Reviews for Enlightening Symbols

From AMS Bulletin, John Stillwell
Mazur is a master story teller, using a much greater word-to-symbol ratio than Cajori. The necessary symbols are there, of course, but not to an extent that impedes the narrative.

From Fourmilab, John Walker's Fourmilab Change Log
This book is a treasure chest of information about how the language of science came to be. We encounter a host of characters along the way, not just great mathematicians and scientists, but scoundrels, master forgers, chauvinists, those who preserved precious manuscripts and those who burned them, all leading to the symbolic language in which we so effortlessly write and do mathematics today.

From AMS Notices
by Robyn Arianrhod

At whatever depth one chooses to read it, Enlightening Symbols has something for everyone. It is entertaining and eclectic, and Mazur’s personal and easy style helps connect us with those who led the long and winding search for the best ways to quantify and analyze our world. Their success has liberated us from “the shackles of our physical impressions of space”—and of the particular and the concrete—“enabling imagination to wander far beyond the tangible world we live in, and into the marvels of generality” [ p. 154].

From The Herald-Tribune
by Donal O'Shea

The book is visually exquisite, great care having been taken with illustrations and figures. Mazur's discussion of the emergence of particular symbols affords the reader an overview of the often difficult primary literature. He carefully explains the relative advantages and disadvantages of different notations, allowing readers to see how good notation opens up new realms of thought. Although the book can be enjoyed at many levels, it will most reward those who have some memory of high school algebra and beginning calculus. I can't imagine any reader, however inattentive, escaping without learning a good deal of history and mathematics. For me, the biggest takeaway is the intellectual debt that every human being, no matter in what society, owes to those who went before.

From Mathematical Association of America
by Tushar Das
Mazur does an excellent job of weaving together a wonderful culturally-rich tapestry, within which he threads the evolution of mathematical notation. His theme is a “tough sell” and therefore the Guggenheim Foundation and his publishers at Princeton University Press should be commended for supporting such an endeavor.

From Ricochet
by John Walker

This book, written with the extensive source citations of a scholarly work yet accessible to any reader familiar with arithmetic and basic algebra, traces the often murky origins of this essential part of our intellectual heritage….
This book is a treasure chest of information about how the language of science came to be. We encounter a host of characters along the way, not just great mathematicians and scientists, but scoundrels, master forgers, chauvinists, those who preserved precious manuscripts and those who burned them, all leading to the symbolic language in which we so effortlessly write and do mathematics today.

From Leonardo, Phil Dyke
From the outset let me say that this is a good book. It is well written by an experienced author and is full of interesting facts about how the symbols used in mathematics have arisen. It would certainly interest anyone who studies the history of mathematics. Even for the enthusiast, however, there is danger as the topic lends itself to being a list of facts. This author avoids this trap mostly through his engaging style but also by breaking the book into short chapters, 24 of them, and avoiding being completely chronological. The first collection of chapters concerns the origins of the numerals themselves, some origins are of course shrouded in obscurity and controversy, and where this is the case the alternatives are honestly treated by the author. The second collection is about algebra and is consequently more about the culture of development and use. This contains a wealth of information and strays into anthropology and religion including more of the beliefs of the author. Researching some of the origins of algebra remains an active area and new forensic techniques are helping to disentangle who did what when. The third and final section on the power of symbols is more philosophical and, dare I say, a little bit self-indulgent. It is still a good read though.

From The European Mathematics Society
by A. Bultheel

Mazur treats only a subset of F. Cajori's monumental A History of Mathematical Notation (Dover, 1993 first edition 1922) and there is overlap with many other mathematical history books, but Mazur adds new findings and insights and it is so much more entertaining . . . and these features make it an interesting addition to the existing literature for anybody with only a slight interest in mathematics or its history.
Click here for full review from the European Mathematics Society.

From Science Magazine
by Gaia Donati

Joseph Mazur’s Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers is a figurative cabinet rich with such curiosities. However, the book is more than a collection of fun facts about mathematics and the evolution of its language....
As Mazur sets out to address such easily overlooked aspects, he also reaffirms their relevance, showing how rich and complex the topic is....
It is gripping to read about the contributions, big or small, of so many human minds—from real game-changers such as René Descartes, Gottfried Leibniz, and Isaac Newton to less-familiar names such as Robert Recorde (who introduced our equal sign) and François Viète (who used dedicated letters to designate knowns and unknowns in a polynomial equation, an idea later formalized by Descartes)....
Thanks to Mazur’s playful approach to the subject, Enlightening Symbols offers an enjoyable read.
Click here for full review in Science

From Nature
by George Sziro

This is a nuanced, intelligently framed chronicle packed with nuggets — such as the fact that Hindus, not Arabs, introduced Arabic numerals. In a word: enlightening.

For the full review go to Reviews on this site

From Publisher's Weekly
Mazur (Euclid in the Rainforest) gives readers the fascinating history behind the mathematical symbols we use, and completely take for granted, every day. Mathematical notation turns numbers into sentences—or, to the uninitiated, a mysterious and impenetrable code. Mazur says the story of math symbols begins some 3,700 years ago, in ancient Babylon, where merchants incised tallies of goods on cuneiform tablets, along with the first place holder—a blank space. Many early cultures used letters for both numbers and an alphabet, but convenient objects like rods, fingers, and abacus beads, also proved popular. Mazur shows how our “modern” system began in India, picking up the numeral “zero” on its way to Europe, where it came into common use in the 16th century, thanks to travelers and merchants as well as mathematicians like Fibonacci. Signs for addition, subtraction, roots, and equivalence followed, but only became standardized through the influence of scientists and mathematicians like René Descartes and Gottfried Leibniz. Mazur’s lively and accessible writing makes what could otherwise be a dry, arcane history as entertaining as it is informative.

From The Guardian
If you enjoy reading about history, languages and science, then you'll enjoy this book. Basically, the author explores where all those mathematical symbols came from, starting with counting numbers and algebraic symbols and ending with the primary operators of modern maths. Even more interesting (to me at least), the author also discusses how symbols affect and inspire mathematical thought. In addition to diagrams, a useful double-page timeline is inset between Parts 1 and 2 that describes the significant initiators, starting with Plato's Academy in 500 BC and progressing upwards past Newton's Principia in 1687 AD. The best part is the writing is compelling enough that you don't have to be a mathematician to enjoy this informative book.

From Library Journal
The author surveys the work of earlier investigators and, where there is disagreement, gives fair weight to the different competing conjectures. For algebraic symbolism, Mazur nicely summarizes the historic record, which is much shorter and therefore less open to controversy. Today, this notation seems so natural that it is hard to imagine doing mathematical work without it. Mazur emphasizes the strength of the system, describing how, once expressed in its algebraic form, problems seem to solve themselves and even to suggest areas for further research. The concluding chapters discuss how the latest developments in cognitive science shed light on how using good notation helps to produce clear thinking. VERDICT Mazur delivers a solid exposition of an element of mathematics that is fundamental to its history. Recommended.

Enlightening Symbols: A Short History of Mathematical Notation and its Hidden Powers

Traversing mathematical history, and the foundations of numerals in different cultures, Enlightening Symbols looks at how historians have disagreed over the origins of the numerical system for the past two centuries. It follows the transfigurations of algebra, from a rhetorical style to a symbolic one, demonstrating that most of algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. The book also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.
From words to abbreviations to symbols, this book examines how math evolved to the familiar forms we use today.

Now available in Japanese and Italian, and soon to appear in Chinese, Korean, Turkish, Portuguese, and Czech.

Selected Works

What are the chances? This is the question we ask ourselves when we encounter the freakiest and most seemingly impossible coincidences, like the woman who won the lottery four times or the fact that Lincoln’s dreams foreshadowed his own assassination.
Hardly any math symbols were used before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve to what we know of today? Enlightening Symbols explains the fascinating history behind the development of our current mathematical notation system, shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.
Princeton University Press (2010). A book about the nature of gambling, emphasizing the dangers and pitfalls of feeling lucky. It will investigate the hooks of gambling and what makes gamblers feel lucky. Using both mathematics and psychology it will illustrate the misconceptions of luck, explore what it means to have a good chance, and to create an awareness of expected outcomes.
Published by Dutton in April 2007. Now available in bookstores. "THIS is one of the most fascinating science books I have ever read . . . Mazur has succeeded in telling a fresh and untold story with clarity and style." -- The New Scientist
One of Choice's Outstanding Academic Titles of the Year 2005-- “This book is a treasure of human experience and intellectual excitement.”
Editor of the revived classic by Tobias Dantzig, Number: The Language of Science.