Formal Mathematics

OpenAI published 722 manuscripts covering 372 mathematical result families from about 4,000 problems. Independent checks found that some headline claims were partial results rather than complete proofs.

Meta published six research collaborations reporting solutions to open mathematics problems with Muse Spark. Mathematicians guided the work through its regular chat interface, independently reviewed results, and marked human contributions.

OpenAI says an internal model resolved more than 100 long-standing mathematical problems, including work on the Navier–Stokes problem. OpenAI also announced an independent mathematicians' group to review emerging results, while outside discussion questioned the training and verification process.

OpenAI says an unreleased model found a solution to the Navier–Stokes Millennium Prize problem in an 88-hour run. The company says roughly 10,000 agents contributed and the result reached Lean formalization.

Anthropic says an unreleased Claude did not solve the Riemann hypothesis but improved a related zeta-zero lower bound from 41.6% to about 67.2%. Posts describe subagents, expert prompting, and Lean formalization.

OpenAI says an internal Astra model generated arguments for ten long-standing math and theoretical CS problems, with Lean 4 certificates in openai/ten-proofs. Posts focused on the reported sub-$2,000 inference cost.

Epoch said an AI-generated solution found a presentation for the absolute Galois group of the 2-adic numbers, marking the second FrontierMath open problem it says AI solved. The result was elicited with Fable 5 and also GPT-5.5 Pro, making it a benchmark milestone rather than a product release.