News
OpenAI Unveils Astra Model That Solved 10 Open Math Problems
An unreleased version of Astra, OpenAI's successor to the GPT series, solved ten math problems that had been open for at least a decade, including one posed in 1999. The computational cost for all ten solutions was about $2,000.
OpenAI has revealed that an internal, not-yet-released version of its new model, called Astra, solved ten problems in mathematics and theoretical computer science that researchers had made no progress on for at least ten years, and in several cases much longer. The company published a complete, automatically verifiable proof for each of the solutions.
Astra is OpenAI's next major model family, described as the successor to the GPT-5.6 series. Unlike models built for short, real-time responses, Astra is designed for long-running tasks, including coordinating multiple agents over extended work sessions. The company has not yet announced a release date or a final product name.
What Was Actually Solved
The most significant result is an explicit construction of a non-sofic group, resolving a question that had remained open since 1999, when mathematician Mikhail Gromov defined the concept of group soficity. Astra also disproved the Connes rigidity conjecture concerning von Neumann algebras, proved the Ehrhart volume conjecture, and solved three problems from Paul Erdős's catalog, including problem number 183 on multicolor Ramsey numbers.
The remaining problems covered sphere packing in high-dimensional spaces, binary and spherical codes, arithmetic circuit complexity, quantum parallel repetition, and the computational hardness of the closest vector problem in lattices, which is relevant to post-quantum cryptography.
Verification and Cost
A key element of the announcement is how the results were verified. OpenAI did not simply publish the proofs as text, it translated them into the formal Lean 4 system, where every reasoning step is checked automatically by computer. The GitHub repository, released under an Apache 2.0 license, contains zero so-called "sorry" markers, meaning gaps left without proof, which in practice means all ten formalized proofs passed full formal verification.
OpenAI estimated that the total computational cost needed to generate all ten solutions was about $2,000 at API prices for the GPT-5.6 Sol model. That is a small sum relative to the scale of the achievement, and it has itself become part of OpenAI's messaging about the growing efficiency of reasoning models.
An internal version of Astra, our next major model family, solved 10 serious open problems in mathematics, quantum complexity, and theoretical computer science. We think this is a big step for scientific reasoning - Noam Brown, OpenAI researcher, on X
Unfortunately, none of the Millennium Prize Problems (yet) - Noam Brown, OpenAI researcher, on X
Mathematicians React
Thomas Bloom, the mathematician who runs erdosproblems.com, a database cataloging the status of Erdős problems, called the results more significant than the earlier unit-distance counterexample announced by another AI model in June 2026. Bloom noted, however, that calling this a replacement for mathematicians misses the point, since the model draws on more than a hundred years of mathematical theory developed by humans. The same researcher had previously been critical of controversial, later partly retracted claims about GPT-5's mathematical abilities from October 2025, calling them a gross misrepresentation of the facts.
Noam Brown acknowledged on X that the team did not devote much compute to each problem and that inference-time compute could be significantly scaled up, suggesting the current results may be just the beginning. None of the Millennium Prize Problems, which carry a million-dollar reward for a solution, have been solved, however.
What's Next for the Model
OpenAI has not disclosed a release date for Astra, its pricing, or its final commercial name, it is unclear whether it will reach the market as GPT-6 or as a separate variant of the GPT-5 series. The company said every public release of the model will go through the United States' federal AI safety review process, similar to the one that previously delayed the rollout of GPT-5.6. Astra could become the first model tested under the US administration's new regulatory framework for AI systems.
For Polish researchers and mathematics departments, the achievement signals that reasoning models are starting to genuinely support research work in fields long considered resistant to automation. However, an ethical debate is unfolding in the background: in June 2026 the International Mathematical Union endorsed the so-called Leiden Declaration, expressing concerns about the use of scientific publications to train AI models without authors' consent and about bypassing the traditional peer-review process.
Astra is also part of a broader race among AI labs for dominance in automating scientific research, in which, alongside OpenAI, Google DeepMind with its Co-Scientist system and other teams working on models that support mathematical and scientific discovery are also taking part. The coming months will show whether Astra's claimed capabilities translate into a real tool available to the scientific community, or remain an impressive demonstration without immediate practical application.
