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.