OpenAI's Astra solves 10 major math problems for $2K

OpenAI has revealed that an unreleased internal model from its next major family, codenamed Astra, has successfully resolved 10 long-open problems in mathematics, quantum complexity, and theoretical computer science. Among these achievements is a proof for the existence of non-sofic groups, which establishes a symmetrical framework that cannot be simulated by a finite shuffle—a mathematical mystery researchers have been hunting since 1999. Additionally, the model settled Alain Connes's rigidity conjecture, Ehrhart's volume conjecture, and three separate challenges from Paul Erdős's famous list, none of which had seen any progress in over a decade.

To ensure the validity of these solutions, each proof was formally verified using the Lean theorem prover, and OpenAI has made the corresponding chain-of-thought walkthroughs public. Remarkably, the computational cost to achieve these breakthroughs was highly economical, totaling approximately $2,000 in tokens when calculated at Sol API rates for all successful execution runs. The ease of these computations was highlighted just 24 hours later when Anthropic researcher Levent Alpoge claimed he successfully reproduced 5 of the 10 proofs. Alpoge achieved this using Anthropic's Fable model, running on a generic prompt without any internet access.

For AI practitioners and research mathematicians, this development represents a paradigm shift in how theoretical research is conducted. Historically, proving complex conjectures required years of highly specialized human labor, but Astra demonstrates that frontier models can now automate the generation of verifiable, prize-caliber proofs at a fraction of the traditional cost. This transition from human-only intuition to machine-assisted verification means that researchers can treat AI as an active collaborator to rapidly test and validate mathematical structures. As these reasoning capabilities scale and token costs decline, the methodology used to crack these decades-old mathematical puzzles will likely expand into practical applied sciences, accelerating discoveries in fields like cryptography, materials science, and molecular biology.