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.

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Review 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 Library Journal
The arithmetical notation we see today developed over many centuries. Although roman numerals still pop up now and then (look at how we number the Super Bowls), the system of decimal place-value notation and so-called Arabic numerals are used almost universally. In this book, Guggenheim Fellow Mazur (emeritus, mathematics, Marlboro Coll.; Euclid in the Rainforest) traces the evolution of these symbols from the earliest archaeological evidence to the present. 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.—Harold D. Shane, emeritus, Baruch Coll. Lib., CUNY


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



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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.

Selected Works

Nonfiction
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.”
--Choice
Editor of the revived classic by Tobias Dantzig, Number: The Language of Science.