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The Universe in Zero Words: The Story of Mathematics as Told through Equations [Kindle Edition]

Dana Mackenzie
3.4 out of 5 stars  See all reviews (9 customer reviews)

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Book Description

Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil?

The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called "a popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.

Illustrated in color throughout, the book tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, the book shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match.

The Universe in Zero Words is the ultimate introduction and guide to equations that have changed the world.

Editorial Reviews


Dana Mackenzie, Winner of the 2012 Joint Policy Board for Mathematics Communications Award

"Quietly learned and beautifully illustrated, Mackenzie's book is a celebration of the succinct and the singular in human expression."--Nature

"The equations Mackenzie exhibits in this wonderful book represent 24 of the most profound discoveries in the history of Mathematics. . . . Mackenzie's writing is understated and clear. The complex ideas he explains so lucidly are beautiful in themselves, but this book is physically beautiful too, imaginatively illustrated and stylishly designed to complement its subject."--Irish Times

"[M]ackenzie provides interesting insights regarding the equations, such as relating whale communications to a model of a non-Euclidean geometry or the role of cigar smoke in the quantization of angular momentum of quantum particles. . . . The book is an enjoyable read . . ."--Choice

"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."--Devorah Bennu, GrrlScentist

"With a book that is both short and very easy to read, Mackenzie manages to introduce a very wide scope of ideas, and to produce a condensate of the history of mathematics that is at the same time enlightening and engaging. He succeeds in discussing highly advanced science while remaining very comprehensible, and in popularizing mathematics and physics while also giving food for thought to the specialist. His Universe in Zero Words will therefore seduce any scientist, but also anyone with some curiosity and desire to get more familiar with the history of human thinking and knowledge."--Jean-Baptiste Gramain, London Mathematical Society Newsletter

"[V]ery absorbing reading. . . . Two hundred pages, twenty-four equations, one endearing and well told story. I wholeheartedly recommend the book."--Alexander Bogomolny, CTK Insights

"A fascinating and informative look behind the equations."--Lucy Sussex, Sydney Morning Herald

"[The book] reads well and quick: I took it with me in the metro one morning and was half-way through it the same evening, as The Universe in Zero Words remains on the light side, especially for readers with a high school training in math. . . . The Universe in Zero Words makes for an easy and pleasant read, as well as a wonderful gift for mathematically inclined teenagers."--Chance Magazine

"MacKenzie has the knack of getting and keeping your attention, and writes with fluency and wit, and he is a good story-teller."--Anthony G. O'Farrell, Irish Mathematical Society Bulletin

"[This] is brilliantly written, and this reviewer who has taught historical aspects of mathematics for a number of years enjoyed the book and learned some details that were unfamiliar. The author possesses a wonderful skill in presenting technical material to those without the facility to understand the mathematics. . . . In summary, a refreshing look at highlights from the History of Mathematics and a welcome addition to the literature, written in a very accessible style."--Phil Dyke, Leonardo Reviews

"Mackenzie has written an accessible account of mathematical equations through the ages, giving strong insights in a historical context and with a wider interpretation that does justice to the title."--Wallace A Ferguson, Mathematics Today

"The book is written in a very transparent and elegant manner; it is both enjoyable and informative reading. The reader will absolutely love exciting historical facts and excellent illustrations, diagrams, pictures carefully selected by the author. The volume concludes with a useful bibliography and a helpful index. A very entertaining text that appeals not only to mathematics enthusiasts, but also to a wide audience with a quite limited mathematical background."--Yuri V. Rogovchenko, Zentralblatt MATH

From the Inside Flap

"Demanding very little prior mathematical knowledge, this is one of the best popular histories of mathematics in recent years. Dana Mackenzie's prose is lively and easy to read, and his mix of historical background and personal biographies of the main characters is engaging."--Eli Maor, author of The Pythagorean Theorem: A 4,000-Year History and e: The Story of a Number

"Dana Mackenzie is a very good writer. I was constantly amazed at his ability to describe complicated mathematics in a few sentences in a way that the average reader--not the average mathematician or the average math major, but the average reader--can understand. This is a very entertaining book."--David S. Richeson, author of Euler's Gem: The Polyhedron Formula and the Birth of Topology

"[A] terrific book. . . . [A] brilliant history of mathematics as told through equations."--Dick Lipton, Professor of Computer Science at Georgia Tech

Product Details

  • File Size: 8338 KB
  • Print Length: 224 pages
  • Publisher: Princeton University Press (April 9, 2012)
  • Sold by: Amazon Digital Services, Inc.
  • Language: English
  • ASIN: B007BP3ATU
  • Text-to-Speech: Enabled
  • X-Ray:
  • Word Wise: Enabled
  • Lending: Not Enabled
  • Amazon Best Sellers Rank: #474,822 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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Customer Reviews

Most Helpful Customer Reviews
14 of 14 people found the following review helpful
The author provides a partial history of mathematics, from ancient to modern times, by presenting vignettes about 24 equations. Although the author concedes his selection of equations reflects "individual taste and preference," he contends the equations selected for the book meet four criteria: each equation is (1) surprising, (2) concise, (3) consequential, and (4) universal. Each vignette focuses on a particular equation, and each vignette describes the equation, places the equation in a historical context, and of explains how the equation has significance in the history of mathematics or science.

The book is written in a style that is pitched for readers who may not be mathematicians by training or experience. However, some of the equations deal with subjects that might be difficult to follow for readers who do not have at least some training or experience with mathematics or science. Parts of the book may be too advanced for some readers looking for a basic, introductory book on the history of mathematics, but it also is probably too basic for readers looking for a detailed or technical history of mathematics.

Readers looking for more detailed or synoptic surveys or histories of mathematics should consider taking a look at the following books: Uta C. Merzbach and Carl B. Boyer, A History of Mathematics; Jan Gullberg, Mathematics: From the Birth of Numbers; Morris Kline,
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4 of 4 people found the following review helpful
3.0 out of 5 stars Lot's of math smatterings November 13, 2012
By Gderf
This is a fairly extensive survey list of mathematical ideas with sparse coverage of each. There are some insights into the thought process behind the equations. The biographical data on mathematicians from Archimedes to Wiener is interesting, though sparse. Coverage of any topic is too sparse for learning, though certainly very good as a lever for subsequent investigation or review. Among items missing are Hamiltonians and tensors, while quantum mechanics coverage is deceptively incomplete. I found Mackenzie's analysis of the shortcomings of Black-Scholes as well as possible future improvements very interesting. Complete coverage of the derivation is available in books by Jarrow and Bookstaber. The book ends with the fanciful purported futuristic equation ?=?.

I would be more impressed if any single topic was given more extensive coverage, but I suppose that's what textbooks are for. Coverage is more complete in the mathematics for idiots series or the " xxx Demystified" series. Other good surveys include Amir D. Aczel's books, 'Fermat's Last Theorem' and 'Descartes' Notebook' and 'The Story of -1' by Paul J. Nathin. A couple of books by the late Richard Feynman do a good job of relating math to physics. This book is an illustration of Shakespeare's idea "A little knowledge is a dangerous thing."
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3.0 out of 5 stars Good, but leaves you wanting more... January 4, 2014
This book would be good for someone who knew almost no math but wanted to get familiar with some of the most important equations from antiquity through the present day. But I have trouble believing that anyone geeky enough to be interested in these equations (especially from 1900 on) would know as little math as the author supposes.

I think the average reader is probably more like me - literate in math but definitely not a mathematician. For me, the book was so lacking in details that a lot of it felt like a tease. There are too many cases where the author uses vague analogies to describe what an equation is doing when a few simple lines of high school math would have made it perfectly clear.

Having said that, there are a lot of bright spots to the book as well. I really enjoyed the first few chapters where the author talks about the "cult of Pythagoras" and describes how until very recently math was being done with incredibly primitive tools (no words, no equals sign, no plots, not even Arabic numerals - it's amazing anything got done at all!), and it's striking how rapidly mathematics would develop when things we take for granted today were introduced (for instance, calculus was invented less than 200 years after the equals sign was introduced, and less than 100 years after people started plotting equations).

There were also a few bright spots in the latter half of the book. I enjoyed the chapter on set theory/cardinality, which is so elementary that it can be explained in relative detail without any prior knowledge of mathematics, and yet which has some incredibly surprising results.
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5.0 out of 5 stars 2, 4, 6, 8, which equations do we appreciate?? November 9, 2013

"In this book, I hope to lift the veil of mystery and secrecy that surrounds mathematics and equations, so that those who are interested can see what lies underneath...

The rest of the world, outside of science, does not speak the language of equations, and thus a vast cultural gap has emerged between those who understand them and those who do not. This book is an attempt to build a bridge across that chasm.

It is intended for the reader who would like to understand mathematics on its own terms, and who would like to appreciate mathematics as an art...

The following chapters will try to explain in words--even if words are feeble and inaccurate--what these equations mean and why they are justly treasured by those who know them."

The above comes from the preface and introduction to this interesting book by Dana Mackenzie. He has a Ph.D. in mathematics from Princeton and was a mathematics professor for thirteen years before becoming a full-time writer and author.

This is a history of mathematics book that uses selected equations to carry its main narrative forward. Little prior mathematical knowledge is demanded.

I appreciated that each chapter gets down to the essentials behind each equation with no unnecessary filler. Thus, this book is never boring.

The equations themselves include those from antiquity (like the world's simplest equation and the laws of levers) all the way to those equations in our own time (such as equations of the photoelectric effect and equations of chaos theory).

How were the equations in this book selected? The author used four main criteria to decide what makes an equation great:

(1) It's inspiring, telling us something we did not know before.
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More About the Author

Writing is my second career, but it was my first love. As a kid, all I wanted to be was a writer. Nevertheless, my academic career took a different direction. I loved mathematics too, and earned a doctorate from Princeton. I taught math for six years at Duke University and seven years at Kenyon College in Ohio. I enjoyed it, but I have to say I never felt that teaching was my true calling.

In 1996, using the newfangled invention called the World Wide Web, I found out about the Science Communication Program at the University of California at Santa Cruz. Suddenly all the pieces of the puzzle clicked together. I could be a writer, as I had always wanted to be, and still make use of my knowledge of math and science.

At UCSC I learned about journalism and made the contacts I needed to hit the ground running. An internship at American Scientist in the summer of 1997 gave me some practical experience in writing and editing with a deadline. Since the fall of 1997, I have been a full-time freelance writer.

Some of the magazines I have written for are Discover, Smithsonian, Science, and New Scientist. "The Big Splat, or How Our Moon Came to Be" published by John Wiley & Sons, was my first book. Since then, I have written two booklets for the American Mathematical Society, called "What's Happening in the Mathematical Sciences," volumes 6 and 7. I am working on another book about mathematics now, and I will post more information as it comes closer to fruition.

The Story of "The Big Splat"

The idea for my first book, "The Big Splat, or How Our Moon Came to Be," came out of a meeting that I covered in 1998 for Science magazine. It was a conference about the origin of Earth and the Moon, and I was the only reporter there. In three days of talks, I was astounded to hear over and over about the giant impact theory of the Moon's origin -- a theory that was completely unfamiliar to me, and yet was really the only one seriously discussed at this conference. I was amazed that the experts had more or less agreed on where the Moon came from, and yet no one outside the planetary science community knew about it! There was clearly a failure of communication between scientists and the public. It was up to me to bridge the gap.

Writing the book was a lot of fun. It was the perfect size for a first book. It came out to be twelve chapters long, and I had about twelve months to write it. That meant that I had to tell one in-depth story a month, which was just the right pace for me. I enjoyed the feel of working on a long-term project, as a change of pace from jumping around from one article to another.

A special treat, which I did not at all anticipate, was doing historical research with original documents. To research one chapter I traveled to Cambridge, England, to delve into the Charles Darwin papers. (What does Charles Darwin have to do with the Moon? Read my book to find out!) It's hard to express the thrill of holding in my hands a letter that Darwin sent to his son a century ago, realizing that I might be he first person to read it since then.

"The Big Splat" came out in the spring of 2003, and received excellent reviews. Booklist, a magazine published by the American Library Association, named it as one of their Editor's Choices for 2003 -- an honor accorded to only 63 books that year, and only four science books.

In June of 2007 I appeared the History Channel's new series, "The Universe," in an episode called "The Moon." In fact, if you watch carefully you will see that about half of the hour-long show is based on "The Big Splat." It was a dream come true to see what was essentially a "TV version" of my book. In August 2009 I appeared on "The Universe" again, this time in an episode about how Earth would be different if we had no moon.

Everything Else You Wanted to Know about Dana Mackenzie

In my free time, I am also an avid chess player. I was the state champion of North Carolina in 1985 and 1987, and earned the National Master title in 1988. In 2006, I joined the team of master teachers at, where I record two video lectures a month. Ironically, I find teaching chess to be more satisfying than teaching math was, and my "students" seem to like me better. Why?!? Maybe because chess is, in the language of academia, an elective course, while math often is not.

My other hobbies include music and dancing. I started folk dancing in college, and years later I met my wife, Kay, in an international folk dance group. Four years ago I joined the Hula School of Santa Cruz, a warm, supportive, and family-oriented group. I strongly encourage any of you who have ever experienced the aloha spirit to find your local halau and give hula a try. The photo shows me before one of our performances.

Kay is also a writer -- we call ourselves the "Mackenzie Publishing Empire"! If you are into quilting, please check out her books, either here at or by visiting her webpage at


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