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.
"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.
"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.
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.
"Dicing with Death" is a rarity: a book about statistics for the general public. Popular maths books are no longer uncommon, popular books on the physical sciences became a publishing phenomenon with Stephen Hawking, but popular statistics books are few and far between. Perhaps this fact is related to the poor public image of statistics, although it is difficult to say which is cause and which effect.
John Allen Paulos is the man who popularised the word "innumeracy", meaning the all-too-common condition of ignorance and bewilderment about maths and numbers in general. A light, cheerful and ever-so-slightly smug look at the problem, his best-known book of the same name (reviewed in Issue 11 of Plus) traces the roots of innumeracy to poor teaching and offers suggestions for antidotes and innoculation.
Despite what the innumerate masses may wish, our daily lives are inextricably tied up with mathematics. On the most mundane level, we use basic arithmetic to do such things as tell the time, to count our change, to programme the video. But on a less obvious level we also need a reasonably good grasp of geometry in order to park the car in the garage or to pack the shopping bags carefully at the supermarket; we collect and interpret statistical data when the football results come in and we all seem to know how easily order turns to chaos.
It is not uncommon for physics students to know more about the history of physics than mathematics students do about the history of mathematics. Physical laws often come with a name attached; mathematics constitutes a more homogenous structure, and thus tracing parentage can be harder.