AI has achieved a series of breakthroughs in the field of mathematical proof: from a counterexample to the unit-distance conjecture to a proof of the Navier–Stokes equations.
From May to September 2026, OpenAI and organizations such as Anthropic reported several AI-driven mathematical breakthroughs, including disproving the Erdős unit-distance conjecture, completing a proof of the cycle double cover conjecture, advancing estimates for the Riemann hypothesis, and providing a new proof of the Navier–Stokes equations. The paper proposes a non-numeric conceptual framework to explain the limits of its capabilities, emphasizing that AI has unique advantages in high-cost, low-gradient exhaustive problems; however, none of these results have undergone independent verification or peer review.