Mathematics in the Humanities and Social Sciences: A Comprehensive Overview

This paper presents a comprehensive overview of the role of mathematics in the humanities and social sciences, highlighting its growing importance in understanding complex human, social, and cultural phenomena. With the emergence of computational humanities and computational social sciences, mathematical methods such as statistical modelling, network analysis, game theory, and formal simulations have become integral to interdisciplinary research. The study examines core quantitative and computational approaches used across disciplines including economics, sociology, psychology, linguistics, history, archaeology, and digital humanities. It further explores advanced mathematical frameworks such as topological data analysis, information theory, differential equations, and Fourier analysis, demonstrating their applicability in analysing social dynamics, cultural patterns, communication systems, and historical processes. While emphasizing the strengths of mathematical precision, scalability, and predictive capability, the paper also critically discusses challenges related to data complexity, model assumptions, and the distinction between correlation and causation. The study concludes that mathematics does not replace qualitative and interpretive traditions but powerfully complements them, enabling richer, data-driven insights into human behaviour and social structures. The interdisciplinary integration of mathematics is thus positioned as a transformative force shaping the future of humanities and social science research.