OpenAI Says New AI Model Cracked a Millennium Prize Problem in 88 Hours

OpenAI has announced that its newest artificial intelligence technology, an unreleased model called GPT-6 Astra, successfully solved one of the seven "Millennium Problems" in mathematics. The company stated that the AI agent took 88 hours to produce a proof for the Navier–Stokes existence and smoothness problem, which concerns the equations that describe fluid movement and are used in applications like weather forecasting.

The problem, selected by the Clay Mathematics Institute in 2000, asks whether these equations can break down under certain conditions. OpenAI claims its proof defines such a case. The institute had offered a million-dollar prize for each solution, and before this announcement, only one of the seven problems had been solved.

According to the company, the solution involved deploying up to 10,000 AI agents working in parallel. During the entire process across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. For the Navier-Stokes problem specifically, they sent 2.7 million messages and used roughly 130 billion output tokens.

OpenAI researchers described the effort as a culmination of progress over the past year. The company acknowledged the computational operation was "very expensive," though it noted that costs typically decline as efficiency improves. It also stated that it focused resources on this problem after learning other mathematicians were examining similar research, but denied seeing any of their work.

The systems rely on reinforcement learning to generate formal proofs in the programming language Lean. OpenAI released a paper outlining its proof to allow outside verification.

The announcement has drawn mixed reactions from the mathematical community. Some experts expressed excitement about AI's role in pushing the boundaries of the field, while others voiced concerns. Terence Tao, a mathematics professor at UCLA, compared the automated approach to a guide finding a single route to a waterfall, noting that while it has value, people may stop looking for alternative paths. He also warned that such technology could weaken human understanding, likening the ease of AI problem-solving to having machines lift weights at the gym instead of training yourself.

The American Mathematical Society welcomed the news, calling it a "milestone advance in human knowledge." The society noted that the achievement builds on decades of work by mathematicians and that the process leading to the solution will have lasting benefits.