The Spirit of Mathematics brings to life the most elementary parts of arithmetic, algebra, and geometry in a new way. It sets out problems and draws out the wonder and 'magic' of finding their solutions with an infectious enthusiasm. Acheson packs a remarkable amount of surprising mathematics into this short work.

What makes mathematics so special?

Whether you have anxious memories of the subject from school, or solve quadratic equations for fun, David Acheson's book will make you look at mathematics afresh. Following on from his previous bestsellers, The Calculus Story and The Wonder Book of Geometry, here Acheson highlights the power of algebra, combining it with arithmetic and geometry to capture the spirit of mathematics. This short book encompasses an astonishing array of ideas and concepts, from number tricks and magic squares to infinite series and imaginary numbers.

Acheson's enthusiasm is infectious, and, as ever, a sense of quirkiness and fun pervades the book. But it also seeks to crystallize what is special about mathematics: the delight of discovery; the importance of proof; and the joy of contemplating an elegant solution. Using only the simplest of materials, it conjures up the depth and the magic of the subject.

Given the author's own specialisms (mainly fluid dynamics and astrophysics), it is good to see a substantial emphasis on the use of algebra in applied mathematics. There are stimulating chapters on passing trains, crossed ladders, rollercoaster dynamics and tuning a guitar. The book ends with some paradoxes involving infinite series and the AM-GM inequality. I can recommend it thoroughly.