OpenAI's Astra Model Solves 10 Open Math Problems

Astra's headline result is the first explicit construction of a non-sofic group, closing a question mathematician Mikhail Gromov opened in 1999 ^[2]. It also produced a disproof of Fields Medalist Alain Connes's 1980 rigidity conjecture. Eight more advances round out the list: the first improvement to the general upper bound on high-dimensional sphere-packing density since 1978, three problems from the Erdos catalogue, a quantum parallel repetition theorem, new circuit complexity lower bounds, and a hardness result for the closest vector problem that bears on lattice-based cryptography ^[3]. OpenAI says the internal, unreleased model produced all ten results for roughly $2,000 in compute ^[1].

Every proof ships as a Lean 4 certificate with a 'sorry' count of zero, meaning no step in any of the ten proofs was left unverified by the checker ^[4]. But the workflow behind that clean record involved more than a model running alone: Astra generated the mathematical arguments, human mathematicians refined them into papers, and the model then converted those arguments into the Lean certificates ^[1]. Because Astra itself is not released, outside researchers can audit the certificates line by line, but they cannot rerun the model, probe its prompts, or see how many attempts preceded the ten successes that made it into the report. That gap has fueled a competing theory that has circulated online: that the real process behind the ten results looked less like an autonomous model working unsupervised and more like a team of specialists given months of extended access to the system, human and machine working in tandem rather than one replacing the other. It echoes a pattern from OpenAI's own history: an earlier claim of having solved an open problem drew public criticism from figures at rival labs, while this round has drawn a more measured response from mathematicians checking the actual certificates.

The exclusivity framing didn't survive first contact with a rival lab. Levent Alpoge, a Harvard mathematician working at Anthropic, reproduced five of the ten results within 24 hours using the publicly available Claude Fable model, a generic prompt, and no internet access ^[5]. The overlap doesn't erase Astra's achievement, but it undercuts the idea that only OpenAI's unreleased system could reach these results, and it sharpens a question raised across critiques of the release: how many failed attempts sat behind the ten problems OpenAI chose to publish.

The math results landed days after Sam Altman demoed Astra to US senators in Washington, D.C. ^[7], ahead of a planned government pre-release review that Astra is expected to be the first OpenAI model to go through ^[8]. Critics like AI researcher Gary Marcus argue the achievement is real but 'vastly oversold': math is an unusually favorable domain for AI systems because it comes with an automatic verifier (Lean) and abundant synthetic training data that most real-world science and business problems lack, so a clean sweep of ten formal proofs doesn't necessarily predict success on messier, unverifiable tasks ^[6].