Mathematics Serving Economics: A Historical Review of Mathematical Methods in Economics

Abstract

This paper offers a historical review of the evolution of mathematical methods in economics, tracing their development from the earliest attempts in the 18th century to the sophisticated models of the late 20th century. The study begins by examining the initial integration of mathematical techniques into economic thought, highlighting key milestones that shaped the field. Symmetry concepts are naturally embedded in many of these mathematical frameworks, particularly in the balance and equilibrium found in economic models. Symmetry in economics often reflects proportional relationships and equilibrium conditions that are central to both micro- and macroeconomic analyses. Then, the paper elaborates on the progression of economic growth models, including the foundational Solow–Swan model, which introduced the concept of technological progress (knowledge) as a key factor influencing growth. The review also encompasses the Lucas growth model and the Mankiw–Romer–Weil model, both of which incorporate human capital into the growth equation, highlighting its importance in driving economic development. Finally, the paper addresses the Nonneman–Vanhoudt model, which extends the analysis of growth by integrating multiple types of capital, providing a more comprehensive framework for understanding economic dynamics. By documenting these developments, the paper demonstrates the significant role that mathematical modeling has played in advancing economic theory, providing tools to quantitatively analyze complex economic phenomena and driving the discipline towards greater analytical precision and rigor. This analysis emphasizes how symmetry principles, such as balance between inputs and outputs, equilibrium in supply and demand, and proportionality in growth models, underpin many economic theories.