OpenAI has announced that its next major model lineup, Astra, was able to solve 10 major open problems in mathematics that had seen little or no progress for at least a decade. The ChatGPT maker says these problems spanned various fields, including geometry, coding theory, group theory, quantum computing, cryptography and graph theory.
“All of these problems are of substantial interest to their respective mathematical communities, and several are of broad interest across mathematics as a whole,” OpenAI wrote in a blog post.
OpenAI says solving these problems cost around $2,000 in token costs, based on GPT-5.6 Sol API pricing.
While Astra generated the mathematical arguments, human researchers used the same AI to prepare research manuscripts before formally verifying the proofs using the Lean proof assistant.
OpenAI says Astra solved decade-old mathematics problems
OpenAI shared the list of 10 long-standing problems that Astra had arrived at an answer to. These include:
- High-dimensional sphere packing
- Binary and spherical codes
- Non-sofic groups
- Connes’s rigidity conjecture
- Arithmetic circuit complexity
- Quantum parallel repetition
- Closest vector problem
- Ehrhart’s volume conjecture
- Multicolor Ramsey numbers
- Extremal number conjectures
Questions about use of AI in mathematics:
Just like any other field touched by AI, the use of the powerful new technology also raises questions about attribution and the role of AI in academia.
As for OpenAI, the company says that it belives attribution ‘should honestly reflect how a result was produced: claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system’s contribution and the nature of genuine human intellectual work.’
“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,” OpenAI wrote.
The company also noted that it hoped that mathematicians would independently evaluate the rseults produced by Astra, build on them and place them in broader context of mathematical research.
Earlier this year, OpenAI had also revealed that an unreleased AI model generated a disproof of the Erdős unit-distance conjecture during internal testing. The company says that this work has since inspired follow-up research in mathematics and theoretical computer science.
OpenAI finds evidence of other AI agents escaping:
In other related news, a recent report by Reuters revealed that OpenAI had found other instances when autonomous AI agents had escaped its containment evironment. The new breakouts were reportedly found during OpenAI’s investigation into the Hugging Face incident where the company’s unreleased AI model and GPT-5.6 Sol went on plan an attack on Hugging Face in order to cheat on the ExploitGym benchmark.
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