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

Luna: Moon Rising (SF) - Ian McDonald ****

I'm not the natural audience for this book. Game of Thrones l eaves me cold - and it's hard not to feel the influence of GoT (and a whole lot of Dune ) underneath a veneer of science fiction and the trappings of a South American drug cartel in the cod-medieval family power battles and chivalric details. There are even dragons (of a sort). I'd be really sad if the future did involve this sort of throwback feudalism. However, remarkably, despite this I found Luna: Moon Rising kept me engaged. The fact is that Ian McDonald can put together a good plot with intricate machinations, which is enough to carry the reader through what can be a bewildering collection of characters. The two page scene-setter saying who did what to whom at the start was useful, but I could have done with family trees for the main family as I was constantly forgetting who was who - especially easy as McDonald endows many families with characters with the same first initial (e.g. Ariel and Al...

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...

The AI Paradox - Virginia Dignum ****

This is a really important book in the way that Virginia Dignum highlights various ways we can misunderstand AI and its abilities using a series of paradoxes. However, I need to say up front that I'm giving it four stars for the ideas: unfortunately the writing is not great. It reads more like a government report than anything vaguely readable - it really should have co-authored with a professional writer to make it accessible. Even so, I'm recommending it: like some government reports it's significant enough to make it necessary to wade through the bureaucrat speak. Why paradoxes? Dignum identifies two ways we can think about paradoxes (oddly I wrote about paradoxes recently , but with three definitions): a logical paradox such as 'this statement is false', or a paradoxical truth such as 'less is more' - the second of which seems a better to fit to the use here. We are then presented with eight paradoxes, each of which gives some insights into aspects of t...

Search This Blog