# Book Review: The Universe in Zero Words

SUMMARY: In this book, mathematician Dana Mackenzie provides a quick tour through the history of mathematics, from ancient to modern times, with short vignettes about 24 equations.

A closer look at the dust jacket for Dana Mackenzie's book, The Universe in Zero Words [embiggen].

Whilst a child, my male teachers informed me that "girls are terrible at math" and "teaching maths to girls is a waste of time". Undeterred by their fondness for their own opinions, I've always been fascinated by the elegance and the pure artistry of mathematics. Perhaps because this passion had been forbidden, I ended up taking (and excelling in) all the college maths courses that I could find, tutoring maths students and in fact, almost pursuing a university maths degree.

I mention this because you will not find that dismissive attitude in Dana Mackenzie's book, The Universe in Zero Words: The Story of Mathematics as Told through Equations [Princeton University Press; 2012: Guardian Bookshop; Amazon UK/kindle UK; Amazon US/kindle US]. As he states in the book's preface, Mackenzie's purpose is "to lift the veil of mystery and secrecy that surrounds mathematics and equations" so his readers "can see what lies underneath."

Comprised of short lively vignettes that are part biography, part history and part mathematics, this aesthetically-pleasing book is liberally embellished with period art and engravings, ancient manuscripts, colour photographs, maps and diagrammes. Even the dust jacket is designed with the mathematical aesthete in mind: a close look at the stars reveals they are mathematical equations superimposed on the night sky!

To write this book, the author combed through centuries of algebra, geometry, applied mathematics and analysis to identify 24 mathematical theorems or physical laws that fulfilled these criteria:

- it is surprising
- it is concise
- it is consequential
- it is universal

In writing about these 24 special mathematical equations, Mackenzie starts with simple practical equations discovered by the ancient Greeks and moves forward to the more sophisticated equations discovered in modern times. As the mathematical complexity of the equations grows, we gain an appreciation for their power and, yes, for their profound beauty. Even though we may not understand all the subtle nuance of these equations, we recognise why they are so intellectually exciting to mathematicians. We also see how these equations can be used to predict and explain natural phenomena and abused to influence economic developments and risk management.

But more than just showing us these equations, Mackenzie goes on to discuss the lives of the people who contributed to mathematical theory, the times they lived in, and how their contributions changed the way that we think about mathematics -- and about the universe.

In this book, you'll read about prime numbers and the the discovery of π. You will read about the Fourier series, Dirac's equation and about the geometry of whales and ants. I suppose it's probably a foregone conclusion that you will also read about what may be the most recognisable equation the world has ever seen, Einstein's famous E=mc^{2}. You'll be introduced to the group of people behind the Pythagorean Theorem and you'll also meet famous mathematicians such as Archimedes, Kepler, Fermat and Gauss.

I especially enjoyed the chapter on chaos theory/Lorenz equations although I was disappointed to see it only mentions where the idea of the "butterfly effect" comes from without going into much depth. I was surprised that the chapter discussing the discovery of zero neglected to mention that Alex the grey parrot discovered zero on his own -- an intellectual achievement that took humans millennia to accomplish.

This book provides a glimpse into the history underpinning some of mathematics' most important equations, a rich and fascinating topic that is rarely mentioned in most classrooms. Further, even though words seldom do justice to the economic beauty of an equation, Mackenzie manages to provide a reasonable idea what these equations communicate.

This attractive 224-page book is a breezy romp through 2500 years of mathematical ideas. It includes four parts that are divided into a total of 24 fairly short chapters, as well as an introduction and conclusion, acknowledgments, bibliography and an index. This well-designed and accessible book will delight and inform the student, mathematician or historian in your life and it may also help you rediscover your forbidden love for mathematics.

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Dana Mackenzie is a freelance science writer who specialises in writing about mathematics. He has a doctorate in mathematics from Princeton and was a mathematics professor for thirteen years. He then pursued his childhood passion to be a professional writer. This is his third book. In his free time, Mackenzie plays and teaches chess: he was the state champion of North Carolina in 1985 and 1987, and won the National Master title in 1988. He lives in California with his wife, three cats and one dog.

**NOTE:** reformatted slightly from the original, which was published on *The Guardian*.

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