Overview of the Physics–Mathematics Transformation

The Physics–Mathematics Transformation (PMT) is a proposed conceptual framework for investigating whether explicitly defined, restricted structural correspondences between physical and mathematical systems can support scientific discovery in either direction. This overview introduces its motivation, central hypothesis, methodological principles, and five-paper research program. It distinguishes mathematical representation from physical realization and emphasizes admissible domains, preservation of relevant structure, information loss, realizability constraints, and independent validation. Mathematics-to-physics inferences require justified interpretation and empirical assessment; physics-to-mathematics investigations may suggest conjectures or constructions, but exact mathematical claims require proof or rigorous verification. The research series examines the conceptual framework, passive analog networks, mathematical operations and physical interactions, emergence and unification, and prediction-error attainability in passive model reduction. The overview distinguishes established analytical results from numerical and computer-assisted evidence requiring further validation. PMT remains a proposed research methodology, rather than an established universal transformation or a new physical law.