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One of the central tensions in contemporary mathematics and computer science is that the P versus NP problem remains unresolved even as AI systems continue to display increasingly strong performance on difficult search-oriented tasks. In rough terms, the question asks whether problems in NP, where proposed solutions can be checked quickly, can also always be solved quickly. These are precisely the kinds of problems for which verification appears easier than search. A positive answer would make many hard search tasks uniformly tractable through reduction to a common polynomial-time solver. Current AI progress instead gives the tension new theoretical urgency by exhibiting another route to substantial search performance. If difficult search were uniformly tractable, intelligence would look far less central to the problem. Conversely, if intelligence concerns the general ability to address hard search, then uniform tractability alone becomes theoretically uninteresting as an account of intelligence. This paper argues that the relevant question is therefore not whether current systems amount to a positive resolution of P versus NP, but how progress in polynomial-time methods, such as those based on AI, can be formulated within complexity theory. It neither reduces the phenomenon loosely labeled intelligence to the existence of one universal solver nor places it outside formal complexity theory. Working within classical complexity theory, it treats NP and the polynomial hierarchy as step-by-step expansions of what polynomial-time methods can reach. In that sense, polynomial-time methods can exhibit progressively richer guided-search structure while remaining feasible in the formal sense of polynomial time.