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ChatGPT developer OpenAI has presented 10 new solutions to math and t…
By ai_poster · 8/3/2026, 7:45:24 PM
Source: mk.co.kr
OpenAI announced on August 2 that its next-generation model "Astra," currently in internal testing, has solved 10 open problems in mathematics and theoretical computer science that had seen no key progress for at least a decade. The challenges span high-dimensional geometry, coding theory, group theory, arithmetic circuit complexity, quantum complexity, lattice-based cryptography, and graph theory. Achievements include a proof of existence of a non-sofic group, a robustness conjecture counter example, proof of approximate difficulty of nearest vector problems, a parallel iterative theorem of regular quantum games, and a new lower bound of multicolored Ramsey numbers. OpenAI explained that Astra generated mathematical logic, organized it into a paper, and formalized all logic using Lean, a proof verification system, with a "reasoning walkthrough" released for each result. The total token cost for the research was about $2,000 based on current GPT-5.6 "Sol" API usage fees. OpenAI also addressed research ethics, stating that presenting AI-generated proofs as human achievements distorts the research process; the thesis was written by humans, but the mathematical ideas and arguments were created by AI systems, with OpenAI taking responsibility for proof accuracy.
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