Burn the mathematics

If you want to do economics well, you at least need to be a decent mathematician. When still at high school, I was warned by my teacher that most economics faculties had one requirement: an above average grade for mathematics. Fair enough, I thought, given the fact that economics is full of equations and statistics. The mathematical approach of economics, however, has not always been the only bar in town. How then, did economics become so obsessed with mathematics? And is this obsession still justified?

Economics is a rather young science (assuming that it is indeed a science). At its inception, economics hardly included any mathematical type of reasoning. The Classical economists (such as Adam Smith, David Ricardo and John Stuart Mill) were used to the discursive way of reasoning that economic phenomena demanded, and they were skeptical about trying to quantify these kinds of phenomena. Sure, mathematical tools could be employed to clarify certain arguments. Ricardo, for example, used some simple calculations to illustrate the concept of marginal revenue. Yet these tools merely aimed to support the inherently qualitative nature of economic inquiry.

This perception started to change over the course of the 19th century. In 1871, William Stanley Jevons claimed that “all economic writers must be mathematical so far as they are scientific at all”. If economics were to become a mathematical science it needed a proper framework. The early mathematical economists turned their eyes to physics and found their framework in the metaphor of the conservation of energy. One of the first applications of this metaphor to economics was Irving Fisher’s ‘Price Machine’, where energy corresponded to utility, force was translated into marginal utility, particles resembled individuals, and so on.

Price Machine
Irving Fisher’s ‘Price Machine’ (1892)

What is interesting about this Price Machine is that it provided a quantified, physical demonstration of the price mechanism. Not only did you get a clear overview of the many interdependencies in the causation of prices, but you could actually use the machine to run experiments. Through this mechanical analogy, economists began to develop a mathematical approach to the study of economic processes.

The physics-based mathematisation of economics reached its zenith around 1900 and can best be characterised by the fearsome Tripos examinations at Cambridge University, England. This eight-day set of examinations became the ultimate standard for a British academic career in economics. They included the most bizarre and unrealistic problems, which barely had anything to do with economics. Nevertheless, mathematical techniques had become an indispensable part of the economics profession.

Alfred Marhall, who claimed second place in the Tripos examinations and became one of the world’s most famous economists, was rather skeptical about the mathematisation of economics, as the following letter to one of his Cambridge colleagues nicely illustrates:

“But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypothesis was very unlikely to be good economics: and I went more and more on the rules (1) use mathematics as a short hand language, rather than as an engine of inquiry; (2) keep to them till you have done; (3) translate into English; (4) then illustrate by examples that are important in real life; (5) burn the mathematics; (6) if you can’t succeed in four, burn three. This last I did often.”

Burn the mathematics! How ironic to read such words from one of the best mathematicians of its time. Unfortunately, his advice seems to have been entirely ignored by contemporary economists. Their physics-envy is still very much alive, which has severely degraded the contextual and detailed type of discourse that the Classical economists would have felt more comfortable with.

Calling for less mathematics is besides the point here, because the mathematisation of economics has not necessarily been a bad thing. For one, it has enabled economists to express their ideas and concepts more precisely. Economic models can sometimes help to better understand the economic factors at play in the real world. The study of macroeconomic developments like a country’s gross domestic product has also benefitted from the expansion of the mathematical toolbox.

It is imperative, however, for economists to be aware of the limitations of their models and other mathematical techniques. Essentially, economics is a social science that focusses on people making choices in certain situations. Besides measuring things like prices and volumes, economics is also about (moral) behaviour, cultural traditions and historical events. No matter how sophisticated an economist’s set of equations, it will never be able to capture the full complexity of our actions and deliberations.

Not too long ago, economists wrote detailed accounts about what caused our economic behaviour. Nowadays, you are not a real economist if you do not have a model that makes your point in less than twenty pages. Due to the persistence of their physics-envy, economists must be reminded that mathematics is a useful “short hand language, rather than an engine of inquiry”. Oh, and don’t forget to burn the mathematics.


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