OpenAI’s Astra Model Solves 10 Long-Standing Mathematics Problems

OpenAI has quietly demonstrated a massive leap in AI reasoning capabilities. The company revealed that an unreleased internal model from its next-generation family, codenamed Astra, has successfully solved ten long-standing open problems across mathematics, quantum complexity, and theoretical computer science. Some of these problems, including questions in geometry and group theory, had remained unsolved by human mathematicians for nearly three decades. Among its achievements, Astra proved the existence of non-sofic groups and resolved Alain Connes’s rigidity conjecture, alongside Ehrhart’s volume conjecture and three challenges from Paul Erdős’s famous list. Remarkably, all ten solutions were verified using the Lean theorem prover. The total computing cost for these successful runs was estimated at just $2,000, suggesting that advanced mathematical research could soon become incredibly cost-effective. The AI community was quick to react. Within twenty-four hours of the announcement, Levent Alpoge from Anthropic claimed he reproduced five of the ten proofs using Fable, running on a generic prompt and no internet access. This rapid replication suggests that the underlying reasoning capabilities required for such breakthroughs are becoming more accessible across competing AI labs. This milestone has reignited a profound debate among academics regarding whether AI-generated proofs should be eligible for prestigious awards like the Fields Medal. As AI systems transition from assisting researchers to independently solving decades-old theoretical challenges, the implications extend far beyond mathematics. Experts believe these reasoning capabilities will soon accelerate breakthroughs in practical fields such as drug discovery and materials science.