# OpenAI's Astra Solves 10 Open Math Problems With $2,000 Compute

> OpenAI says an internal model it calls Astra cracked ten previously open problems in mathematics and theoretical computer science, and did it for roughly two thousand dollars of compute. The haul reportedly includes a construction of a non-sofic group, a question that had sat open since 1999, along with fresh results in quantum complexity and lattice cryptography. What makes the claim unusually checkable is that every proof was written in Lean 4 with zero placeholder gaps, meaning a machine verified each step rather than a tired referee. The team published a 249-page manuscript and the accompanying code on GitHub so outsiders can rerun the verification themselves. That matters, because AI math claims have a habit of collapsing on inspection, and formal proofs are much harder to fake than a confident-sounding paragraph. If the results hold up under independent scrutiny, the interesting part is not any single theorem but the cost curve. Ten genuine contributions to research mathematics at hobby-project prices hints at a near future where formalized, verifiable proof search becomes a routine tool on a working mathematician's desk rather than a stunt.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: Quartz · Published Saturday, August 22, 2026_

## Wortins' read

OpenAI says an internal model it calls Astra cracked ten previously open problems in mathematics and theoretical computer science, and did it for roughly two thousand dollars of compute. The haul reportedly includes a construction of a non-sofic group, a question that had sat open since 1999, along with fresh results in quantum complexity and lattice cryptography. What makes the claim unusually checkable is that every proof was written in Lean 4 with zero placeholder gaps, meaning a machine verified each step rather than a tired referee. The team published a 249-page manuscript and the accompanying code on GitHub so outsiders can rerun the verification themselves. That matters, because AI math claims have a habit of collapsing on inspection, and formal proofs are much harder to fake than a confident-sounding paragraph. If the results hold up under independent scrutiny, the interesting part is not any single theorem but the cost curve. Ten genuine contributions to research mathematics at hobby-project prices hints at a near future where formalized, verifiable proof search becomes a routine tool on a working mathematician's desk rather than a stunt.

## Source

[Read the full story at Quartz](https://qz.com/openai-astra-model-math-problems-lean-proofs-080326)

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