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The role of mathematics in economic analysis is not yet a settled question. Smith, Ricardo, Mill and other eminent classical economists did not use mathematics in their economic theorizations. We have defined classical mathematical economics as the whole body of literature in mathematical treatment of economics originating mainly from the contributions of Cournot, Jevons and Walras. There are a number of different explanations for the origin of classical mathematical economics suggested by different authors, which may also explain the lack of general interests among classical economists in using mathematical methods in economic analysis. This paper attempts to examine critically the views put forward by Debreu, Cournot, Walras and von Neumann and Morgenstern on the origin of mathematics in economics. Using historical evidences through direct references to their original works, we have demonstrated that none of their views are convincing. It is also shown that the tradition of classical mathematical economics did not have any significant impact on the process of economic theorization within the framework of classical economics.

Economists were interested in economic stabilization policies as early as the 1930’s but the formal applications of stability theory from the classical control theory to economic analysis appeared in the early 1950’s when a number of control engineers actively collaborated with economists on economic stability and feedback mechanisms. The theory of optimal control resulting from the contributions of mathematicians Lev Semenovich Pontryagin and Richard Ernest Bellman in the late 1950’s was first applied successfully to models of economic growth in the 1960’s by the economists who were interested in discovering the optimality properties of economic growth trajectories. It is shown that the collaborations of control engineers with econometricians in the 1970’s on the computation of optimal state and control trajectories in econometric models were the earliest attempts to demonstrate the possibility of applying deterministic, stochastic and adaptive optimal control to the numerical solution of optimal economic policies. We have explained why the collaborations of control engineers with econometricians on formulating and computing optimum system design in macroeconomic optimal planning models failed and why the economic applications of optimal control theory have proved to be more productive in the analysis of optimality conditions in mathematical economics and not in the computation of optimal trajectories in econometric models.

We have first demonstrated that Debreu’s view regarding the publication of The Theory of Games and Economic Behavior by von Neumann and Morgenstern in 1944 as the birth of modern mathematical economics is not convincing. In this paper, we have proposed the hypothesis that the coordinated research programs in the 1930’s, initiated by the Econometric Society and the Cowles Commission for Research in Economics with the objective of unifying economic theory, mathematics and statistics, can be regarded as the beginning of modern mathematical economics as well as econometrics. We have argued that this unification has failed to satisfactorily bridge the gap between mathematical economics and the real world economic issues. However, contrary to Marshall's view that mathematics is not an engine of inquiry in economics but is only a shorthand language, we have established in this paper that the application of mathematics in modern mathematical economics can, under certain conditions, produce economic results of value.