Skip to main content

The Story of Mathematics in 24 Equations – Dana Mackenzie ****

This book was previously published with the misleading title The Universe in Zero Words - the new title is a much better fit. In awarding this book four stars I am reminded of the infamous Samuel Johnson quote on women preachers: ‘A woman’s preaching is like a dog’s walking on his hind legs. It is not done well, but you are surprised to find it done at all.’ The reason I say this is because I’m reviewing a book about mathematical equations. There have been plenty of histories of mathematics (more, if anything, that histories of the whole of science), so to make its mark, a new one has to have a good hook - some different way of looking at the subject that gives it structure and gains our interest. Dana Mackenzie's approach of picking out 24 great equations is risky, because you have to wonder whether people who find maths scary or boring will be drawn in by this concept.

 We meet, for example, 1-1=0, used to explore the nature of zero, while a squared + b squared = c squared introduces not just the Pythagorean theorem with its tortuous history. but also Euclid and irrational numbers. Beginning with simple equations we work forward to the likes of the Chern-Gauss-Bonnet equation (no, me neither), the continuum hypothesis and the economists' favourite, the Black-Scholes equation.

 In the early chapters, Mackenzie holds the interest with a good mix of contextual history stories and the details of the mathematics itself, but as the approach gets more complex it becomes harder to keep the interest levels up as the description of what the equation is doing is inevitably more opaque, making the approach feel more summary and less engaging. The best part of the book is the context – we learn about the individuals behind these equations (not always the obvious ones when it comes to, say, Pythagoras) and the historical setting of their devising. There are also some rather beautiful illustrations, though one aspect of this book I found positively counter-helpful was the text in the images (including all the equations), which was in such a stylised, pseudo-handwriting font that I couldn't read a good few of them. It looked pretty, but it doesn't help understanding if you can't tell the difference between an f and an s.
I have two specific gripes apart from this. One concerns the introduction. We are told how the great Richard Feynman took on someone with an abacus and beat them on the calculation of cube roots because he knew ‘a famous equation from calculus called Taylor’s formula’ – yet we aren’t told what the equation is. In a book that is all about making equations visible, this rankled.
The other problem I have was with a bizarre mini-rant that Mackenzie has about those who worry about the impact of mobile phones on their brains. He points out that the photons produced by a mobile phone have not got enough energy to ionise atoms, so don’t present a danger. But this entirely misses the point. After all, the photons produced by microwave ovens aren’t ionising radiation either, but few us would feel comfortable sticking our heads in a functioning microwave. It’s not that I agree with the ‘danger from phones, phone masts and wifi radiation’ lobby – I don’t – but Mackenzie muddies the water with this strange irrelevancy.
That’s a minor complaint, though. If you’ve always been puzzled by mathematical formulae, or wondered why mathematicians bother to get out of bed in the morning, this book may let you into their secret world. Mackenzie has a light style and is clearly passionate about the subject, though I felt that for the general reader the hook was too weak, leading to a gradual loss of interest. This book would be ideal for a student starting a maths or maths-based degree who wanted some background to help ground the mathematics they will learn in history.
Paperback:  
Using these links earns us commission at no cost to you
Review by Brian Clegg
Labels:

Comments

Post a Comment

Popular posts from this blog

It's On You - Nick Chater and George Loewenstein *****

Going on the cover you might think this was a political polemic - and admittedly there's an element of that - but the reason it's so good is quite different. It shows how behavioural economics and social psychology have led us astray by putting the focus way too much on individuals. A particular target is the concept of nudges which (as described in Brainjacking ) have been hugely over-rated. But overall the key problem ties to another psychological concept: framing. Huge kudos to both Nick Chater and George Loewenstein - a behavioural scientist and an economics and psychology professor - for having the guts to take on the flaws in their own earlier work and that of colleagues, because they make clear just how limited and potentially dangerous is the belief that individuals changing their behaviour can solve large-scale problems. The main thesis of the book is that there are two ways to approach the major problems we face - an 'i-frame' where we focus on the individual ...
Post a Comment
Read more

Introducing Artificial Intelligence – Henry Brighton & Howard Selina ****

It is almost impossible to rate these relentlessly hip books – they are pure marmite*. The huge  Introducing  … series (a vast range of books covering everything from Quantum Theory to Islam), previously known as …  for Beginners , puts across the message in a style that owes as much to Terry Gilliam and pop art as it does to popular science. Pretty well every page features large graphics with speech bubbles that are supposed to emphasise the point. Funnily,  Introducing Artificial Intelligence  is both a good and bad example of the series. Let’s get the bad bits out of the way first. The illustrators of these books are very variable, and I didn’t particularly like the pictures here. They did add something – the illustrations in these books always have a lot of information content, rather than being window dressing – but they seemed more detached from the text and rather lacking in the oomph the best versions have. The other real problem is that...
Post a Comment
Read more

The Laws of Thought - Tom Griffiths *****

In giving us a history of attempts to explain our thinking abilities, Tom Griffiths demonstrates an excellent ability to pitch information just right for the informed general reader.  We begin with Aristotelian logic and the way Boole and others transformed it into a kind of arithmetic before a first introduction of computing and theories of language. Griffiths covers a surprising amount of ground - we don't just get, for instance, the obvious figures of Turing, von Neumann and Shannon, but the interaction between the computing pioneers and those concerned with trying to understand the way we think - for example in the work of Jerome Bruner, of whom I confess I'd never heard.  This would prove to be the case with a whole host of people who have made interesting contributions to the understanding of human thought processes. Sometimes their theories were contradictory - this isn't an easy field to successfully observe - but always they were interesting. But for me, at least, ...
Post a Comment
Read more