By Newstake · Updated
Has AI solved unsolved math problems?
OpenAI says yes. In September 2026, it said an internal AI system produced a proof about the Navier–Stokes equations, one of the seven Millennium Prize Problems, with a machine-checked version in the Lean proof language. A result like this counts once other mathematicians have checked and accepted it.
Photo by @roman_lazygeek on Unsplash
Latest brief
Updated
OpenAI says an internal AI system produced a proof of finite-time singularity for the Navier–Stokes equations, with a Lean formalization; its publication describes a verification process but does not say mathematicians have accepted the result. OpenAI also reports new AI-generated mathematical results in its October updates, but the provided descriptions do not name the problems or explain how those results were checked.
Its later announcement mentions results involving the local smoothing conjecture, the Exponential Time Hypothesis, and quantum chromodynamics and Yang–Mills theory, but does not specify which were mathematical proofs or how they were verified. These are OpenAI’s claims, not evidence here of community acceptance.
Written by AI from the publications below.
The announcements
- Claim
Who says the problem is solved?
- Proof
Is there a formal proof?
- Review
Do other mathematicians accept it?
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What has been claimed
OpenAI says its system showed that solutions to the Navier–Stokes equations, which describe how fluids flow, can break down in finite time. In October 2026 it published more results on open problems, with the proofs on GitHub.
Other labs, including Google DeepMind, also publish AI results in mathematics. The brief on this page sums up the newest ones.
How a proof gets checked
A formal proof in a language such as Lean can be checked by a computer, step by step. That makes errors in the reasoning much less likely, but people still need to check that the formal statement says what the problem asks.
For a Millennium Prize, the Clay Mathematics Institute waits until a proof is published and accepted by the mathematical community.
Has AI passed the Turing test?
The Turing test asks whether a person can tell a machine from a human in a written chat. Today’s chatbots can hold such chats well, so researchers now use harder tests, such as new math problems, to measure what AI can do.
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