OpenAI claims to have solved a major mathematics problem that has stumped humans for nearly a century after spending millions of dollars on the artificial intelligence-led endeavour. The company behind ChatGPT said it had cracked the Navier-Stokes problem, one of seven Millennium Prize Problems published by the Clay Mathematics Institute to highlight some of the biggest unsolved puzzles in the field. However, the announcement swiftly became mired in controversy after mathematician Tristan Buckmaster, a professor at New York University, said OpenAI accelerated its work on the problem after hearing that he and another researcher at Anthropic, an OpenAI rival, were poised to announce their own breakthrough.
Buckmaster had further concerns because the pair’s work in progress was stored in OpenAI’s Codex model, which is used for writing computer programs, potentially making the work visible to the OpenAI team. In a document posted on his website, he added: “I do not know what their model did, or how. I do not know whether our data was used.
I am not accusing anyone of anything.” At a press briefing on Tuesday, OpenAI researcher Sebastien Bubeck denied that the company had used the pair’s work or accessed material shared with OpenAI’s servers. OpenAI’s announcement on the breakthrough gave more details, saying that the company was inspired to launch the effort after hearing rumours that two Millennium Prize Problems had been solved. It also said it could not rule out that data from the pair’s use of their products “helped improve our models.” OpenAI said it tackled the Navier-Stokes problem with an internal OpenAI system that was more powerful than its latest GPT-6 Astra model.
About 10,000 AI agents – AI systems that carry out tasks autonomously – worked on the problem at once and reached the solution in 88 hours. The breakthrough is the latest to demonstrate how advanced artificial intelligence models consuming enormous amounts of computing power are encroaching on and reshaping the field of mathematics. In May, OpenAI claimed progress in another mathematical problem first proposed 80 years ago, while Google DeepMind has also claimed maths achievements with its models.
Bubeck said the solution to the Navier-Stokes problem was “a spectacular culmination of the arc we have seen over the past 12 months”. The Navier-Stokes problem asks whether equations that are used to describe the movement of fluids like air and water fail under particular conditions. OpenAI’s proof suggests that they do, with the equations occasionally “blowing up” with the speed of fluids becoming impossibly infinite.
It took OpenAI’s GPT-6 Astra about 17 hours to verify the solution. Mathematicians who solve any of the Millennium Prize Problems are in line for a $1m (£740,000) reward from the Clay Mathematics Institute. OpenAI, which is preparing for a flotation that could value the business at around $1tn, said it did not intend to claim the prize.
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