFP)