3 min readNew DelhiAug 3, 2026 11:21 AM IST OpenAI has quietly unveiled that its next major family of AI models will be called ‘Astra’, and claimed that an internal version of one such model cracked ten long-standing unsolved mathematical problems, signalling a major leap in AI reasoning.
The ChatGPT-maker on Saturday, August 1, said that its unreleased Astra model either resolved or “made substantial progress” on ten complex, long-standing open problems.
These problems relate to a wide range of mathematical topics, such as high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics.
The AI-generated mathematical proofs were later prepared into manuscripts by humans with each argument formalised in a Lean certificate, according to OpenAI. It further said that it will be publishing the model’s narration of its thinking process for each solution.
While OpenAI did not provide technical details about the Astra model, it said that the total number of tokens needed to find solutions to these problems would cost roughly $2,000 at GPT-5.6 Sol API rates. It suggests that the model could be relatively compute-efficient for problems of this complexity.
OpenAI has been steadily advancing AI models capable of completing long-running tasks. In May 2026, the company announced that an unreleased model was used to generate a disproof of the Erdős unit-distance conjecture that had remained unsolved for over 80 years. It was also one of OpenAI’s models to break out of containment during testing and hack into the internal systems of external platforms such as Hugging Face.
However, the rise of AI models capable of generating mathematical proofs has ruffled feathers. In the first-ever Leiden declaration published in June 2026, hundreds of mathematicians warned that the growing use of AI in the field poses several challenges, including unreliable mathematical proofs, lack of citation, improper disclosure of information, and research bias.Story continues below this ad
While AI models appear to be making progress in mathematical capabilities, an expanding group of mathematicians have questioned the purported milestones. “Mathematicians should find it quite striking that tech companies are suddenly interested in their work. The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space,” Kevin Buzzard, a mathematician at Imperial College London, previously said in a statement.
“There are many views as to the role of AI in mathematics, and we have deep respect and understanding for those concerned with its impact, including the signers of the Leiden declaration on AI and Mathematics,” OpenAI said in a blog post on Saturday.
“We believe attribution should honestly reflect how a result was produced […] We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness, while the mathematical arguments themselves were generated by our system,” it added.
Meanwhile, OpenAI recently announced a new initiative called ‘ChatGPT for Academic Researchers’ which provides 1,00,000 scientists and mathematicians with free access to its latest and most advanced models.