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Imagine stepping inside your favourite painting, walking around the lightfilled music room of Vermeer's "The Music Lesson" or exploring the chapel in the "Trinity" painted by Masaccio in the 15th century. Using the mathematics of perspective, researchers are now able to produce threedimensional reconstructions of the scenes depicted in these works.

One of Oxford University Press's series of "Short Introductions", this book is a rigorous and challenging description, by one of the greatest pure mathematicians alive (Timothy Gowers is Rouse Ball Professor of Mathematics at the University of Cambridge, and a Fields Medal recipient), of what mathematics is. Perhaps too challenging, in fact  on page 23 we are introduced to an axiomatisation of number systems, and things only get tougher. Clearly, as one of a highly intellectual series, the book is intended to stretch its readers' abilities to the utmost.

Paul Erdös is reported to have said "A mathematician is a machine for turning coffee into theorems". We may never know if he appreciated the mathematics behind the perfect dunk of a biscuit into said coffee, but we can all begin to understand the ubiquity of maths in our lives, thanks to Len Fisher's delightful book. The subtitle is "The science of everyday life", though pretty much all the content is maths with the equations (mostly) taken out. Perhaps Professor Fisher was advised that sales would suffer if they weren't, but anyone interested in the applications of mathematics to the real world will find plenty to amuse and educate.

Gerd Gigerenzer is not a mathematician or statistician per se, but primarily a psychologist, working across disciplines to understand how human beings make decisions in the face of uncertainty. What he offers here is nothing less than a prescription for how to think, how to choose, and how to live, when the information on which we base our decisions is necessarily incomplete and flawed. For example  how worried should you be if you have a positive mammogram as part of a screening programme for breast cancer, or a positive HIV test despite the fact that you are in a lowrisk group?

Geoff Wilson is an air traffic controller for the Royal Air Force. Recently back from Kabul in Afghanistan, he tells Plus how logical thinking under pressure is crucial in his job.



In 1694, a famous discussion between two of the leading scientists of the day  Isaac Newton and David Gregory  took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.
