The Role of Mathematical Methods in the Formation of Scientific Conceptions: Elementarity and Mathematics

This article presents a systematic philosophical and methodological analysis of the role of mathematical methods in the formation of scientific knowledge and theoretical frameworks. Particular attention is given to the concept of elementarity and its function as a fundamental methodological principle in mathematical reasoning, scientific modeling, and the construction of theoretical structures. The study argues that mathematics should not be regarded merely as a technical instrument for describing empirical phenomena, but rather as a constitutive and normative foundation of scientific thought. In addition to classical philosophical perspectives—those of Plato, Aristotle, and Kant—the article examines major developments in contemporary philosophy of science, including Hilbert’s axiomatic program, Gödel’s incompleteness theorems, and Lakatos’s theory of research programmes. Through a comparative analysis, it is demonstrated that mathematical methods provide the conditions for universality, precision, and logical coherence in the formation of scientific conceptions. It is concluded that the principle of elementarity, together with the systematic application of mathematical methods, constitutes one of the essential foundations for the rational development and methodological integrity of science.