Where Does Mathematics Come From? A Structural and Signal-Based Account

Where does mathematics come from? It is often treated as a priori and universal, yet this view does not explain how mathematical structures emerge within cognitive systems. This paper proposes a signal- and structure-based account: under finite constraints, systems must differentiate, compress, and stabilize inputs, leading to the formation of stable structures. Number, form, and computation arise naturally from these processes rather than from abstract givens. Reasoning patterns such as induction, deduction, and analogy can be understood as structural overlap, extension, and path reinforcement. Mathematics operates only on already-formed structures and cannot explain generation itself, nor does it transfer uniformly across different cognitive systems. Based on this, the paper motivates the development of a new mathematical framework for modeling structure formation in cognition and AI.