The Spirit of Mathematics Algebra and all that

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.

1 - Introduction
2 - Whatever Happened to A, B, and C?
3 - The 1089 Trick
4 - Another Kind of Magic
5 - Just Imagine...
6 - A Most Unusual Lecture
7 - Why are Mathematicians Obsessed by Proof?
8 - Puzzling Mathematics
9 - Why Does (-1) × (-1) = +1?
10 - It's a Square World
11 - Algebra in Action
12 - 'Compleating the Square'
13 - Slices of Pi
14 - The Golden Ratio
15 - Proof by Chocolate
16 - The Puzzled Farmer
17 - Mathematics and Snooker
18 - The Wicked Schoolteacher
19 - Trains, Boats, and Planes
20 - I've Seen That Before, Somewhere ...
21 - An Apple Falls ...
22 - Rollercoaster Mathematics
23 - The Electric Guitar Revisited
24 - The Domino Effect
25 - Real or Imaginary?
26 - The Square Root of Minus One
27 - Inspector Riemann Investigates ...
28 - Infinite Danger
29 - 1 + 1 to the Rescue!
30 - And Finally ...

David Acheson is Emeritus Fellow of Jesus College, Oxford, and was the University's first winner of a National Teaching Fellowship in 2004. He was President of the Mathematical Association from 2010 to 2011, and now lectures widely on mathematics to young people and the general public. In 2013, Acheson was awarded an Honorary D.Sc. by the University of East Anglia for his outstanding work in the popularisation of mathematics. His books include 1089 and All That (OUP, 2002), The Calculus Story, (OUP, 2017), and The Wonder Book of Geometry, (OUP, 2020).