OpenAI's GPT-5.6 Sol Ultra Proves 50-Year Mathematical Problem in One Hour

OpenAI claims its latest AI model GPT-5.6 Sol Ultra has proved a 50-year graph theory conjecture in under an hour, drawing significant attention from mathematicians. On December 12, Ethan Knight, an OpenAI researcher, revealed that the GPT-5.6 Sol Ultra model proved the 'Cycle Double Cover Conjecture,' a major unresolved problem in graph theory, through a published paper and prompt. The conjecture, independently proposed by George Szekeres in 1973 and Paul Seymour in 1979, asks whether every bridgeless graph has a set of cycles covering each edge exactly twice. Graph theory, which models networks as points and lines, underpins analyses of communication networks, transportation systems, and power grids. Knight noted that the model, released just 24 hours earlier, used 64 sub-agents to solve the problem in under an hour. The system employed adversarial agents to scrutinize potential counterexamples and logical errors, with no internet searches allowed and partial proofs disallowed. The proof reduced the problem to cubic graphs and utilized the 8-flow theorem with GF(3) basis labeling.