# OpenAI's Unreleased Astra Model Solved Ten Decades-Old Math Problems for About $2,000

The model, which OpenAI has not yet released and has not confirmed will ship as GPT-6, produced fully machine-verified proofs across group theory, cryptography, and combinatorics, according to a 249-page manuscript posted August 1.

- Published: 2026-08-07T14:43:44.448Z
- Canonical: https://polylog.news/ai/2026-08-07/openai-s-unreleased-astra-model-solved-ten-decades-old-math
- Publisher: Polylog (AI desk)
- Section: tech
- Sources: [Polylog editors](https://polylog.news)

OpenAI has not released its next major model, code-named Astra, and has not said whether it will ship under the GPT-6 label or as another point release. But the company used Astra on August 1 to produce a striking demonstration: solutions to ten open problems in mathematics and theoretical computer science that had each gone unsolved for at least a decade, according to [Forbes](https://www.forbes.com/sites/jonmarkman/2026/08/03/openais-astra-solved-10-decades-old-math-problems-for-just-2000/) and [the-decoder](https://the-decoder.com/openai-announces-its-next-major-model-astra-by-dropping-ten-previously-unsolved-math-solutions/).

The results span group theory, high-dimensional geometry, coding theory, quantum complexity, lattice cryptography, and extremal combinatorics. Among the more notable: an explicit construction of a non-sofic group, closing a question that had been open since mathematician Mikhail Gromov defined the concept of soficity in 1999. Other results include a disproof of Connes's rigidity conjecture on von Neumann algebras, a proof of Ehrhart's volume conjecture, and solutions to three problems from mathematician Paul Erdős's catalog, including problem 183 on multicolor Ramsey numbers.

OpenAI published a 249-page manuscript along with Lean 4 proof certificates, files checked by a formal proof-verification program, on GitHub under an Apache 2.0 license. According to [thezvi's analysis](https://thezvi.substack.com/p/openais-astra-solves), the repository's automated "sorry" count, which flags unverified proof steps, is zero across all ten formalized results. That means the proofs check out mechanically rather than resting on Astra's own unverified assertions. OpenAI said the total inference cost across all ten solutions was roughly $2,000 at GPT-5.6 Sol's API rates. Sam Altman, OpenAI's chief executive, reportedly gave US lawmakers and regulators a private Astra demonstration in Washington in late July, ahead of the public math release.

## What this means

Machine-checked proofs remove the usual objection to AI math claims, that a model merely produced plausible-looking but unverified text, so the result is harder to dismiss as an unverified or overstated claim than prior "AI solves math" announcements. It also signals that OpenAI is building Astra's launch narrative around verifiable scientific output rather than benchmark percentages, a framing that pressures Google DeepMind and Anthropic to counter with similarly checkable claims rather than leaderboard scores alone.

## What to watch

- Whether independent mathematicians confirm the proofs hold up to scrutiny beyond the automated Lean 4 checker. Formal verification confirms internal logical consistency, not that Astra's approach generalizes beyond these ten specific problems.
- Whether OpenAI sets a release date or confirms the GPT-6 label for Astra. That would convert a research demonstration into a competitive product move that rivals must respond to on a timeline.