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

Comments

Popular posts from this blog

Patricia Fara - Four Way Interview

Patricia Fara lectures in the history of science at Cambridge University, where she is a Fellow of Clare College. She was the President of the British Society for the History of Science (2016-18) and her prize-winning book, Science: A Four Thousand Year History (OUP, 2009), has been translated into nine languages. An experienced public lecturer, Patricia Fara appears regularly in TV documentaries and radio programmes. She also contributes articles and reviews to many popular magazines and journals, including History Today, BBC History, New Scientist, Nature and the Times Literary SupplementHer new book is Erasmus Darwin.

Why history of science?
I read physics at university, but half-way through the course I realised that had been a big mistake. Although I relished the intellectual challenge, I was bored by the long hours spent lining up recalcitrant instruments in dusty laboratories. Why was nobody encouraging us to think about the big questions – What is gravity? Does quantum mechani…

The Idea of the Brain: Matthew Cobb *****

Matthew Cobb is one of those people that you can’t help but admire but also secretly hate just a little bit for being so awesome. He is professor for zoology at the University of Manchester with a sizable teaching load that he apparently masters with consummate skill. He’s a scientific researcher, who researches the sense of smell of fruit fly maggots; I kid you not!  He’s also an attentive and loving family father but he still finds time and energy to write brilliant history of science books, three to date. His first, The Egg and Sperm Race, describes the search for the secret of human reproduction in the seventeenth and eighteenth centuries and is one of my favourite history of science books, on the period. His second, Life’s Greatest Secret is a monster, both in scope and detail, description of the hunt to decipher the structure and function of DNA that along the way demolishes a whole boatload of modern history of science myths. The most recent, and the subject of this review, is

The Big Ideas in Science - Jon Evans ***

The starting point of a review like this has to be to congratulate the author on his achievement, Jon Evans, because getting all of science into one relatively short book is a massive (and thankless) task. Although inevitably the result is a fairly hectic dash through the material, with limited space for subtleness, Evans manages to make the experience readable and has a light touch that is effective without becoming too simplistic.

There is only one reason this book doesn't get four stars - it's not the quality of the writing but rather the selection of the contents. Of course, there is bound to be plenty of stuff missed out - how else could you get all of science into 269 pages? But the balance is strangely skewed. Chemistry is pretty much omitted, though aspects of chemistry occur under other headings. But for me, the real problem is that physics is really under-represented. It's interesting to use Jim Al-Khalili's recent excellent physics summary title The World Acc…