Euler's Pioneering Equation - Robin Wilson ***

The concept of a 'beautiful equation' is a mystery to many, but it seems to combine a piece of mathematics that expresses something sophisticated in relatively few terms and something that looks satisfying. The equation that has proved standout amongst mathematicians, as by far the most beautiful (and is only placed second to Maxwell's equation amongst physicists) is Euler's remarkable e^iπ +1 = 0. What seems remarkable to me about this is that it just seems bizarre that this combination of things produces such a neat result. (Incidentally, as far as I can see, the only reason for the 'pioneering' in the title was to enable the fancy graphic on the cover of the book.)

Getting popular maths books right is incredibly difficult. When I started reading this book, I really thought that Robin Wilson had cracked it. After an introduction, he gives us a chapter on each of the elements of the equation (except the plus and equals signs), from the more basic aspects like 1 and 0 to the more sophisticated components. Then, in a final chapter, he pulls it all together to show why Euler's equation works and why it's useful.

So far, so good. And up to and including pi, except for giving us rather too many series to approximate to it, Wilson does this very well. I really enjoyed the first few chapters. But once we get onto e and i, things go downhill. What had been pitched at a level for the general reader becomes too maths-heavy and lacks readability - and this isn't resolved in the final chapter. If anything things get worse.

I'd say the bare minimum to get through the whole book is a maths A-level, but more than that, in those final chapters, only a total mathematician could enjoy what they were reading. It's such a shame, as the concept is great, the equation is fascinating and the first few chapters work so well. It's almost as if two different books have been involved in a crash and this is the result of welding together the front of one and the rear of the other. A worthy topic, but not quite the book it could have been.

Hardback:

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

Target Earth – Govert Schilling *****

I was biased in favour of this great little book even before I started to read it, simply because it’s so short. I’m sure that a lot of people who buy popular science books just want an overview and taster of a subject that’s brand new to them – and that’s likely to work best if the author keeps it short and to the point. Of course, you may want to dig deeper in areas that really interest you, but that’s what Google is for. That basic principle aside, I’m still in awe at how much substance Govert Schilling has managed to cram into this tiny book. It’s essentially about all the things (natural things, I mean, not UFOs or space junk) that can end up on Earth after coming down from outer space. That ranges from the microscopically small particles of cosmic dust that accumulate in our gutters, all the way up to the ten kilometre wide asteroid that wiped out the dinosaurs. Between these extremes are two topics that we’ve reviewed entire books about recently: meteorites ( The Meteorite Hunt...

The Language of Mathematics - Raúl Rojas ***

One of the biggest developments in the history of maths was moving from describing relationships and functions with words to using symbols. This interesting little book traces the origins of a whole range of symbols from those familiar to all, to the more obscure squiggles used in logic and elsewhere. On the whole Raúl Rojas does a good job of filling in some historical detail, if in what is generally a fairly dry fashion. We get to trace what was often a bumpy path as different symbols were employed (particularly, for example, for division and multiplication, where several still remain in use), but usually, gradually, standards were adopted. This feels better as a reference, to dip into if you want to find out about a specific symbol, rather than an interesting end to end read. Rojas tells us the sections are designed to be read in any order, which means that there is some overlap of text - it feels more like a collection of short essays or blog posts that he couldn't be bothered ...

The Decline and Fall of the Human Empire - Henry Gee ****

In his last book, Henry Gee impressed with his A (Very) Short History of Life on Earth - this time he zooms in on one very specific aspect of life on Earth - humans - and gives us not just a history, but a prediction of the future - our extinction. The book starts with an entertaining prologue, to an extent bemoaning our obsession with dinosaurs, a story that leads, inexorably towards extinction. This is a fate, Gee points out, that will occur for every species, including our own. We then cover three potential stages of the rise and fall of humanity (the book's title is purposely modelled on Gibbon) - Rise, Fall and Escape. Gee's speciality is palaeontology and in the first section he takes us back to explore as much as we can know from the extremely patchy fossil record of the origins of the human family, the genus Homo and the eventual dominance of Homo sapiens , pushing out any remaining members of other closely related species. As we move onto the Fall section, Gee gives ...

Search This Blog