Terence Tao, Pelican (UK, 27 October) Quanta Books (US, 10 November)
For Terence Tao, mathematics has never been anything other than a relentless preoccupation. When he was 2, so goes one story, he used blocks to teach other children how to count. Now, Tao is understood to be the world鈥檚 greatest living mathematician, prolific as a researcher as well as someone who writes about maths.
His latest book (and first for a popular audience) is . It showcases how much more meaningful and alive maths is than stereotypes about it may suggest. It is a short and accessible invitation to even the most inexperienced reader to give maths a chance, and also a helpful starting point for deeper future reading. Whether you loved or hated maths in school, Tao鈥檚 writing just might convince you that the field really is worthwhile and exciting.
Maths equips us with the knowledge we can work out how just about anything works, including technology
The book is split into six chapters, each of which tackles one type of maths: numbers, algebra, geometry, probability, analysis and dynamics. Tao introduces each by recounting its history, outlining its basics and offering helpful commentary about what is exciting and important about it within contemporary maths.
For instance, early on he writes that numbers are a gateway to quantitative thinking, and geometry is a way to go beyond what we can see. 鈥淎lgebra is elegant precisely because it frees us from needing a concrete interpretation for every expression,鈥� he states in a later chapter, explaining the role of all the x and y variables that crowd homework assignments and final exams.
His explanations of the role of statistical models and probabilities (quantifying probability conveys something about our model of the universe, not about the universe itself) are similarly informative and sharp, as is his chapter on dynamics, which is a type of maths that captures change, for example in the relationship between forces and the motion of bodies.
But in its brevity and accessibility, Six Maths Essentials sometimes leaves out details: for instance, making examples of open maths problems sound vaguer than they really are. This is an unfortunate trade-off that comes with telling a story as big as that of the field of maths within an afternoon of reading鈥檚 worth of pages. The result is that the book may best serve as a foundation for, or a gateway into, more detailed explorations.
Writing in a friendly and encouraging tone, Tao steadfastly advocates for using it that way. Poignantly, he writes that 鈥渉aving some understanding of what mathematics is, and how it connects to the modern world, can provide some serenity, reassurance, and perspective on the complexity we see around us. It equips us with the knowledge that, if needed, we can work out from first principles how just about anything works 鈥� including any piece of modern technology 鈥� and analyse its strengths and weaknesses鈥�.
Tao ends Six Maths Essentials by imploring readers to find a restored sense of agency and empowerment in pursuing maths, which struck me as timely. In an age when it is so easy to become inundated with technology and information, I would certainly recommend hearing him out 鈥� and spending time with his book.
An intriguing problem
One wonderful way of heeding the call of maths, and finding joy and a new sense of self in it, is exemplified by another new book: Dana Mackenzie鈥檚 . Mackenzie is a science writer and former maths professor who, in his own words, 鈥渨ent rogue鈥�. The book follows him as he becomes obsessed with a problem that has roots in ancient China, ultimately solving it as if it were the most thrilling action-adventure story you can imagine.
The titular problem centres on finding the best strategy to win in a game between two players (say, a card game). It has relevance to military strategy, too, in how some cards are sacrificed based on the information you have about an opponent鈥檚 hand.
This problem is deceptively simple yet sets Mackenzie off on a vivid mathematical journey. We learn about a mysterious email from a nearly forgotten classmate, a crucial trip to a redwood forest, an animated comment section in The New York Times and the formation of an unlikely team of mathematical heroes who save the day (solve the problem, that is).
Mackenzie does something remarkable in this book: somehow, he manages to elucidate every single step of a mathematician鈥檚 process, including errors and dead ends, without ever becoming boring or unrelatable. Master Sun鈥檚 Problem is replete with equations and diagrams, but, instead of being off-putting or intimidating, Mackenzie imbues them with suspense and passion.
While he can occasionally sound overly knowing and almost avuncular, the sheer emotional thrust of the desire to know more, to understand better and advance human knowledge, is undeniable here. Any young person or adult could benefit from reading this book 鈥� it will stoke a new kind of fire in their heart.
Or, as Tao writes and Mackenzie clearly shows: 鈥淚 encourage everyone to fool around with numbers.鈥�
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