Brooks – famous for The Quantum Astrologer’s Handbook (2017), and with a PhD in quantum physics – uses a wide-ranging historical canvas to show how various mathematical breakthroughs have led to sophisticated systems of commerce, architecture, agriculture, art, technology, and, unfortunately, war. The obverse holds, too: these pursuits led to the development of mathematics, for Brooks cites evidence that we did not evolve to do complex maths. In fact, it seems our brains haven’t even evolved an innate ability to handle numbers larger than three – hence the title, The Art of More. Brooks suggests that such skills may have been kick-started when astronomer–priests wanted to predict times of flood or omen, and rulers and merchants needed to measure fields, weigh goods, and keep accounts for taxation and trade.

Brooks begins with the revolutionary book-keeping power of basic arithmetic. After exploring numbers, he moves to geometry, gradually introducing more sophisticated concepts in loosely chronological order. Some of these oblige us to go back to memories of Year 12 mathematics, but the book is rich in historical anecdotes and surprising mathematical applications that will absorb anyone interested in history, maths, and technology.

The Art of More follows in the tradition of mathematician Morris Kline’s landmark Mathematics in Western Culture (1953). Kline was one of the first to promote interest in the connection between mathematics and culture. He was also an inspiring writer, whose seminal book still thrills readers today, albeit with due recognition of its limitations, including his exclusively Western focus. By contrast, Brooks provides a carefully balanced view of the multicultural heritage of modern mathematics.

Also, unlike Kline, Brooks is keen to emphasise the nexus between mathematics and profit, machines, and weapons – he doesn’t give much time to mathematical creativity and beauty. Perhaps it’s a sign of our neoliberal times. Yet Patrick Bangert’s whimsical report, published in the Australian Mathematical Society’s Gazette in 2004, suggests that many mathematicians themselves think their subject has more to do with patterns, language, art, or logic than with applications.

Similarly, earlier this year, Ole Warnaar reported in the Gazette on feedback from the Society’s members regarding proposed revisions to the Australian Mathematics Curriculum: criticisms included its excessively utilitarian approach. It’s certainly exciting to apply mathematics usefully, and Warnaar applauds teaching such skills, but he also laments that ‘not enough effort has been made to try to convey the intrinsic beauty of mathematics’.

This quote also expresses my main criticism of Brooks’s ambitious book. (There’s also the odd mistake, and occasionally nuances are sacrificed for the sake of a good story.) Perhaps I’m being romantic, but ‘civilisation’ surely includes the opportunity to appreciate an elegant proof, even if it has no immediate practical application? Besides, it took nearly a century for Einstein’s beautiful mathematics to find an everyday application (GPS), to take just one example. Brooks nods to beauty, and delves a little into science, but his focus is business and technology.

Still, these are vital subjects, and Brooks is not aiming for a complete history. He knows how to tell a good yarn, too, no mean feat for a popular book that actually includes some mathematics. He has a nose for interesting stories and unusual angles, such as the role of algebra in the success of Google, FedEx, and the sleek, aerodynamic design of French cars; why Silicon Valley was ‘literally founded on’ imaginary numbers; the role of calculus in fighting AIDS and winning the Battle of Britain, and, conversely, the role that ignorance of calculus played in the Global Financial Crisis; and the misuse of statistics in criminal trials. Indeed, Brooks shows that mathematics underpins almost every aspect of modern life, depending as it does on technology, finance, business, and statecraft that require the handling and interpretation of increasingly huge amounts of data.

Brooks’s cast of characters includes the quarrelsome sixteenth-century mathematicians Jerome Cardano and Niccolò Tartaglia. The latter accused the former of stealing his method of solving cubic equations, a big deal in a modernising world where mathematical ability was a prized commodity. After much vitriolic correspondence, the matter was to be settled in a public duel – not with swords but with a problem-solving competition. Cardano refused, but his loyal student and collaborator Lodovico Ferrari stepped in. I won’t give away who won.

Then there’s the eighteenth-century algebra teacher who created a paper-folding problem whose solution eventually produced the A-series of paper sizes, which enables designers to readily scale up or down. Brooks is terrific at digging out such lesser-known players. Others include Ingrid Daubechies, whose streamlined data-handling method makes medical and other imaging analyses more efficient; John Snyder, whose work on geometrical projections made satellite maps of Earth possible; and William Gosset, whose still-valuable statistical research helped the Guinness brewery perfect its stout a century ago.

Brooks understandably skates over the more famous mathematicians, blithely assuming most of them were brilliant but unpleasant. He does like the playful, eccentric IT pioneer Claude Shannon, and gives an interesting overview of the development of information theory – and of much else.

With its array of interesting characters, real-world applications, and tantalising mathematics, Brooks’s fascinating book is an engaging contribution to our maths-shy but maths-dependent culture.