Skip to main content

Cracking Mathematics - Colin Beveridge ****

This kind of book is puzzling, though as we shall discover, Cracking Mathematics is a particularly effective example of the genre. Generally, it's difficult to be sure what a book like this is for, a bafflement not helped in this case by the Zen subtitle 'you, this book and 4,000 years of theories'.

The kind of book I'm talking about is a heavily illustrated summary of a big scientific subject - in this case the whole of mathematics - often covering each topic in as little as a pair of pages with sufficient pictures that the text can only ever be very summary. I can see this format would appeal as a gift book, something to give someone who is difficult to buy for, but I struggle to get a feel for why you would want to sit down and read a book like this from cover to cover - yet it's not a reference book either.

Such books are often big coffee table numbers, but the books in this particular series come in a virtually pocket-sized format - smart hardbacks just 17.5x15 centimetres, so they are far more manageable as, say, a loo book, or something to keep in your bag for boring journeys to keep yourself entertained. And perhaps that format is part of the reason why this particular example works so well - that and some genuinely interesting text from Colin Beveridge.

Along the way, Beveridge takes us on a journey through the origins of mathematics, the renaissance, with the introduction of negative and imaginary numbers, calculus and the infinitesimal, powers and logs, the infinite, codes and some of the more exotic modern ideas. Unlike some of the summary maths texts I've read, it isn't a collection of dull facts, but provides plenty of little gems along the way, from the 20,000 year old Ishango bone to the mysteries of elliptic curves and John Conway's Game of Life. Sometimes the format is a little forced - there's a section labelled 'The Curious Maths of Alice in Wonderland' which certainly does contain some Dodgson maths, but equally includes things like quaternions and non-Euclidian geometry, where the connection to Lewis Carroll, let alone Alice, is rather weak.

In other places, the attempt to make the discussion populist overstretches a little. There is some great material on games and probability, with, for instance, an really good description of the famous Monty Hall problem and the controversy it caused in Parade magazine - but quite why there is a double page spread on poker player Chris 'Jesus' Ferguson, even if he did apply game theory to poker, is a little baffling. My general feeling about this was 'So what?'

Maths is often portrayed as a very dry subject - a necessary evil, rather than something to enjoy - and when maths enthusiasts such as Ian Stewart try to make it seem that mathematics is pure fun they can often misunderstand what the general reader actually finds entertaining, or even faintly interesting. Beveridge does not fall into this trap, and consistently gives us interesting material - in part because the book focusses on the people involved and the history of maths as much as it does on the actual mathematics. Because of this, this title lifts itself above the other books of this type that I've read to make it feel that it really is worth popping into your bag to lighten your next wait at the station.


Hardback 

Kindle 
Using these links earns us commission at no cost to you
Review by Brian Clegg

Comments

  1. Just browsed a few pages and was appalled to read Pythagoras "threw Hippasus into the Mediterranean". That is rubbish! I hope the rest is better researched.

    ReplyDelete
  2. To be fair it says 'The story goes...' 'it is said...' and 'myths abound' - the idea of Hippasus being drowned is a well-known story that will inevitably be included (admittedly I've never seen it attributed to Pythagoras before). Beveridge takes a light approach throughout and this can sometimes bring a slight looseness of language.

    ReplyDelete

Post a comment

Popular posts from this blog

Models of the Mind - Grace Lindsay *****

This is a remarkable book. When Ernest Rutherford made his infamous remark about science being either physics or stamp collecting, it was, of course, an exaggeration. Yet it was based on a point - biology in particular was primarily about collecting information on what happened rather than explaining at a fundamental level why it happened. This book shows how biologists, in collaboration with physicists, mathematicians and computer scientists, have moved on the science of the brain to model some of its underlying mechanisms. Grace Lindsay is careful to emphasise the very real difference between physical and biological problems. Most systems studied by physics are a lot simpler than biological systems, making it easier to make effective mathematical and computational models. But despite this, huge progress has been made drawing on tools and techniques developed for physics and computing to get a better picture of the mechanisms of the brain. In the book we see this from two directions

The Ten Equations that Rule the World - David Sumpter ****

David Sumpter makes it clear in this book that a couple of handfuls of equations have a huge influence on our everyday lives. I needed an equation too to give this book a star rating - I’ve never had one where there was such a divergence of feeling about it. I wanted to give it five stars for the exposition of the power and importance of these equations and just two stars for an aspect of the way that Sumpter did it. The fact that the outcome of applying my star balancing equation was four stars emphasises how good the content is. What we have here is ten key equations from applied mathematics. (Strictly, nine, as the tenth isn’t really an equation, it’s the programmer’s favourite ‘If… then…’ - though as a programmer I was always more an ‘If… then… else…’ fan.) Those equations range from the magnificent one behind Bayesian statistics and the predictive power of logistic regression to the method of determining confidence intervals and the kind of influencer matrix so beloved of social m

How to Read Numbers - Tom Chivers and David Chivers *****

This is one of my favourite kinds of book - it takes on the way statistics are presented to us, points out flaws and pitfalls, and gives clear guidance on how to do it better. The Chivers brothers' book isn't particularly new in doing this - for example, Michael Blastland and Andrew Dilnot did something similar in the excellent 2007 title The Tiger that Isn't - but it's good to have an up-to-date take on the subject, and How to Read Numbers gives us both some excellent new examples and highlights errors that are more common now. The relatively slim title (and that's a good thing) takes the reader through a whole host of things that can go wrong. So, for example, they explore the dangers of anecdotal evidence, tell of study samples that are too small or badly selected, explore the easily misunderstood meaning of 'statistical significance', consider confounders, effect size, absolute versus relative risk, rankings, cherry picking and more. This is all done i