Each generation of maths teachers has to convince its pupils that what they're learning has practical applications outside the classroom.

Jordan Ellenberg's approach is similar to that of a teacher of philosophy: that a decent grounding in maths helps bring about a logical, critical way of looking at the world. The main planks of this book are statistics and probability, and it shows how the claims of politicians, aided by a mathematically illiterate media, can be punctured by being aware of the context, understanding proportionality and "statistical significance", and applying a few basic principles. From avoiding scams by people who try to pass themselves off as hotshot players of the stock market to making shrewd guesses as to what banks aren't telling you about their mutual funds, there are lessons here that can genuinely be applied to real life. Ellenberg is an engaging and witty populariser, keeping formulae to a minimum and making some candid admissions about the mathematical life.