- OpenAI's unreleased Astra model solved ten major open mathematics problems, including high-dimensional sphere packing, binary codes, non-sofic groups, Connes's rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, closest vector problem, Ehrhart's volume conjecture, multicolor Ramsey numbers, and extremal number conjectures.
- The results were achieved at a cost of roughly $2,000 in compute using an internal version of Astra, with Lean formalizations and human-prepared manuscripts.
- Some of these problems were also solvable by earlier models like Sol and Fable when pointed to the specific questions, indicating a degree of 'mathematical proofs overhang'.
- The achievement is considered a major step for scientific reasoning, though not yet AGI, and has sparked discussions about the future of mathematics, human roles, and the potential for recursive self-improvement in AI.
- Reactions from mathematicians range from awe and excitement to concern about deskilling, understanding proofs, and the pace of progress outpacing human ability to digest.
- The results shift expectations for AI capabilities, suggesting faster timelines and broader automation of intellectual work, particularly in verifiable domains.