Machine Translation and Mathematics: From Thought to System

Abstract

The graduate course Text Information Processing and Machine Translation at Northeastern University serves as a core component of the computer science curriculum. In recent years, the course has increasingly emphasized the centrality of mathematical thinking to the understanding and advancement of machine translation. This paper, the second in the Mathematics and Machine Translation series, examines the intricate and multidimensional interrelations between mathematics and machine translation from both educational and theoretical perspectives. This paper contends that mathematics functions not merely as a technical instrument but as an epistemological foundation for machine translation, shaping its development across multiple dimensions: cognitive paradigms, symbolic representation, historical trajectories, innovative methodologies, and systematic architectures. By tracing how mathematical reasoning has informed the evolution of translation paradigms, from rule-based frameworks to neural network models, and by analyzing the synergistic roles of linear algebra, calculus, and probability theory, we demonstrate that cultivating deep mathematical literacy is essential for sustained innovation in machine translation research and pedagogy.