# OpenAI Announces Astra Model Solves 10 Previously Unsolved Math Problems

> OpenAI says its Astra model has closed the book on ten mathematical questions that had resisted human proof for more than a decade, spanning group theory, functional analysis, combinatorics and theoretical computer science. Among the claimed results are a construction of non-sofic groups and a refutation of Connes's rigidity conjecture, the sort of problems that usually consume careers rather than compute budgets. What separates this from the usual benchmark boasting is the paper trail. OpenAI published a 249-page manuscript alongside Lean 4 proof certificates on GitHub, meaning every step can be machine-checked with no unverified hand-waving in between. The company puts the total compute bill for all ten solutions at roughly $2,000 in its GPT-5.6 Sol API rates. If the proofs hold up under scrutiny from working mathematicians, this is a meaningful shift in what these systems can do, moving from summarizing known results to generating genuinely new ones. The formal verification is the crucial detail here, because it lets the community trust the output without simply taking OpenAI's word for it.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: OpenAI · Published Friday, August 28, 2026_

## Wortins' read

OpenAI says its Astra model has closed the book on ten mathematical questions that had resisted human proof for more than a decade, spanning group theory, functional analysis, combinatorics and theoretical computer science. Among the claimed results are a construction of non-sofic groups and a refutation of Connes's rigidity conjecture, the sort of problems that usually consume careers rather than compute budgets. What separates this from the usual benchmark boasting is the paper trail. OpenAI published a 249-page manuscript alongside Lean 4 proof certificates on GitHub, meaning every step can be machine-checked with no unverified hand-waving in between. The company puts the total compute bill for all ten solutions at roughly $2,000 in its GPT-5.6 Sol API rates. If the proofs hold up under scrutiny from working mathematicians, this is a meaningful shift in what these systems can do, moving from summarizing known results to generating genuinely new ones. The formal verification is the crucial detail here, because it lets the community trust the output without simply taking OpenAI's word for it.

## Source

[Read the full story at OpenAI](https://openai.com/index/introducing-astra/)

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