OpenAI Says Its Astra Model Solved 10 Decades-Old Math Problems

OpenAI has announced that an internal version of its next-generation AI model, Astra, has successfully solved ten long-standing open problems in mathematics and theoretical computer science. According to the company, the problems had remained unresolved for at least a decade—and in many cases much longer. Rather than simply publishing benchmark scores, OpenAI released a 249-page technical manuscript, detailed reasoning notes, and machine-checkable proof certificates created using the Lean proof assistant, allowing researchers around the world to independently verify the formal proofs.

The reported breakthroughs span a wide range of mathematical fields, including high-dimensional geometry, coding theory, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. Among the most notable claims are the construction of the first known non-sofic group, new advances in sphere-packing theory, stronger lower bounds in arithmetic circuit complexity, and progress on several famous problems proposed by renowned mathematician Paul Erdős. OpenAI emphasized that these are not benchmark exercises but original research contributions intended to advance multiple areas of mathematics.

One of the most significant aspects of the announcement is the way the results were verified. Instead of relying solely on human reviewers, OpenAI formalized every proof in the Lean 4 proof assistant, which mechanically checks every logical step for correctness. This provides a much higher level of confidence than traditional AI-generated outputs, where subtle reasoning errors can be difficult to detect. However, OpenAI acknowledged that formal verification does not replace independent peer review, and mathematicians will still need to confirm that each proof addresses the intended problem and represents a genuinely novel contribution to the field.

OpenAI also revealed that the computational cost of generating the core arguments for all ten discoveries would have been roughly $2,000 using current API pricing, although that estimate excludes the cost of training Astra, human collaboration, and the extensive verification process. The company described Astra as its next major model family, designed for long-duration reasoning tasks that may take hours or even days to complete. Despite the announcement, Astra has not yet been released publicly, and OpenAI has not provided a launch date or details about its capabilities for ChatGPT or API users.

If the mathematical claims withstand scrutiny from the global research community, Astra could represent one of the most important demonstrations yet of AI’s ability to contribute to original scientific discovery rather than simply answering questions or generating content. Researchers believe this milestone could accelerate breakthroughs across mathematics, computer science, cryptography, and other scientific disciplines by enabling AI systems to assist with problems that have challenged experts for decades. While peer review will ultimately determine the significance of each result, OpenAI’s release has already sparked widespread discussion about the growing role of advanced AI in shaping the future of scientific research.