- OpenAI's next major model Astra has successfully solved major math problems and published a page and PDF detailing ten advances across pure math and theoretical computer science.
- The release includes 10 Astra proofs with Lean certificates and chain-of-thought (CoT) walkthroughs.
- The arguments were generated by an internal version of Astra at a total compute cost of about $2,000 using Sol API rates.
- Humans then turned the core ideas into manuscripts with model assistance.
- OpenAI describes the output as “genuine research-level discoveries” with machine-checkable Lean certificates, demonstrating AI's role as a collaborator in producing novel proofs.
- Additional advances include a Connes rigidity counterexample in von Neumann algebras / II factors and sharper bounds in packing/coding, circuit, lattice, Ramsey, and extremal-graph problems.
- The packing/coding, circuit, lattice, Ramsey, and extremal-graph results give sharper quantitative bounds or settle specific Erdős-type questions.
- This accelerates progress, provides new tools/examples for human mathematicians, and demonstrates AI as a collaborator capable of generating novel proofs across distant fields.
OpenAI's Astra model has made waves in the mathematical community by solving ten significant problems, including the long-standing question of whether every countable discrete group is sofic, which remained open for nearly 27 years.
Sebastien Bubeck of OpenAI highlighted that Astra has produced "many new beautiful results," including proofs that are accompanied by Lean certificates and CoT walkthroughs.
The results span various fields, from rigidity theory for von Neumann algebras to sharper quantitative bounds on Erdős-type questions.
The total compute cost for generating these arguments was approximately $2,000 at OpenAI's Sol API rates, demonstrating the model's efficiency.3
The collaboration between humans and Astra has led to the transformation of core ideas into manuscripts, showcasing the model's ability to assist in genuine research-level discoveries.
This advancement not only accelerates mathematical progress but also provides new tools and examples for human mathematicians, illustrating AI's potential as a collaborator in generating novel proofs across diverse fields.
“The proofs were generated by an internal version of Astra at a total compute cost of about $2,000 using Sol API rates, and humans then turned the core ideas into manuscripts. The advances also include a Connes rigidity counterexample and sharper bounds in packing/coding, circuit, lattice, Ramsey and extremal-graph problems.”
