# OpenAI's Astra solves 10 decades-old math problems

> OpenAI says its internal Astra model has cracked ten mathematical problems that had gone unsolved for at least a decade, and it published the proofs rather than just claiming victory. The headline result is the first explicit construction of a non-sofic group, a question open since Mikhail Gromov raised it in 1999. Astra also reportedly disproved Connes's rigidity conjecture, proved Ehrhart's volume conjecture, and settled three problems posed by Paul Erdos. What separates this from earlier AI math hype is verification. Every proof ships with a machine-checkable Lean 4 certificate containing zero unproven gaps, so mathematicians can confirm the logic without trusting the model's prose. The whole run cost around 2,000 dollars in compute, a striking figure for results that human specialists chased for a generation. If the proofs hold up under community scrutiny, this is a meaningful shift in what automated reasoning can contribute to frontier mathematics. The open questions now are whether the techniques generalize beyond curated targets, and how the field credits work where a machine did the heavy lifting.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: SiliconANGLE · Published Thursday, August 20, 2026_

## Wortins' read

OpenAI says its internal Astra model has cracked ten mathematical problems that had gone unsolved for at least a decade, and it published the proofs rather than just claiming victory. The headline result is the first explicit construction of a non-sofic group, a question open since Mikhail Gromov raised it in 1999. Astra also reportedly disproved Connes's rigidity conjecture, proved Ehrhart's volume conjecture, and settled three problems posed by Paul Erdos. What separates this from earlier AI math hype is verification. Every proof ships with a machine-checkable Lean 4 certificate containing zero unproven gaps, so mathematicians can confirm the logic without trusting the model's prose. The whole run cost around 2,000 dollars in compute, a striking figure for results that human specialists chased for a generation. If the proofs hold up under community scrutiny, this is a meaningful shift in what automated reasoning can contribute to frontier mathematics. The open questions now are whether the techniques generalize beyond curated targets, and how the field credits work where a machine did the heavy lifting.

## Source

[Read the full story at SiliconANGLE](https://siliconangle.com/2026/08/02/openais-astra-solves-10-long-open-math-problems-publishes-proofs/)

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