Ten advances in mathematics and theoretical computer science

OpenAI has announced ten new results that resolve or make substantial progress on long-standing open problems in mathematics and theoretical computer science. The achievements cover fields such as high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. According to the company, these solutions were produced by an internal version of Astra, its next major model, at a token cost of roughly 2,000 dollars at Sol API rates. Following the generation of the mathematical arguments by the AI system, humans helped prepare the manuscripts, and the model subsequently formalized each argument into a Lean certificate. OpenAI is also releasing the model's narration of its thinking process for each solution. This follows a previous disproof of the Erdős unit-distance conjecture shared in May. OpenAI emphasizes that attribution should honestly reflect how results are produced, noting that while humans helped prepare manuscripts and take responsibility for correctness, the mathematical arguments were generated by the system. The emergence of such systems raises important questions about AI's role in mathematics, prompting the company to encourage deep engagement from the mathematical community.