## Mathematical Representation in Economics and Finance: Philosophical Preference, Mathematical Simplicity, and Empirical Relevance

**Abstract** As Keynes pointed out, classical economics was similar to Euclidean geometry, but the reality is non-Euclidean. Now we have abundant evidence that market movements are nonlinear, non-equilibrium, and economic behavior is collective in nature. But mainstream economics and econometrics are still dominated by linear, equilibrium models of representative agent. A critical issue in economics is the selection criteria among competing math models. Economists may choose the preferred math representation by philosophical preference; or by mathematical beauty or computational simplicity. From historical lessons in physics, we choose the proper math by its empirical relevance, even at the costs of increasing mathematical dimensionality and computational complexity. Math representations can be judged by empirical features and historical implications. Recent historical events of financial crisis reveal the comparative advantage of the advanced math representation. Technology progress facilitates future advancements in mathematical representation and philosophical change in economic thinking.

Mathematical Representation in Economics and Finance Philosophical Preference Mathematical Simplicity and Empirical Relevance