Reviews for Enlightening Symbols
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.
by John Walker
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 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 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.
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.
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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.