OpenAI's Next-Gen Model Astra Cracks Ten Mathematical Problems for $2,000 in Compute

On August 1, OpenAI announced ten breakthroughs in mathematics and theoretical computer science, which were achieved by an internal version of its next-generation main model, Astra. According to Sol API pricing, the total cost of tokens needed to find solutions to these problems was approximately $2,000. The ten breakthroughs include upper bounds on dense sphere packing in high dimensions, improvements to binary and spherical code bounds, a proof of the existence of non-solvable Sophie groups, refutation of the Connes rigidity conjecture, new lower bounds for arithmetic circuit complexity, a quantum parallel repetition theorem, proof of polynomial-factor approximation hardness for the closest vector problem, the Ehrhart volume conjecture, super-exponential lower bounds for multicolor Ramsey numbers, and extremal number conjectures.