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

Why Nobody Understands Quantum Physics - Frank Verstraete and Céline Broeckaert **

It's with a heavy heart that I have to say that I could not get on with this book. The structure is all over the place, while the content veers from childish remarks to unexplained jargon. Frank Versraete is a highly regarded physicist and knows what he’s talking about - but unfortunately, physics professors are not always the best people to explain physics to a general audience and, possibly contributed to by this being a translation, I thought this book simply doesn’t work. A small issue is that there are few historical inaccuracies, but that’s often the case when scientists write history of science, and that’s not the main part of the book so I would have overlooked it. As an example, we are told that Newton's apple story originated with Voltaire. Yet Newton himself mentioned the apple story to William Stukeley in 1726. He may have made it up - but he certainly originated it, not Voltaire. We are also told that ‘Galileo discovered the counterintuitive law behind a swinging o...

How to Keep a Plane in the Sky - Alex Davies ****

If there's one big gap in the science writing sphere, it's popular engineering (you can quibble over whether engineering is science, but where else would you put popular engineering?). Alex Davies does the field a real service with this insightful introduction to the world of test engineering. The concept is simple. If we build something and sell it, we need to test it to make sure that it won't fail in a way that's dangerous to the consumer. The most obvious example is airliners, which feature at some length, but this applies to everything from cuddly toys to hair straighteners: someone needs to predict what could go wrong and to put the product through its paces to see if it will survive under any reasonable circumstances. When Davies is telling a story of test engineering in action, the book is a delight. He opens with the way that real bears are used to test if bears can get into coolers and trash cans - and the impressive ways these animals can circumvent human in...

On the Equality of All Things - Carlo Rovelli ****

There is a wide gulf between the worldviews of physicists and philosophers. Many physicists present a rather sweetly naive, child-like view of the world, where philosophers bring a distinctly more adult, cynical tone. This being the case, it can be a little worrying when a physicist dips a toe into the philosophical mire. Infamously, in The Grand Design , Stephen Hawking and co-author Leonard Mlodinow told us that philosophy was now dead because science could deal with anything it had previously been needed for. Thankfully, Carlo Rovelli is not trying to do away with philosophy, though it has to be said that when he veers into the topic that physicist's naivety can make it feel like the philosophising of an earnest eighteen-year-old. Take the opening paragraph, which tells us 'electrons and minds, stones and laws, judgements and galaxies do not essentially differ in nature from one another. They are notions that illuminate each other'. I almost expected a Pink Floyd soundtr...

Search This Blog