On the use of mathematics in economics

6 Jan, 2020 at 13:54 | Posted in Economics | 4 Comments

Balliol Croft, Cambridge
27. ii. 06
My dear Bowley,

I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses 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 4, burn 3. This last I did often …

Your emptyhandedly,

Alfred Marshall

As social researchers, we should never equate science with mathematics and statistical calculation. All science entail human judgement, and using mathematical and statistical models don’t relieve us of that necessity. They are no substitutes for doing real science.

amathMathematics is one valuable tool among other valuable tools for understanding and explaining things in economics.

What is, however, totally wrong, are the utterly simplistic beliefs that

• “math is the only valid tool”

• “math is always and everywhere self-evidently applicable”

• “math is all that really counts”

• “if it’s not in math, it’s not really economics”

And in case you — still — think this critique is some odd outcome of heterodox idiosyncrasy, well, maybe you should think twice …

einsteinIn mathematics, the deductive-axiomatic method has worked just fine. But science is not mathematics. Conflating those two domains of knowledge has been one of the most fundamental mistakes made in modern economics. Applying it to real-world open systems immediately proves it to be excessively narrow and hopelessly irrelevant. Both the confirmatory and explanatory ilk of hypothetico-deductive reasoning fails since there is no way you can relevantly analyze confirmation or explanation as a purely logical relation between hypothesis and evidence or between law-like rules and explananda. In science, we argue and try to substantiate our beliefs and hypotheses with reliable evidence. Propositional and predicate deductive logic, on the other hand, is not about reliability, but the validity of conclusions given that premises are true.


  1. My reading of recent analysis of findings in archeo-economics concerning Mesopotamia (ca 5000 to 2000 BC) has led me to think that mathematics in the beginning was an ideological – false thinking – motivating tool. It was first used in bookkeeping but later used to extract and privatize surplus from the working population. The (for that time) very advanced methods for computing interest rates must have been a sort of irrefutable argument. Just like econometrics are used today.

    • I would be very interested in seeing the archeo-economics sources. When I started my studies in economics I searched my library on Mesopotamia and the Hittites, and did a post on Dumuzid and Enkimdu.

      • One of the papers I have read on the question analyses the text on a clay cone in which compound interest was computed and the result used as a casus belli, reason for war. https://arxiv.org/ftp/arxiv/papers/1510/1510.00330.pdf The text in Your post seems to me to describe representatives for the new class of sedentary farmers and the new/old class of hunters which had been transformed to shepherds. Some historians think that the population in the cities was moving back and forth between city life and older economics depending on pests in the cities and crop failure in the countryside and such. The big change was the creation of the two non farming/hunter-collector classes, the administrators (priests/kings) and the private enterprisers, traders and ursurers. And as a mirror to those the inside – outside contradiction, where the outside were bandits/rebels, robbing cities of their concentrated wealth. (Against the Grain, James C. Scott)

  2. The other problem with believing it “because it’s mathematics” is that, as far as I know, mathematics has purposely set out to contain everything that fits within a particular logical style. If you want a geometry, for instance, there are at least three classical ones (Euclidean being one) — and including geometries off in the direction of topology might get you hundreds more. So unless you have a sensible reason for choosing the mathematics you choose, any fanciful thing at all might be your result.

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