OpenAI's unreleased Astra model solves 10 long-standing math problems
What's the story
OpenAI has announced that its unreleased artificial intelligence (AI) model, Astra, has solved 10 long-standing mathematical problems. The problems span various fields such as cryptography, quantum computing, geometry, and graph theory. The AI-generated solutions were formalized using Lean, a software system that verifies mathematical proofs. Each proof was accompanied by reasoning narratives generated by Astra itself.
Mathematical breakthroughs
Model disproved Connes's rigidity conjecture, resolved 3 Erdos open problems
Among the problems solved by Astra are new results on high-dimensional sphere packing, binary and spherical codes, arithmetic circuit complexity, and quantum parallel repetition.
The model also disproved Connes's rigidity conjecture and resolved three open problems posed by mathematician Paul Erdos.
OpenAI estimates that generating these solutions would have cost around $2,000 using its Sol application programming interface (API) pricing.
Caution
Some researchers have urged caution
Despite these advancements in using AI for mathematical research, some researchers have urged caution. Cognitive scientist and AI researcher Gary Marcus wrote on X that while Astra is "great at math," it doesn't guarantee that broader reliability issues with generative AI have been resolved.
Peer review
Astra yet to be made publicly available
Notably, OpenAI has not yet made Astra publicly available.
The results are likely to be scrutinized by the wider mathematics community through peer review and independent verification.
This comes after OpenAI's earlier announcement in May of another unreleased model that produced a claimed disproof of Erdos unit-distance conjecture during testing.