An internal version of OpenAI's Astra model has achieved a mathematical breakthrough, solving 10 problems in mathematics and computer science that had remained open for over a decade. The results are presented as rigorous proofs, according to the website infohub.kz.
OpenAI has published a 249-page handwritten compilation and digital Lean 4 certificates for the 10 unsolved problems on GitHub under the Apache 2.0 license. All proofs generated by the algorithm have successfully passed formal machine verification without a single gap in the logical chains.
Among the solved problems are the disproof of Conn's rigidity hypothesis, proposed back in 1980, the construction of a proof of the existence of a non-sofic group, and the solution of Paul Erdős's problem No. 183 related to multicolored Ramsey numbers. Additionally, Astra found solutions in the areas of sphere packing in high-dimensional spaces, quantum repetition, and algorithmic complexity.
The new AI system Astra is designed for long-term work on complex tasks by coordinating multiple agents. Researcher Noam Brown noted that token costs amounted to only about $2,000. However, all presented results still await expert peer review by scientists.