I have never before read a book that has so frequently made me think "wow, that's interesting!". "Mathematics for the Imagination" is an absolutely fascinating account of mathematical methods and discoveries and the people behind them, with the sordid histories of mathematicians through the ages jostling for the reader's attention next to their elegantly simple proofs.
After years of publications on popular science and mathematics, we all know that mathematics can provide answers to questions arising from everyday life. If we want to find out when the two hands of a clock will be in exactly the same position or to calculate the volume of a doughnut, we will certainly need to use some maths. But how difficult can this be?
"Economic theory predicts that you are not enjoying this book as much as you thought you would", remarks Steven E. Landsburg at the start of one of the most enjoyable chapters of The Armchair Economist. The point turns out to be this: the fact that you have chosen to read it is a sign that you have probably overvalued it in relation to all the other books you could have read instead.
Although this book is 50 years old this year, its wisdom is needed now more than ever, as increasing computer power and our headline-obsessed media look set to drown us all in a sea of "statisticulation". This is the word coined by Darrell Huff to describe misinformation by the use of statistical material. Biased samples, dubious graphs, semi-attached figures: he describes all the usual suspects clearly and simply, rounding off with the most useful topic of all: How to Talk Back to a Statistic.
Most people think that mathematics consists of either just arithmetic, or a collection of very abstract and technical topics which the layperson has no chance of grasping. But this really is not true: of course many areas are too technical for the non-mathematician, but there are also many beautiful and non-trivial facts which can be expressed in ordinary language for everyone to appreciate.
We live in a world that obeys many physical laws, and that can be modelled by a variety of mathematics. It is surprising what a variety of problems can be described by very similar models. Robert B. Banks does not concentrate on the most common examples of applied mathematics, but instead covers a fascinating selection of topics as varied as the US national debt, the Eiffel Tower, and the flight of golf balls.
"As long as a branch of science offers an abundance of problems", proclaimed David Hilbert, "so is it alive". These words were delivered in the German mathematician's famous speech at the 1900 International Congress of Mathematics. He subsequently went on to describe 23 problems which he believed would spur on mathematical thought for the upcoming century.
"Mathematical Apocrypha" is, as its subtitle intimates, a book of stories and anecdotes about mathematicians and the mathematical. However, in contrast with many books about mathematicians, Steven Krantz focuses on contemporary figures such as Wiener, Littlewood and Hardy, and says very little about the usual myths regarding Pythagoras, Descartes or Euler.