The True Role of Mathematics in Physics

During the development of modern physics, the status of mathematical tools has been continuously elevated, and many studies have reversed the primary and secondary relationship between mathematics and physics. The ontology of physics refers to the operating mechanisms that objectively exist in the real world. Physics is essentially human reflection of objective reality. Its fundamental foundation lies in the real world, phenomenon observation and repeatable experimental data, and it cannot be arbitrarily constructed through human subjective imagination. Natural language and mathematics both serve as expression carriers for physics, each with distinct boundaries of division of labour. Natural language is suitable for elaborating underlying physical mechanisms, causal chains, material structures and interaction logics. For quantitative accounting contents such as total quantity, income and expenditure, proportion and magnitude change involved in conservation of energy, ordinary natural language can hardly provide clear description, and mathematics has to be adopted for expression and calculation. Mathematics is merely a tool for handling quantitative conservation relations. It cannot create physical mechanisms out of thin air, nor can it determine the operating rules of the universe. Some theoretical studies show a tendency to construct physical pictures through pure mathematical deduction and subjective hypothesis without relying on observation and experiment. When people mistake tools for entities, construct physical interpretations in reverse based on mathematical equations, and judge the authenticity of objective mechanisms by the degree of self consistency of equations, the dislocation phenomenon occurs where mathematics dominates physics, and theoretical models disconnected from reality will be produced in the end. This paper clarifies the non confusable primarysecondary relationship between ontology and expression carriers, and reaffirms the fundamental principle that physics must be rooted in observational facts and experimental data.