OpenAI recently announced that its internal, unreleased model, Astra, has successfully solved ten long-standing open problems in mathematics and theoretical computer science. The company released a 249-page manuscript with Lean 4 proof certificates on GitHub to support its claims. This achievement reportedly cost around $2,000 in compute for the final successful runs, a figure that has sparked discussion about the changing economics of scientific research, although it doesn't account for training costs or failed attempts. The solutions include an explicit construction of a non-sofic group, a disproof of Connes's rigidity conjecture, a proof of Ehrhart's volume conjecture, and resolutions of several problems from Paul Erdős's catalog. However, none of these are considered Millennium Prize Problems.
The announcement from OpenAI, made in August 2026, generated significant buzz. While the company stated that the mathematical arguments were generated by their system, humans were involved in preparing the manuscripts and formalizing the proofs in Lean. The firm emphasizes that attribution should reflect how a result was produced, advocating against claiming human authorship for AI-generated proofs. As of September 1, 2026, these results have not yet undergone traditional academic peer review.
Despite the significant advances, none of the problems solved by Astra qualify as Millennium Prize Problems, which are a set of seven highly complex mathematical problems, each carrying a $1 million reward from the Clay Mathematics Institute. Six of these problems remain unsolved, including the Riemann Hypothesis and the P versus NP question. The distinction is crucial, as the criteria for solving a Millennium Prize Problem are strict, requiring the substantial work to be done by an AI system, not merely human assistance to AI.
Separately, other AI-driven mathematical progress has been observed. Google DeepMind, in collaboration with NYU, Stanford, and Brown, identified new unstable singularities in fluid equations in early 2026, related to the Navier-Stokes family. In August 2026, Anthropic's Claude model raised the Riemann zeta lower bound from 41.6% to 67.2%. While these are genuine advances, they also fall short of solving a Millennium Prize Problem. Market speculation on Manifold, a forecasting platform, currently places the probability of an AI solving a Millennium Prize Problem in 2026 at 38%, driven more by recent momentum and narrative than confirmed solutions.
The Wall Street Journal, in early June 2026, reported on an AI solving a famous math problem that had stumped humans for a century, referring to an AI-generated disproof of the Erdős unit-distance conjecture. This earlier report highlighted the potential for AI to explore large search spaces in combinatorial or geometric problems, leading to discussions about the role of AI in mathematical discovery and the interpretability of AI-generated proofs. Some critics, however, raised concerns about the verifiability and reproducibility of such claims, noting that the training data and methodologies for these internal models are often undisclosed.
