The uncanny precision with which mathematics maps onto the physical cosmos remains a profound challenge for the philosophy of science. Why should abstract formalisms, cultivated within the boundary of human cognitive processes, align so flawlessly with the objective fabric of reality? This paper advances the Structural Correspondence Hypothesis (SCH), arguing that mathematics serves as an interface between mind and matter because both domains instantiate deeply related, invariant structural configurations. By synthesizing recent insights from cognitive neuroscience—specifically predictive processing and the geometry of neural manifolds—with foundational physics, including gauge theories and quantum information, we propose a category-theoretic framework to formalize these parallels. Rather than endorsing a naive reductionism, this model offers a topological and relational account of how cognitive systems adaptively mirror environmental invariants. We conclude by presenting a tentative empirical roadmap to test these structural homomorphisms, opening new avenues for artificial general intelligence (AGI) and the foundations of physics.
Hasti Moradi Motlagh (Thu,) studied this question.
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