OpenAI's internal 'Astra' model claims ten advances on decade-old math problems

OpenAI published 'ten advances in mathematics and theoretical computer science' produced with an internal model reportedly named Astra, describing it as its 'next major model' built for complex, long-running tasks. The claimed results span sphere packing, group theory, lattice-based cryptography, geometry and complexity theory, complete with formal proofs — including a claimed first construction of a nonsofic group, a problem that had seen no progress for at least a decade. Individual solutions reportedly cost around $2,000 at current Sol API rates.

The methodology centers on long-horizon autonomous reasoning: Astra runs extended problem-solving sessions and outputs proofs formalized in Lean 4, a machine-checkable proof assistant. OpenAI explicitly framed the release as research output rather than a launched product, positioning it as evidence of a new capability threshold rather than a consumer feature.

Competitively, the claim intensifies the frontier-capability race against Anthropic's Opus line and Google's Gemini, and feeds directly into OpenAI's 'building abundant intelligence' full-stack narrative. But provenance drew immediate scrutiny: commenters noted the 37,000+ line Lean file is '100% AI-generated,' and that constructions were renamed across versions, muddying attribution. Ethan Mollick said he was waiting for a verdict from a level-headed, AI-aware math professor before celebrating.

On Reddit, r/singularity ran an 831-upvote thread on the advances and a 903-upvote post on the leaked nonsofic-group paper, while r/OpenAI's 'new threshold in AI' thread drew hundreds of comments. What to watch: independent verification by working mathematicians of whether these are genuinely novel results or sophisticated reconstructions of known techniques — the difference between a landmark and a very expensive proof-formatting exercise.