According to the maths professor Jordan Ellenberg, geometry is not simply the branch of his science that deals with shapes, angles and space, but a defining rule of life. The word “geometry”, he points out, comes from the Greek and means “measuring the world”. So, he says, geometry underlies all the world’s big concepts – “information, biology, strategy, democracy” and a host of others too. In this fat and breezy book, as liberally spattered with hand-drawn diagrams as the prose is with exclamation marks, he shows that geometry has become increasingly important. Scratch the surface of artificial intelligence, the spread of Covid, finance, the American political system and gerrymandering, and modern fact checkers, and you will find geometry driving their processes. Ellenberg’s frame of reference is impressively wide – Noah, Wordsworth, Spinoza and Hobbes all appear, as well as Euclid and his scientific heirs – and he loves an anecdote and chooses explanatory examples, such as chess-playing computers and Google, carefully. Non-mathematically inclined readers will still need to keep their wits about them but Ellenberg, in both his arguments and his enthusiasm, is persuasive.
By Michael Prodger
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