The mathematics used in economics for decades may be the wrong kind

The underlying logic needs a rethink.

- Tim Harford

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 American economist 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 Isaac 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.