**[OpenAI's New Model Astra Debuts: Solves 10 Decade-Old Unresolved Math Problems in One Go]** According to monitoring by Dongcha Beating, OpenAI has officially unveiled its next flagship model, Astra, for the first time. The internal version has achieved new results on 10 long-standing unresolved problems in mathematics and theoretical computer science. The core conclusions of these problems had seen no progress for at least 10 years, with most being stagnant for even longer. Some of these problems have been directly solved or disproven. Astra has, for the first time, constructed a non-sofic group, addressing a core open problem in group theory. It also disproved Connes' rigidity conjecture and resolved three Erdős problems. Other achievements include new bounds and hardness proofs related to sphere packing, coding theory, quantum complexity, and post-quantum cryptography. OpenAI stated that the tokens used by the model to arrive at these 10 results cost approximately $2,000, based on Sol API pricing. These mathematical proofs were generated by Astra. Humans then assisted in organizing the findings into papers, and the model subsequently converted each proof into Lean certificates, allowing computers to verify the derivations step by step. OpenAI has made the papers, proof certificates, and the model's reasoning process publicly available. [Original Link]