Mathematical Precarity in the Age of Artificial Intelligence: Reconceptualizing Levels of Mathematical Thinking

Not long ago, the ability to truly understand why a mathematical truth holds — not just that it does — was a reliable sign of genuine mathematical talent. That game has changed. AI can produce sophisticated mathematical proofs and explanations on demand, without developing any of the thinking those outputs once required. My central claim is precise: AI has not, strictly speaking, broken the link between mathematical output and mathematical understanding; rather, it has decoupled them as objects of inference, so that the production of a sophisticated output is no longer reliable evidence of the cognitive development that previously produced such an output. A five-level model is proposed that describes what students are actually doing cognitively, rather than what outputs they produce — and what that distinction means for identification, curriculum, and teaching in an AI-saturated classroom.