The Maths Handbook – Richard Elwes ***

I can’t score this book more than 3 stars because it’s not really popular maths, but it does what it sets out to do rather well, so it should be seen in this context. As Richard Elwes points out in his introduction ‘I was never any good at maths,’ is something you hear all the time. What he sets out to do – and succeeds in admirably – is taking the reader step by step through the basics of maths to be able to manage those slippery figures with ease.

The approach is not as heavy as a textbook, though occasionally I did get the feel of a slight older, fussy teacher at work. (It’s notable that the precise expression we’re told Elwes has heard from ‘a thousand different people’ is ‘I was never any good at mathematics.’ Hardly anyone would say ‘mathematics’ rather than ‘maths’. Now it’s possible he was trying to avoid the UK/US maths/math split – but it still fits that slightly fussy precision we meet on a regular basis through the text.)

I really can’t fault the step-by-step progress, starting with basic arithmetic, taking us on to fractions and powers, roots and logs, percentages, algebra, geometry and even a brief intro to probability and statistics. Each of the sections is quite short, easily digested, well laid out and illustrated and finished off with a little quiz that’s not too taxing but helps reinforce the message. I suppose the only question is whether it’s best to arrange such an introduction by the structure of maths itself (as this book is) or by application, taking the reader through typical mathematical chores from checking a shopping bill to calculating odds at a bookies. That way you could cover the same ground but perhaps make it seem more real world. However, Elwes doesn’t resort to an excess of mathematical jargon, keeping the focus simple – and at least by structuring the book on the maths itself it can have the most logical progression of experience.

As I mentioned at the start, this isn’t popular maths. A popular maths book is not a tutorial in how to use it, with tests, but an exploration of some aspect of maths, the people involved, the history and its significance. This is much more a practical book. I would it see it being particularly useful to an adult learner who had trouble with maths at school and now wants to come back to it and take it on. It is a lot less condescending than most modern maths textbooks and would appeal more to a mature reader. So for this particular audience it is definitely an option well worth considering – and it’s excellent value, priced like cheap paperback but actually a good size and well-made book. Just not really for someone wanting a voyage of discovery about the history or nature of mathematics.

Paperback:  

Review by Brian Clegg

Maths 1001 [Mathematics 1001] – Richard Elwes ***

Like its sister title Science 1001, this book takes on an enormous task: telling us ‘everything we need to know about mathematics in 1001 bite-sized explanations’.

It’s a handsome, if rather heavy book, somewhere between a typical hardback and a small coffee table book in size (though with floppy covers). Inside, it’s divided into 10 main sections – from the obvious ones like geometry and algebra, through to the exotics from statistics to game theory. Each section is split into topics – so in geometry you might get ‘Euclidian geometry’ and within each topic there may be around 12 entries.

In a sense, then, this is a mini-encyclopaedia of maths, though arranged by subject, rather than alphabetically. I had mixed feelings about the science entry in the series and those feelings are more extravagantly mixed than ever here. There is no doubt whatsoever that this is a useful book. A good marker of this is that, unlike many of the books that come into the review pile, I intend to keep this one. I think I will come back to it time and again to brush up on what some specific aspect of maths is. (As it is, really, a reference book, it would have been more helpful if the topics were alphabetic, but hey, what do you expect from a mathematician?)

However, as a popular science book to read from cover it has a number of deep flaws. Firstly it’s much too broken up into tiny segments. There is a bit of a flow, brought in by the way the topics are organized, but it’s very weak, and certainly doesn’t make for casual reading matter.

Secondly, far too much of the book is definitions. Time after time, a topic consists of defining what a mathematical term means. I feel a bit like Richard Feynman, who was told in a biology class, when explaining what the various bits of a cat were called, that everyone would be expected to memorise these. He said something to the effect of ‘no wonder this course takes so long’ – he didn’t see why people need to keep all those definitions in memory, and I rather feel the same about maths.

Then there’s the difficulty that the structure has in terms of dealing with some of the essentials of maths. Time after time, the author refers to the number e, without telling us what it is until over 200 pages after it is first mentioned. The assumption for a reader who hasn’t come across it might be that e is just a placeholder, the way j is used elsewhere – although many definitions here aren’t necessary, explaining what something like e is, and why it’s important, is pretty crucial.

As someone with a physics background, I particularly struggle to understand why there’s a whole section in here called ‘mathematical physics.’ No, it’s just physics. Newton’s laws don’t belong in a book on maths – there’s much too much to get your head around already without straying into a different subject.

And to top it all, I think the approach taken is often wrong. Popular science/maths, as opposed to textbooks, adds in explanation and context, not just the theory. By being so strong on definitions, there doesn’t seem to be room for this here. We find very little out about all the fascinating people involved. But even if you decide the format doesn’t allow for context and history, there is still far too little explanation. Two example out of literally hundreds: we are told ‘Up until the early 20th century, 1 was classed as prime, but no longer.’ Why? There are good reasons for this, but it is totally counter-intuitive. The number 1 seems like a prime. After all, it is only divisible by 1 and itself. We need explanation, not statement from authority. Another example is the topic on Bayes’ theorem. This is fascinating in its application, but the explanation is almost unreadable, being mostly equations, and there is nothing about its application in that section (a later one does make use of it, but doesn’t mention it is doing so). Highly frustrating.

Overall then, this is a very useful book if you dip into maths and need a quick reminder of what various things mean. It really is a great resource as a reference book. But it just doesn’t work as popular maths.

Paperback (US is hardback):  

Review by Brian Clegg

Richard Elwes – Four Way Interview

Richard Elwes is a writer, teacher and researcher in Mathematics and a visiting fellow at the University of Leeds. Dr Elwes is passionate about the public understanding of maths, which he promotes at talks and on the radio. His more recent book is Maths 1001.

Why maths?

I don’t know anything else!

I have always enjoyed the subject, and the more I have studied, the more I have realised how incredibly deep it goes, and just how much there is to know. At the same time, I am aware of the gulf between how most people see maths (a horrendous mix of tedious equations and incomprehensible jargon), and how I see it, which is as a whole other world, packed full of amazingly cool, interlocking ideas. So, as well as enjoying studying maths myself, I suppose I have a drive to try to close this gap.

Why this book?

There are two answers, both true.

The first is that I don’t think a book like this has ever been attempted before. Of course, there are plenty of excellent books discussing various mathematical topics for a general audience. But I don’t believe any have tried to be as comprehensive as this. It’s ambitious, there’s no doubt about it, and I was excited by the challenge.

At the same time, there seems to be a gap between ‘popular’ books on one hand, which take a completely equation-free, discursive approach to a mathematical subject, and ’technical’ volumes or textbooks on the other, which go fully into all the gory details. My book treads a middle path. I didn’t want to sex things up too much, I wanted the mathematics to speak for itself, and for the book to work as a reference volume. At the same time, some of the material is undoubtedly difficult and unfamiliar, and people need a way in, to understand what fundamental questions are being addressed. I wanted it to be enjoyable to read, and for people genuinely to learn from it. In some ways, I suppose I wanted to write the book that I would like to have read aged 17.

The second answer is… someone offered me money to write it.

What’s next?

I’m pleased to say that I have a couple of projects in the pipeline. In Spring 2011 I have a book called “How to build a brain (and 34 other really interesting uses of mathematics)” coming out, which has been a fun one to write. It covers some of the same areas as Mathematics 1001, but in a much more light-hearted and less technical style. Perhaps you could guess that from the title.

There are other things in the works too… but it is probably still too early to go into details. I can say that I am looking forward to working on them though!

What’s exciting you at the moment?

Maths 1001 is my first book, and it’s just come out. I’m quite excited about that, to be honest!

Otherwise, I find that the internet makes a wonderful blackboard, these days. There are so many people out there talking about maths, from primary school teachers discussing games kids can play to start to enjoy numbers, right up to Fields medallists presenting their latest research. I follow several mathematical and scientific blogs (I’ve got my own too, may I plug it? www.richardelwes.co.uk/blog Thank you!). It is just fun to be a part of that huge conversation.

In terms of mathematics itself, I have been thinking about recent work by the logician Harvey Friedman, which I find very exciting. It’s a sort of sequel to Kurt Gödel’s famous work. I think it will turn out to be important. I am getting quite interested in ideas from logic to do with provability, computability, and randomness, and how they relate. My background is not in exactly this type of logic, but I do find it fascinating.