One of the founders of neoclassical economics, William Stanley Jevons, thought that economics should be a mathematical science, and this is why, even today, most neoclassical economists use a large amount of mathematics in their work. The father of rational expectations theory, Robert Lucas, claimed, in a lecture at Trinity University in 2001, that: “Economic theory is mathematical analysis. Everything else is just talk and pictures”. Motivated, among other things, by these positions, British philosopher of science Donald Gillies wrote an interesting article on the comparison of the use of mathematics in physics and in neoclassical economics. (Sylos Labini, Francesco. Science and the Economic Crisis (Kindle Locations 1788-1793). Springer International Publishing. Kindle Edition.)

Gillies first recalled that physicists have learned to critically consider each theory within the precise limits that are dictated by the assumptions used and by the experiments available. From the times of Galileo and Newton, physicists have, therefore, learned not to confuse what is happening in the model with what instead is happening in reality. Physical models are compared with observations to prove if they are able to provide precise explanations: an example of this type is represented by the procession of the perihelion of Mercury, which we discussed in the previous chapter. Otherwise, theoretical models can provide successful predictions. For example in 1887, Hertz generated the electromagnetic waves postulated by Maxwell in 1873. The question is therefore: can one argue that the use of mathematics in neoclassical economics serves similar purposes? Otherwise, this usage is reduced to a mere rhetorical exercise, which employs the flaunted use of a relatively refined tool to precisely calculate irrelevant quantities. Gillies’s conclusion is that, while in physics mathematics was used to obtain precise explanations and successful predictions, one cannot draw the same conclusion about the use of mathematics in neoclassical economics in the last half century. This analysis reinforces the conclusion about the pseudo-scientific nature of neoclassical economics we reached previously given the systematic failure of the predictions of neoclassical economists. (Sylos Labini, Francesco. Science and the Economic Crisis (Kindle Locations 1794-1804). Springer International Publishing. Kindle Edition.)

To show this, Gillies has examined the best-known works by a selection of the most famous neoclassical economists (Paul A. Samuelson, Kenneth J. Arrow, Gerard Debreu and Edward C. Prescott) in the period from 1945 to the present. The most famous work of Samuelson is one of the classics of mathematical economics, “*Foundations of Economic Analysis*”. Gillies notes that Samuelson, in his book of over 400 pages full of mathematical formulas, does not derive a single result that can be compared with the observed data. There is even no mention of any empirical data in the book Samuelson! (Sylos Labini, Francesco. Science and the Economic Crisis (Kindle Locations 1804-1808). Springer International Publishing. Kindle Edition.)

As for the seminal work of Kenneth Arrow and Gerard Debreu, published in 1954 and previously discussed, Gillies highlights that the general equilibrium models considered by the authors are based on such simplistic assumptions of reality that they cannot be compared with the observed data. In fact, as Samuelson, they do not derive any result that can be compared with the empirical data, which are indeed absent in their work. (Sylos Labini, Francesco. Science and the Economic Crisis (Kindle Locations 1809-1812). Springer International Publishing. Kindle Edition.)

Finally, Gillies takes into account the article by Edward C. Prescott called “*The Equity Premium. A Puzzle*”, written in collaboration with Rajinish Mehra. In this article, the authors try to compare the general equilibrium model of Arrow-Debreu with theoretical data obtained from a real economy, namely the US economy in the period 1889– 1978. In this case, there is no agreement between the theoretical results and empirical data. In conclusion, neoclassical economics, unlike physics, has not achieved either precise explanations or successful predictions through the use of mathematics. Thus, this is the main difference between neoclassical economics and physics. (Sylos Labini, Francesco. Science and the Economic Crisis (Kindle Locations 1812-1817). Springer International Publishing. Kindle Edition.)