Artificial intelligence has taken aim at one of mathematics’ greatest unsolved problems – and reportedly claims to have cracked it.
On 8th September 2026, OpenAI announced that an advanced internal AI system had produced a solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute.
Each problem carries a $1 million prize, although OpenAI says it will not claim the award.
The mathematical problem
The Navier–Stokes equations describe how fluids such as water and air move. The mystery is whether these equations can always produce smooth, well-behaved solutions, or whether they can develop a mathematical singularity – effectively becoming infinite in a finite amount of time.
AI soloution
What makes the breakthrough particularly remarkable is how AI was used. Rather than relying on a single chatbot producing an answer, OpenAI deployed around 10,000 autonomous AI agents working together on the problem.
They generated ideas, tested approaches and communicated with one another on an enormous scale. After about 88 hours, the system had produced a proposed proof. A further AI system then spent around 17 hours formalising the result in Lean, a computer language designed to verify mathematical proofs.
Did AI combine its resources?
So, in a sense, yes, it did – AI combined its own computing power. Thousands of AI agents attacked different aspects of the same problem, creating something closer to a digital mathematical research team than a single artificial mathematician.
However, the claim still requires scrutiny. Independent mathematicians have yet to complete a full review of the proof, and controversy has already emerged over the originality of some of the ideas involved.
If ultimately confirmed, this would represent a remarkable change in mathematics: AI would not merely calculate answers – it would discover new mathematics.
Has it fully resolved the mathematical problem, or opened a door for further discussion?
We could also equally argue that humans having created a ‘machine’ that solved the problem actually solved it themselves.