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

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

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by Joseph Mazur
     
 

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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren’t available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer

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Overview

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren’t available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He 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.

Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He 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 shows how math evolved to the familiar forms we use today.

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Editorial Reviews

Publishers Weekly
02/10/2014
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. (Apr.)
From the Publisher

"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."--Publishers Weekly

"[A] fascinating narrative. . . . 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."--George Szpiro, Nature

"Mazur begins by illustrating how the ancient Incas and Mayans managed to write specific, huge numbers. Then, for more than 200 pages, he traces the history of division signs, square roots, pi, exponents, graph axes and other symbols in the context of cognition, communication, and analysis."--Washington Post

"Mazur delivers a solid exposition of an element of mathematics that is fundamental to its history."--Library Journal

"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."--European Mathematical Society

"Symbols like '+' and '=' are so ingrained that it's hard to conceive of math without them. But a new book, Enlightening Symbols: A Short History of Mathematical Notation and its Hidden Power, offers a surprising reminder: Until the early 16th century, math contained no symbols at all."--Kevin Hartnett, Boston Globe

"Enlightening Symbols retraces the winding road that has led to the way we now teach, study, and conceive mathematics. . . . Thanks to Mazur's playful approach to the subject, Enlightening Symbols offers an enjoyable read."--Gaia Donati, Science

"If you enjoy reading about history, languages and science, then you'll enjoy this book. . . . The best part is the writing is compelling enough that you don't have to be a mathematician to enjoy this informative book."--Guardian.com's GrrlScientist blog

"[I]nformative, highly readable and scholarly."--Brian Rotman, Literary Review

"[T]his insightful account of the historical development of a highly characteristic feature of the mathematical enterprise also represents a valuable contribution to our understanding of the nature of mathematics."--Eduard Glas, Mathematical Reviews Clippings

"Joseph Mazur's beautiful book Enlightening Symbols tells the story of human civilization through the development of mathematical notation. Surprises abound. . . . 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."--Donal O'Shea, Sarasota Herald-Tribune

"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.'"--Robyn Arianrhod, Notices of the AMS

"Mazur introduces the reader to major characters, weaves in relevant aspects of wider culture and gives a feel for the breadth of mathematical history. It is a useful book for both student and interested layperson alike."--Mark McCartney, London Mathematical Society

"[T]his 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."--Phil Dyke, Leonardo

"Mazur is a master story teller."--John Stillwell, Bulletin of the American Mathematical Society

Library Journal
04/01/2014
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

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Product Details

ISBN-13:
9781400850112
Publisher:
Princeton University Press
Publication date:
03/23/2014
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
312
File size:
27 MB
Note:
This product may take a few minutes to download.

Meet the Author

Joseph Mazur is the author of Euclid in the Rainforest (Plume), which was a finalist for the PEN/Martha Albrand Award, as well as The Motion Paradox (Penguin) and What’s Luck Got to Do with It? (Princeton). He lives with his wife, Jennifer, in Vermont.

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Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers 4 out of 5 based on 0 ratings. 1 reviews.
Anonymous More than 1 year ago
This is a great account of the development of mathematical symbols and the associated history of mathematics. The content is first rate, but in a text about mathematical symbols, why are so many replaced with little squares? I would think that knowing the nature of the subject matter, the publishers of the electronic edition would have taken more care to preserve the symbols used. The section on the use of Hebrew letter as numbers ends up looking like some strange game of hopskotch. 5 stars for content, minus one star for typography.