On August 1, OpenAI published solutions to ten mathematical problems that had remained unsolved since at least 2016, generated by an internal version of Astra, the next major model from the developer of ChatGPT. According to OpenAI, the cost of tokens used to find the answers would have been approximately $2000 based on Sol’s API rates. The manuscripts were prepared by humans using the same model, which then formalized each proof in Lean, a language for machine-verified theorems. The company has released all certificates and reasoning records to the public. Astra will be a separate class of models alongside Sol, Terra, and Luna, according to The Information, which reports that OpenAI has not yet decided whether it will be released as GPT-6 or as a version within the GPT-5 lineup, and has not set a release date. On July 26, the company’s CEO, Sam Altman, demonstrated Astra to politicians and regulators in Washington. The model could be the first to be tested under new rules from the administration of U.S. President Donald Trump, which require AI developers to submit new systems for federal evaluation before public launch. Key results include a construction proving the existence of non-sofic groups, addressing a central question since 1999 when Mikhail Gromov introduced the concept of soficity, refuting Connes’ rigidity conjecture on von Neumann algebras, solving Ehrhart’s conjecture on volume, and addressing Erdős problem No. 183 on multicolored Ramsey