Zoologica Mathematica: Proposing a Formal Mathematical Framework for Zoological Science

Abstract

Zoology has historically relied on descriptive, experimental, and statistical approaches to investigate animal form, function, behavior, and ecological interactions. While mathematics is frequently employed as a supporting tool in zoological research, it has seldom been treated as a foundational language for expressing zoological principles. This paper proposes Zoologica Mathematica, herein referred to as Zoothematics, as a new sub-discipline of zoology that formally integrates mathematical structures into zoological theory. Zoothematics emphasizes the use of geometry, topology, dynamical systems, game theory, graph theory, and quantitative modeling to represent and analyze animal morphology, physiology, behavior, and ecological relationships. Unlike biostatistics or mathematical biology, which primarily apply mathematics post hoc, this proposed field treats mathematical formulation as an intrinsic component of zoological understanding. The paper outlines the conceptual rationale, scope, methodological framework, and potential applications of Zoothematics, positioning it as a foundational step toward predictive, integrative, and theory-driven zoological sciences.