# OpenAI announces Astra model solved 10 decades-old mathematics problems for $2,000

> OpenAI says an internal model it calls Astra resolved ten problems that had stubbornly resisted mathematicians, in some cases for decades. The headline result is the first explicit construction of a non-sofic group, a question left open since 1999, but the batch also spans high-dimensional geometry, coding theory, quantum complexity, and extremal combinatorics. What makes the claim more than a press release is verification. Every proof was formalized in Lean, a proof assistant that mechanically checks each logical step, and the results were posted to GitHub so outside researchers can confirm them independently. The company also attached a price tag, roughly $2,000 in API costs, a figure meant to show how cheap this kind of reasoning has become. If the proofs hold up under scrutiny, this is a meaningful marker, AI moving from solving known exercises to producing genuinely new mathematics that experts had failed to crack. OpenAI is pairing the announcement with free frontier-model access for 100,000 academic researchers through 2027, a bet that putting these tools in scholars' hands accelerates the next round of discoveries.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: The Next Web · Published Thursday, August 6, 2026_

## Wortins' read

OpenAI says an internal model it calls Astra resolved ten problems that had stubbornly resisted mathematicians, in some cases for decades. The headline result is the first explicit construction of a non-sofic group, a question left open since 1999, but the batch also spans high-dimensional geometry, coding theory, quantum complexity, and extremal combinatorics. What makes the claim more than a press release is verification. Every proof was formalized in Lean, a proof assistant that mechanically checks each logical step, and the results were posted to GitHub so outside researchers can confirm them independently. The company also attached a price tag, roughly $2,000 in API costs, a figure meant to show how cheap this kind of reasoning has become. If the proofs hold up under scrutiny, this is a meaningful marker, AI moving from solving known exercises to producing genuinely new mathematics that experts had failed to crack. OpenAI is pairing the announcement with free frontier-model access for 100,000 academic researchers through 2027, a bet that putting these tools in scholars' hands accelerates the next round of discoveries.

## Source

[Read the full story at The Next Web](https://thenextweb.com/news/openai-astra-model-ten-math-proofs-non-sofic-groups)

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