The first term of my master’s degree in economics was an alarming experience. The econometrics was bewildering. The macroeconomics was even more mysterious. Everything was drenched in incomprehensible mathematics — or, to be more honest, maths that I could not comprehend.
Most worrying of all was the microeconomics: this was a subject that had felt so natural and so enjoyable as an undergraduate, but now, it, too, had retreated into an austere stronghold of calculus. Some relief came with a lecture on Kenneth Arrow’s general possibility theorem, which relies on a different type of mathematics: formal logic.
Why had economists become so enamoured of mathematics — and was any of it useful?
It may be worth winding the clock back to 1960, when the physicist Eugene Wigner published an article with the title “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. Physics and mathematics had been bedfellows for so long that their partnership seemed inevitable, but Wigner took a step back and asked why.
Take Newton’s law of gravity. Wigner noted that it was based on some commonalities between the orbit of the moon and the parabolic path a stone takes when hurled through the air. Scientists could observe cannonballs dropped from the Tower of Pisa all they liked, but lacking vacuum chambers, stop-motion photography and precise clocks, all their observations were inevitably vague. And yet based on “a single, and at that time very approximate, numerical coincidence” Newton constructed a mathematical law of great precision and generality.
Wigner’s next example was the application of matrix algebra in quantum mechanics. It proved successful, despite the fact that the mathematicians who developed matrix algebra had done so long before the scientific ideas in question had arisen. Time and again, purely mathematical ideas were unleashed upon the natural sciences and, against any reasonable expectation, had conquered all.
Wigner’s essay was influential and widely emulated. One author flipped the title to explore the unreasonable effectiveness of physics in mathematics. The era of Big Data was heralded by three researchers at Google with their article “The Unreasonable Effectiveness of Data”. Economist Vela Velupillai took a swipe at mathematical economics with “The Unreasonable Ineffectiveness of Mathematics in Economics”.
Velupillai’s piece made a surprising attack. Instead of the usual criticism that economics uses unrealistic assumptions, he focused on some of the deep foundations of the most complex theorems in mathematical economics. Velupillai argued that those foundations were built on disputed mathematical territory, and so the proofs were mathematically unsound.
I’m not enough of a mathematician to adjudicate, but I certainly agree with Velupillai this far: if mathematics is to be useful in economics, much depends on choosing the right kind of mathematics. The formal logic I loved so much delivers some delightful insights about the nature of infinity, or whether we can ever coherently talk about “what society prefers” rather than the preference of an individual. But I’m not sure how useful it is for practical policy.
(I have some evidence for this. More than three decades ago, I had the privilege of taking a term of formal logic tutorials with Liz Truss as my tutorial partner. She seemed to acquire a reasonable grasp of Peano arithmetic and Cantor’s diagonalisation argument, and yet somehow these insights did not spare her — or us — from an economic train-wreck. We have just passed the third anniversary of Liz Truss becoming the prime minister, meaning the third anniversary of her no longer being prime minister will be on us before we know it.)
Mainstream economics continues to rely on what we might call Newtonian mathematics: using calculus to optimise, subject to constraints. What is the most profitable combination of price and output for a manufacturer? Which basket of goods maximises consumer utility while staying within a budget?
All useful enough, and yet not really suited to understanding the behaviour of macroeconomic cycles, or weak points in a financial system, or how consumers are persuaded to act against their own interests by sleazy app-designers and conmen.
A variety of alternatives have emerged. Behavioural economists favour a more psychologically realistic description of human behaviour. This is obviously appealing, but the problem is that psychologically realistic humans are not mathematically predictable. Behavioural public-policy wonks thus have to resort to testing promising ideas to see what works. The mathematics required for these experiments was developed by statistician Ronald Fisher and (sadly less famous) the head brewer of Guinness, William Sealy Gosset. The cheerful Gosset was a man who well understood the power of small but rigorous experiments.
I am all in favour of this experimental approach, but we need to be realistic about what can be achieved. Behavioural economics can tell us a bit about the psychology of bubbles, but rather less about why the bursting of the dotcom bubble was mostly confined to the stock market, while the US housing bubble of a few years later developed into the largest financial crisis for decades. That’s not a question about the madness of crowds, but about the deep structure of financial markets. Recommended James Fergusson What are the limits of the AI mathematician?
Another approach, then, is to introduce ideas of economic complexity, borrowing mathematical tools from ecology and late 20th-century physics, used to study networks, chaotic systems and emergent behaviour. Over the years this column has described insights from complexity science ranging from the economics of solar panels to how to prevent a housing bubble.
All this suggests that maybe the problem economics faces isn’t that it is too mathematical, but that the mathematics it has used for decades — one heavily based on classical physics — is needlessly narrow.
A modern economy can be studied in many ways. Historians, anthropologists and even psychiatrists might have something useful to say. But let’s not turn our backs on mathematics. As long as we are broad-minded about what kind of maths might help, and as long as we don’t expect maths to be as unreasonably effective as it is in physics, the mathematicians might still have something to teach us.
Written for and first published in the Financial Times on 25 Sep 2025.
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