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Conventions of generality and mathematical elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity and literary vagueness... It may well be that the slovenly and literary borderland between economics and sociology will be the most fruitful building ground during the years to come and that mathematical economics will remain too flawless in its perfection to be very fruitful.
--
Boulding (1948) "Samuelson's Foundations: The Role of Mathematics in Economics," In: Journal of Political Economy, Vol 56 (June). as cited in: Peter J. Boettke (1998) "James M. Buchanan and the Rebirth of Political Economy". Boettke further explains "Boulding's words are even more telling today than they were then as we have seen the fruits of the formalist revolution in economic theory and how it has cut economics off from the social theoretic discourse on the human condition."

 

Kenneth Boulding

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If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.

 

George Dantzig

 

Allow me to define more specifically the inherent limitations of our numerical knowledge which are so often overlooked. I want to do this to avoid giving the impression that I generally reject the mathematical method in economics. I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation. We could scarcely have achieved that comprehensive picture of the mutual interdependencies of the different events in a market without this algebraic technique. It has led to the illusion, however, that we can use this technique for the determination and prediction of the numerical values of those magnitudes; and this has led to a vain search for quantitative or numerical constants.

 

Friedrich Hayek

 

[In] economics... you can disguise charlatanism under the weight of equations and nobody can catch you since there is no such thing as a controlled experiment. Now the spirit of such methods, called scientism by its detractors, continued into the discipline of finance as a few technicians thought their mathematical knowledge could lead them to understand markets. The practice of financial engineering came along with massive doses of pseudoscience. (page 115)

 

Nassim Nicholas Taleb

 

It is clear that economics, if it is to be a science at all, must be a mathematical science.

 

William Stanley Jevons

 

I have been accused of being ignorant of economics (although I am the founder and Chairman of the Board of a company which publishes seven professional economic newsletters), of being ignorant of sociology (although I am trained in sociology and was C. Wright Mills' research assistant at Columbia), of being unable to use statistics (although I earned my living as a professional statistician for five years) and of ignoring political factors (although all my graduate training was in political science).

 

Lloyd deMause