THE MATHEMATICS OF TRANSLATION: ANALYZING LINGUISTIC STRUCTURES THROUGH MATHEMATICAL MODELS

Abstract

This study explores the intersection of mathematics and translation by investigating how mathematical models can be used to analyze and represent linguistic structures. Translation, traditionally viewed as a linguistic and cultural activity, is increasingly influenced by formal systems that allow for the objective comparison and manipulation of language. This research examines the role of mathematical tools such as formal logic, set theory, graph theory, and vector space models in representing syntax, semantics, and meaning across languages. By mapping linguistic elements onto mathematical structures, the study seeks to identify patterns, equivalences, and inconsistencies that influence translation quality and accuracy. The paper also evaluates applications in both human and machine translation, demonstrating how statistical and algebraic models contribute to the development of translation algorithms. Ultimately, the research aims to deepen the theoretical understanding of translation as a structured, rule-governed process and to highlight the potential of mathematics as a bridge between languages.