Ten advances in mathematics and theoretical computer science

Summary

OpenAI's internal Astra model solved ten mathematics problems that had been stagnant for years, producing formal Lean 4 proofs and a paper; spending less than $2,000 per problem.

Why it matters

These breakthroughs demonstrate that large language models can contribute to high-level mathematical research, potentially reshaping mathematicians' workflows. Making formalizations and logical traces public signals a new level of transparency in AI-assisted proofs and sparks a debate about the role of machines in creative discovery.

Highlights

• The formal Lean 4 proofs of ten-year-old problems published in the OpenAI/ten-proofs repository.
• Cost-effective solution: under $2,000 per problem at GPT‑5.6 token rates.
• Catalyzing the 'big mathematics' shift envisioned by Terence Tao, with AI taking on technically demanding tasks.

Critical take

The lack of disclosed prompts and the ambiguous success rate for unsolved problems raise questions about reproducibility and the true scope of Astra's capabilities.