The Upward Migration of Cognitive Value: A Theory of AI-Induced Bottleneck Migration in Science with Mathematics as a Case Study

Artificial intelligence is commonly analyzed as a technology that expands scientific capability or substitutes for particular research tasks. This paper proposes a different perspective. The central effect of AI on science may lie not simply in what machines become capable of doing, but in how uneven automation changes the relative scarcity of different cognitive operations. I call the underlying mechanism \emph{differential cognitive cost compression}. When AI sharply reduces the cost of one scientific operation while complementary operations remain comparatively scarce, the bottleneck of knowledge production moves. As a result, the marginal value of scientific cognition migrates toward activities that remain constraining. When the most strongly compressed tasks are those performed within an already specified representational or theoretical framework, this relocation tends to move toward higher-order choices over problems, abstractions, representations, frameworks, interpretation, and epistemic direction. I call this process the \emph{upward migration of cognitive value}. The theory does not assume that these higher-order functions remain permanently human. If AI later compresses problem formulation or framework construction, the bottleneck can migrate again. The proposed mechanism is therefore dynamic and recursive rather than a claim about an immutable human--machine boundary. Mathematics provides an unusually clear case. Mathematical activity combines reality-grounded abstraction, formal constraints, recursive abstraction over existing formal structures, within-framework inference, and higher-order interpretation. Recent AI systems have sharply reduced the cost of increasingly sophisticated mathematical search and proof, while contemporary work already identifies problem selection and expert review as emerging bottlenecks. Tao's characterization of a transition from proof scarcity toward proof abundance captures one manifestation of this process. This paper extends that insight by arguing that value migration occurs both downstream, toward verification, explanation, integration, and canonization, and upstream, toward problem formation, abstraction, framework construction, and research direction. The framework yields testable implications for scientific organization, training, evaluation, and the design of AI research systems. More generally, it suggests that the long-run significance of AI for science may be a recursive reorganization of where epistemic scarcity resides.