# OpenAI's Astra model solves 10 long-standing math problems using just $2,000 in compute

> OpenAI says an unreleased system it calls Astra has produced mathematical arguments that resolve or advance ten problems that had resisted specialists for more than a decade. The list spans high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, cryptography and extremal combinatorics, and the headline result is an explicit construction of a non-sofic group, a question left open since 1999. What makes the claim hard to wave away is the receipts. OpenAI published a 249-page manuscript with Lean 4 proof certificates, and the company says every proof checks out with zero 'sorry' placeholders, meaning the formal verifier accepted them end to end. The kicker is the price tag: the full batch of ten solutions cost roughly $2,000 in compute at current API rates. If it holds up under outside scrutiny, this is a different kind of milestone than a chatbot demo. It suggests frontier models can now do original, machine-checkable mathematics cheaply enough that the real bottleneck becomes picking the right problems, not paying for the search.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: Quartz · Published Tuesday, August 25, 2026_

## Wortins' read

OpenAI says an unreleased system it calls Astra has produced mathematical arguments that resolve or advance ten problems that had resisted specialists for more than a decade. The list spans high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, cryptography and extremal combinatorics, and the headline result is an explicit construction of a non-sofic group, a question left open since 1999. What makes the claim hard to wave away is the receipts. OpenAI published a 249-page manuscript with Lean 4 proof certificates, and the company says every proof checks out with zero 'sorry' placeholders, meaning the formal verifier accepted them end to end. The kicker is the price tag: the full batch of ten solutions cost roughly $2,000 in compute at current API rates. If it holds up under outside scrutiny, this is a different kind of milestone than a chatbot demo. It suggests frontier models can now do original, machine-checkable mathematics cheaply enough that the real bottleneck becomes picking the right problems, not paying for the search.

## Source

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

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