4 The Assumption of “Mathematical Structures”

Physics often treats mathematics as the language of reality itself. Equations, symmetries, and structures are interpreted as uncovering the deep order of the universe, as if the cosmos were pre-written in symbols waiting to be discovered. Mathematical forms are elevated from descriptive tools to ontological mirrors.

Yet mathematics is never observed; it is a human artefact used to model relational potential. Numbers, functions, and geometric constructs are ways of codifying patterns we detect, stabilising them through repeated construal. The “truth” of a mathematical structure lies not in the universe itself, but in its ability to capture regularities as construed from particular perspectives.

By treating mathematical structures as absolute, physics projects modulation onto modality: the relational patterns we can describe are misread as inherent decrees of reality. Equations become laws, symmetries become mandates, and structures become agents of constraint. In reality, mathematics is a tool, a lens for interpreting and organising potentialities, not a pre-existing scaffolding of the cosmos.

Recognising the relational and perspectival nature of mathematics preserves its explanatory power while correcting its ontological misplacement. The universe is not written in symbols; symbols are our means of making sense of the universe. To see the frame is to acknowledge the act of modelling as a construal, and mathematics as a lens, not a lawgiver.