# OpenAI's Astra Model Solves 10 Long-Open Math Problems

> OpenAI is claiming a milestone that would have sounded like science fiction a year ago: its Astra model reportedly cracked ten math problems that had gone unsolved for years, including a non-sofic group construction that had been open since 1999. The results were not just asserted but formalized. OpenAI published a 249 page manuscript with proofs written in Lean 4, the machine checkable proof language, and says every step verified cleanly with zero placeholder gaps. The detail that will make researchers sit up is the cost. OpenAI puts the total compute bill at roughly 2,000 dollars at current API rates, which reframes automated theorem proving from a moonshot into something a well funded lab could run on a whim. If the proofs hold up under scrutiny from human mathematicians, it is a concrete sign that frontier models have moved from imitating reasoning to producing genuinely new, checkable mathematics. The caveat is that formal verification confirms the logic is sound, not that the problems were as hard or as open as billed. Expect the math community to spend the coming weeks pressure testing exactly that.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: SiliconANGLE · Published Wednesday, August 19, 2026_

## Wortins' read

OpenAI is claiming a milestone that would have sounded like science fiction a year ago: its Astra model reportedly cracked ten math problems that had gone unsolved for years, including a non-sofic group construction that had been open since 1999. The results were not just asserted but formalized. OpenAI published a 249 page manuscript with proofs written in Lean 4, the machine checkable proof language, and says every step verified cleanly with zero placeholder gaps. The detail that will make researchers sit up is the cost. OpenAI puts the total compute bill at roughly 2,000 dollars at current API rates, which reframes automated theorem proving from a moonshot into something a well funded lab could run on a whim. If the proofs hold up under scrutiny from human mathematicians, it is a concrete sign that frontier models have moved from imitating reasoning to producing genuinely new, checkable mathematics. The caveat is that formal verification confirms the logic is sound, not that the problems were as hard or as open as billed. Expect the math community to spend the coming weeks pressure testing exactly that.

## 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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