OpenAI Solves Ten Long-Standing Math and Computer Science Problems Using Next-Gen AI
OpenAI has announced ten major advancements in mathematics and theoretical computer science, solving decade-old problems using an internal version of its next-generation model, Astra. The mathematical proofs were generated by the AI system and formally verified by human researchers using the Lean theorem prover. This breakthrough demonstrates the growing capability of AI to assist in or drive advanced scientific discovery and formal mathematical reasoning. It highlights a shift where AI is not just generating text but solving complex, long-standing theoretical problems that have stumped human mathematicians for over a decade. The total token cost to find these solutions was approximately $2,000 based on Sol API rates. The solved problems span diverse fields, including sphere packing, non-sofic groups, Connes's rigidity conjecture, and quantum parallel repetition.
## BACKGROUND
Lean is an open-source programming language and proof assistant developed to enable the formal verification of mathematical proofs and code correctness. The Cohn-Elkies threshold refers to linear programming bounds used to establish upper limits on the density of sphere packings in high dimensions. Non-sofic groups are a class of groups in group theory whose existence was a major open question until these recent constructions.