Mathematical Economics History

The history of mathematical economics is reexamined carefully from the point of view of a historian of mathematics in the dissertation. By making full use of the research method and research results of the history of mathematics, the author has succeeded in obtaining a series of new results while correcting some wide-spread wrong opinions. 1.As to the periodization of the history of mathematical economics, the author suggested a new periodization after pointing out the shortcomings of a traditional periodization method which employs concrete mathematical tools as its main criterion. According to the methodological tendencies that most mainstream mathematical economists have, the author divides the whole history of mathematical economics into three major periods. The first one is called the prehistory period and it began from the Aristotle period and ended in 1838; The second one is called the first period of algorithm tendency, with calculus as its typical mathematical tool, this period began in 1838 and ended in 1937; The third period is called the period of axiomatic mathematical economics, it began in 1937 and lasts up to now.2.In order to determine the origin of mathematical economics before Cournot, the author has compared the achievements of John Graunt, William Petty, Giovanni Ceva and Daniel Bernoulli. The main conclusion of the comparison is that: (1)Although Petty is the first person who has made great contributions to the application of mathematics in economics, he restricted himself in the field of econometrics.(2)Ceva advocated enthusiastically the methodology of mathematical economics but he did little practical work.(3)It is Daniel Bernoulli who made the first outstanding contribution to mathematical economics. Furthermore, the author connects the origin of mathematical economics and econometrics with two different Greek mathematical traditions, i.e. the geometry tradition and the logistica tradition respectively.3.Cournot's work is among the most intensively studied area in the history of mathematical economics. The author puts forward some creative ideas even here. It is showed that Cournot's work marked the first convergence of econometrics and mathematical economics. However, the author discovered one more logical defect of Cournot's work, that is, Cournot failed to realize an aggregate demand function could neither be continuous nor stable at high price field when it is formed from individual demand functions. 4.It is an important as well as a disturbing question in the history of mathematical economics that why the works of most early authors of mathematical economics were generally ignored by the contemporary economics community. The author answers this question satisfactorily for the first time by considering the history of mathematical economics in relation to the history of mathematics. According to the author the lack of a sound foundation of calculus before the arithmetization of analysis is one of the main barriers for the economists to accept higher mathematics as a useful analysis tool. This conclusion also gives light to the question why the marginal revolution bursts out around 1870 and this conclusion improves greatly the 1982 Nobel laureate George Stigler's answer to the same question.5.Some important arguments on the axiomatization of economics are found in the essays or notes of David Hilbert, therefore Hilbert is supposed to have made direct contributions to the axiomatization of mathematical economics. The whole progress of axiomatic mathematical economics from its rise to its prosperity is carefully examined and the historical accomplishments of the Vienna mathematical Colloquium led by Karl Menger is acknowledged. It is argued that the major contributions of Cassel and Hicks in mathematical economics lie in the fact that they spread the general equilibrium theory in German-speaking and English-speaking countries. A reasonable explanation of Weintraub's conundrum is found which asserts that Schlesinger returned to Walras' tradition rather than he created a tr...