An LLM found 10 new circle-packing records for $28
The model did not solve the packing problem directly. It repeatedly rewrote the optimizer, checked each candidate with an independent verifier, and kept only genuine improvements. In 15 iterations, that loop beat Packomania's best-known solutions for 10 values of N from 101 to 114, with gains of 2.4% to 5.4%, at a total LLM cost of $27.72. The interesting shift is from asking AI for an answer to using it as a cheap search operator for algorithms.