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In case someone wants to read Boulding's essay you can find it in the Journal of Political Economy, issue 3, volume 56, from 1948. The text is also availbale from JSTOR.

A few comments on this. First of all, there is a good, though not recent article by Schwartz, 'The pernicious influence of mathematics in science' in "Logic, Methodology and Philosophy of Science" eds Nagel, Suppes and Tarski, 1962. To summarise, he argued that even in physics the maths can often obscure as much as it illuminates, and he suspected that the problem is even more intense in the social sciences. Perhaps the main reason for the success of physics, at least celestial mechanics, was less the use of maths than the incredible good fortune to have a stable and isolated system to work on, with a convenient scale, so it only took earth a year to do a circuit and not several decades a la Halley's comet.

Second, there is a fascinating book by two Italians that describes the origins and evolution of mathematic equilibrium theory in economics. There is a summary here.
http://oysterium.blogspot.com/2006/02/maths-invades-economics.html

This is an extract: In the chapter on developments in the US the authors pause in their narrative to provide an overview of four developing lines of research that can be discerned.

First, von Neuman’s decisive step towards the strongest possible mathematical approach. Developments in this line mostly employed convex analysis and fixed point theorems.

Second, the application of game theory to economic behaviour.

Third, adherence to the “ideal” Walrasian model, “the boldest and most consistent program of axiomatization, which was carried out by G Debreu and achieved the greatest successes of GET.” (259)

Fourth, Paul Samuelson’s work, which assimilated the Hicks approach but provided a more sophisticated mathematical apparatus and “a deeper understanding of physicomathematical culture.” (259)

Samuelson was a “child prodigy” in economic theory. His move from Chicago to Harvard, in his own words ‘put me right in the forefront of the three great waves of modern economics: the Keynesian revolution…the monopolistic or imperfect-competition revolution, and finally, the fruitful clarification of the analysis of economic reality resulting from the mathematical and econometric handling of the subject – including an elucidation for the first time of the welfare economic issues that had concerned economists from the days of Adam Smith and Karl Marx to the present’. (quoted on page 260)

“Samuelson’s work [during the 1930s and 1940s] marks a decided step forward in the mathematization of the discipline. It is the first treatise of economic theory in which the formal apparatus is not confined to the appendices but is one with the main argument”. (262)

Finally, Talcott Parsons thought that a closed system of equations represented the ultimate in theoretical development, even for sociology. He also spent most of his career at Harvard and I wonder if he was subjected to any direct influence from the Cowles Commission people and the Samuelson circle or whether they were all just drowning in the same current.

For a number of criticisms of the abuse of maths in economics and sources of other critical commentary, see the Appendix to Chapter 4 in Bill Hutt's book "The Keynesian Episode".

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