OpenAI announced that GPT-5.6, a version of its large language model, solved a 30-year-old open problem in convex optimization when guided by a specific prompt. The company posted the results in a technical note on its research blog. The prompt directed the model to generate an algorithmic solution that matched the mathematically proven optimum. Independent experts in optimization confirmed the correctness of the output. Convex optimization, a fundamental area of applied mathematics, underpins many engineering and economic models. A particular gap in the field, described in research literature since the early 1990s, had remained unsolved despite numerous attempts. The announcement indicated that the model’s ability to interpret and execute the prompt enabled it to produce a concise derivation that aligned with established proofs. The note included code snippets and a description of the prompt structure. Researchers not involved in the project said the result demonstrated progress toward using language models as reasoning tools in mathematics. The outcome suggests a new avenue for AI-assisted theorem proving, but the work has not yet undergone peer review, and the broader applicability of the method remains uncertain.