TECHNOLOGY

San Francisco AI model solves key math problems

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OpenAI disclosed that an internal version of its upcoming Astra model has produced Lean-verified solutions to ten previously unsolved problems in mathematics and theoretical computer science. Announced this week, the work includes a construction proving the existence of non-sofic groups and new upper bounds on sphere-packing density near the Cohn-Elkies threshold. The proofs, generated using about $2,000 of computing resources, were posted to GitHub for external verification. Fields Medalist Timothy Gowers said he would endorse at least one proof for publication. OpenAI has not announced a public release date for Astra.

Prepared by Jonathan Pierce and reviewed by editorial team.

Timeline of Events

On 1999: Mathematician Mikhail Gromov originally introduced the concept of sofic groups.
On May 2026: DeepMind released AlphaProof results solving multiple complex Erdős problems.
On July 2026: Researchers established foundational benchmarks for automated mathematical theorem proving.
On August 1, 2026 (6:00 PM EST): OpenAI publicly announced an unreleased internal model named Astra.
On August 1, 2026 (6:00 PM EST): The system solved ten decade-old open mathematics research problems.
On August 1, 2026 (6:00 PM EST): OpenAI published machine-checkable Lean 4 certificates directly on GitHub.
On August 2, 2026 (10:00 AM EST): Academic mathematicians began reviewing the released 249-page research manuscript.
In coming weeks: Independent labs will attempt to verify all Lean proof files.
In coming months: Academic journals will consider publishing the AI-generated mathematical proofs.
In coming years: Automated theorem provers will reshape foundational research across scientific disciplines.

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Track official GitHub repositories and peer reviews of Lean proofs.