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Ten advances in mathematics and theoretical computer science
OpenAI has released solutions to ten open problems in mathematics and theoretical computer science that had seen no progress for at least a decade. These results were produced by an internal version of the model Astra.
Why it matters
These findings may advance practical technologies like post-quantum cryptography and spark discussions about how AI authorship is attributed in scientific research.
The details
- The token cost to find these solutions was roughly $2,000 at Sol API rates.
- Each solution includes a Lean certificate formalization and a narration of thinking processes.
- Humans worked with the model to prepare the resulting arguments into manuscripts.
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Key connections
Astra is OpenAI's next major internal reasoning model.
Sol API is OpenAI's API tier for running models.
OpenAI owns ChatGPT for Academic Researchers
OpenAI launched the ChatGPT for Academic Researchers initiative.
Astra formalized mathematical arguments in Lean certificates.
Related events
Aug 1, 2026•30d ago
•Research BreakthroughAstra Achieves New Results on Ten Longstanding Mathematical Problems
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