Shape by Jordan Ellenberg
Allen Lane, 480pp, £20
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
The Triumph of Nancy Reagan by Karen Tumulty
Simon & Schuster, 672pp, £25
Whatever you think of Ronald Reagan, his was a transformative presidency, and his wife was, as the Washington Post political columnist Karen Tumulty puts it in her introduction to her biography of the former first lady, “the only person in the world to whom the president was truly close… Nancy rarely stepped foot in the West Wing, but her presence was felt by everyone who worked there.” Every first lady arguably shapes history. But while some political spouses – such as Abigail Adams and Eleanor Roosevelt – are remarkable for their independence, what distinguishes Nancy Reagan is how tied she was to her husband (indeed, she said her life only truly began once she met him). Those who wanted to get close to Ronald Reagan had to go through her; his big ideas, such as meeting Mikhail Gorbachev, the then-president of the Soviet Union, was first approved by her too. One imagines Nancy Reagan would be a particularly challenging subject for a biographer, as her life clearly revolved around someone else’s accomplishments. But Tumulty achieves this difficult feat, offering a richly detailed, highly researched work that is sympathetic but never hagiographic.
By Emily Tamkin
Heaven by Mieko Kawakami trs Sam Bett and David Boyd
Picador, 176pp, £14.99
The second novel to appear in English by the bestselling Japanese author Mieko Kawakami is tauter and even more perceptive than its predecessor. Breasts and Eggs, which caused a small sensation upon its publication in the UK and US last year, was a fierce yet thoughtful tale of working-class womanhood. Heaven is less than half the length and holds double the emotional force. Its protagonist is a quiet 14-year-old schoolboy who we know only as “Eyes”, the nickname a group of cruel bullies give him on account of his lazy eye. His school days are full of their calculated torment. Then he forms a friendship with Kojima, a girl in his class who is also targeted by the bullies. The pair begin meeting in secret, their shared bond based on a deep understanding of what it is to suffer in silence. As the violence and humiliation they are subjected to grows more distressing – one day after school, “Eyes” is used as the ball in a game of “human soccer”– the meaning of their surrender to terror grows more complicated, and Kawakami’s talent at articulating the moral conundrum of their situation becomes ever clearer. “If we’re weak, our weakness has real meaning,” says Kojima. “We may be weak, but we get it. We know what’s important, and we know what’s wrong.”
By Ellen Peirson-Hagger
How Iceland Changed the World by Egill Bjarnason
Icon Books, 288pp, £10.99
To get a sense of how small Iceland is, consider a minor episode in the evolution of its language: until 1995, the Icelandic word for “nepotism” – froendhygli – did not exist. In a country where most people know everyone else or are somehow related to them, there was for a long time no notion of patron-client favouritism. Indeed, in a population of around 356,000 – the majority of whom are descended from the same Norse and Celtic settlers of 1,200 years ago and live in and around the capital Reykjavik – the chance of an Icelander sleeping with someone they are related to is apparently high enough to justify the creation of a smartphone app to help them avoid accidental incest. So, it might be surprising to read that this tiny, sparsely populated island in the North Atlantic has altered the course of history far beyond its borders. But that is the argument of the Icelandic journalist Egill Bjarnason, who shows the connection – sometimes convincingly, sometimes not – between events in Iceland (an eruption of a volcano in 1783) and their global ramifications (the French Revolution of 1789). Bjarnason’s intriguing book might be about a cold place, but it’s tailor-made to be read on the beach.
By Gavin Jacobson