Mathematics has actually been used in economic theory, perhaps even in an exaggerated manner. In any case, its use has not been highly successful. This is contrary to what one observes in other sciences...That's a quote from the top of page 3 of this edition of one of the most important economics texts of the mid-twentieth century, von Neumann and Morgenstern's Theory of Games and Economic Behaviour. It has stuck in my mind because the second part of the first sentence is one of the best examples of understated academic cattiness I've ever encountered, and it made me laugh out loud when I first read it.
The chapter in which it occurs, Formulation of the Economic Problem, is an important reference for anyone considering the question of whether or not economics is a science. In trying to apply, in the 1940s, a new branch of mathematics, Game Theory (which von Neumann, one of the most important mathematicians of the twentieth century, had begun working on in 1928) to economics the authors had first to consider whether or not such an exercise would be appropriate.
They compared economics with physics and found that there were similarities, especially between economics at the time of writing and physics of an earlier age. Economics, they felt, was still at a stage when the work of painstaking measurement and description was very incomplete; with physics that work was more advanced. They suggested that the application of mathematics to physics from the late sixteenth century on, and to other sciences at other times, helped the development of rigour in measurement and description. So might it be with economics:
The precise measurements of the quantity and quality of heat (energy and temperature) were the outcome and not the antecedents of the mathematical theory. This ought to be contrasted with the fact that the quantitative and exact notions of prices, money and the rate of interest were already developed centuries ago.So why had the application of maths to economics theory (we are not talking here about the use of statistical methods in information gathering and assimilation) been so unsuccessful up until then? The authors suggested two reasons:
... economic problems were not formulated clearly and are often stated in such vague terms as to make mathematical treatment a priori appear hopeless because it is quite uncertain what the problems really are.And:
... the empirical background of economic science is definitely inadequate. Our knowledge of the relevant facts of economics is incomparably smaller than that commanded in physics at the time when the mathematization of that subject was achieved.By the seventeenth century, there were observations, especially of astronomical phenomena, that stretched back a couple of millennia. No such record exists in economics.
To the authors of this book, economics is a science, but it is an immature one. That didn't mean that the attempt to develop a theoretical framework, as had happened in sciences like physics, chemistry and biology, was inappropriate, but it did mean that the results that could be expected initially would be likely to be modest:
It is essential to realize that economists can expect no easier fate than that which befell scientists in other disciplines. It seems reasonable to expect that they will have to take up first problems contained in the very simplest facts of economic life and try to establish theories which explain them and which really conform to rigorous scientific standards. We can have enough confidence that from then on the science of economics will grow further, gradually comprising matters of more vital importance than those with which one has to begin.1That was published in 1944. Why, then, has so little progress been made since then? Economics has not undergone the sort of structural revolution the authors thought possible.
The field covered in this book is very limited, and we approach it in this sense of modesty. We do not worry at all if the results of our study conform with views gained recently or held for a long time, for what is important is the gradual development of a theory, based on a careful analysis of the ordinary everyday interpretation of economic facts. This preliminary stage is necessarily heuristic, i.e. the phase of transition from unmathematical plausibility considerations to the formal procedure of mathematics. The theory finally obtained must be mathematically rigorous and conceptually general. Its first applications are necessarily to elementary problems where the result has never been in doubt and no theory is actually required. At this early stage the application serves to corroborate the theory. The next stage develops when the theory is applied to somewhat more complicated situations in which it may already lead to a certain extent beyond the obvious and the familiar. Here theory and applications corroborate each other mutually. Beyond this lies the field of real success: genuine prediction by theory. It is well known that all mathematized sciences have gone through these successive phases of evolution.
1 The beginning is actually of a certain significance, because the forms of exchange between a few individuals are the same as those observed on some of the most important markets of modern industry, or in the case of barter exchange between states in international trade.
The answer must be that so many people come to the field not to discover the reality of the world, but to find plausible justifications for their pre-existing political views. Economics is like an early science - alchemy, say. Too often, it combines activities that look a bit like serious work, with religion.
That's why there's a second part to this post.