OpenAI's Astra model solves ten long-standing open problems in mathematics and theoretical computer science
Research publication ● Confirmed 92% confidence first seen
OpenAI used its unreleased next-generation model Astra to discover solutions to ten previously unsolved mathematical problems spanning geometry, cryptography, group theory, and complexity theory. Each solution was formalized as a machine-checkable proof in Lean 4, with the total computational cost estimated at approximately $2,000 in API tokens. The achievement demonstrates AI's capability to tackle frontier-level mathematical research, though some coverage notes that older OpenAI models could replicate several of the solutions.
Decision brief
- What changed
- OpenAI used an internal, unreleased version of its next major model to generate solutions to ten mathematics and theoretical computer science problems that had seen no progress for at least a decade, at a cost of roughly $2,000 in compute tokens per problem, and published the results with Lean 4 formal proof verifications.
- Why it matters
- This signals that frontier AI models may now be capable of contributing to unsolved technical research problems at low marginal compute cost, which has implications for how R&D-intensive organizations allocate research budgets and evaluate AI as a research tool rather than just a productivity aid. It also serves as a capability marker ahead of OpenAI's next major model release, which competitors and enterprise buyers will use to gauge readiness for advanced reasoning tasks.
- Evidence
- The claim is corroborated by OpenAI's own blog post, an independent write-up by Simon Willison, and TLDR's summary, all describing the same ten problems, the ~$2,000 per-problem token cost, and the Lean 4 formalizations; TLDR additionally names the underlying model 'Astra,' a detail not confirmed by the other two sources.
- What remains uncertain
- It is unverified whether 'Astra' is an official or accurate name for OpenAI's next major model, and the coverage does not clarify whether the ten problems were selected favorably (cherry-picked) versus representative of general model capability. There is also no independent third-party mathematical verification mentioned beyond the Lean formalizations OpenAI itself published.
- Monitor next
- Watch for independent mathematician or academic community verification of the Lean 4 proofs and any official announcement or release timeline for OpenAI's next major model.
Analytical support, not advice — assumptions and open questions stated above.