In this delightfully chatty and informative book, the prolific historian of mathematics Benjamin Wardhaugh steers well away from Fermat’s last theorem, imaginary numbers and the other esoteric topics that specialists usually delight in. Instead, in a welcome and refreshing change, he examines how ordinary men and women of Georgian Britain used arithmetic and geometry for practical purposes: keeping household accounts, checking the alcohol content of beer, surveying fields, steering ships, aiming guns, or detecting dodgy ticket allocations in a lottery. All over the country, gentlemen formed societies to study astronomy, discuss the mathematical principles of musical harmony, draw up tables of logarithms, or make an optimistic bid for the Longitude Prize money (the reward offered by the British government for a simple and precise method of determining a ship’s longitude). Amazingly, handwritten documents and workbooks have survived centuries of house clearances, and Wardhaugh skilfully uses these evocative testimonies to recreate the everyday experiences that are missing from more conventional accounts.

Britain’s engineering and scientific supremacy stemmed from the practical traditions that Wardhaugh describes. Non-Anglicans, such as the country’s leading chemist, Joseph Priestley, were banned from universities but could enrol in dissenting academies, where the only permissible subjects were practical ones such as accountancy, navigation and mechanics. It was thanks to