A math-solving AI spent two hours thinking about a single problem before correctly deciding that the answer was impossible to know.

Language models can demonstrate a form of intellectual honesty called calibrated meta-cognition when faced with unsolvable math. This specific model identified a hidden algebraic trapdoor that made a problem undecidable and chose to stay silent rather than guess. Most people expect AI to hallucinate an answer when it gets stuck, but this system recognized its own limits. This behavior mimics the way high-level human mathematicians approach problems they know are potentially flawed. It suggests that future AI systems can be trained to know when they are out of their depth, preventing confident but wrong answers in critical fields.