OpenAI Shares Mathematical Results on GitHub

OpenAI published new mathematical results on a GitHub repository on October 6, 2026, produced by an internal frontier model. The release includes formalizations of many proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer.

The repository contains 10 summaries of the model’s reasoning. According to OpenAI, the average mathematical result in the release used the equivalent compute of roughly three hours of ChatGPT Pro thinking.

Development and Review Process

OpenAI consulted the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study to develop best practices for releasing these results.

Next Steps

OpenAI stated it is working to responsibly release the internal frontier model that produced the mathematics results. The company said it will fund a series of workshops, conferences, and special programs around the understanding of major results produced by AI in mathematics.

Anthropic Advances on Riemann Hypothesis with Unreleased Claude Model

An unreleased research version of Anthropic’s Claude model raised a lower bound for the fraction of zeros of the Riemann zeta function satisfying the Riemann hypothesis from 41.6% to 67.2%. The Riemann hypothesis is one of the seven Clay Millennium Prize Problems, each carrying a $1 million reward.

Anthropicstated explicitly that its model “didn’t succeed” at the primary challenge—the unreleased Claude model did not solve the Riemann hypothesis. Two of Anthropic’s in-house mathematicians reviewed the Riemann result internally, and outside experts were also brought in to check the work before publication.

Fermat’s Last Theorem Formalization

Anthropicreportedly completed a formalization of Fermat’s Last Theorem using a multi-agent system in under two weeks. The formalization generated approximately 13 million lines of Lean code and established 29,500 intermediate theorems.

Claude-Assisted Scientific Work Across 18 Fields

On October 1, 2026, Anthropic published a ‘Claude-shaped science’ roundup describing Claude-assisted work spanning 18 scientific fields with 19 human co-authors. The roundup included the resolution of Watson’s ‘final problem’—a lattice-integral problem that mathematician George Watson had begun working on in 1939 and had remained unsolved for 87 years.

OpenAI Claims Proposed Solution to Navier-Stokes Problem

OpenAI has reportedly claimed a proposed solution to the Navier-Stokes existence and smoothness problem, according to a September 10, 2026 report from Campus Technology.

GPT-6 Astra Advances on FrontierMath Benchmark

GPT-6 Astra has solved 2 of the 68 problems on the FrontierMath Erdős benchmark, a 3% clearance rate.

DeepMind’s AlphaProof and AlphaGeometry 2 Achieve IMO Silver-Medal Level

Google DeepMind’s AlphaProof and AlphaGeometry 2 systems jointly solved four of six problems at the 2024 International Mathematical Olympiad, a result described as equivalent to a silver-medal performance.

Source: OpenAI