Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers [NOOK Book]

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 ...

See more details below
Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook - Course Book)
$16.49
BN.com price
(Save 44%)$29.95 List Price

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.

Read More Show Less

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

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
Read More Show Less

Product Details

  • ISBN-13: 9781400850112
  • Publisher: Princeton University Press
  • Publication date: 3/23/2014
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition description: Course Book
  • Pages: 312
  • Sales rank: 343,449
  • File size: 26 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.
Read More Show Less

Table of Contents

Introduction ix
Definitions xxi
Note on the Illustrations xxiii
Part 1 Numerals 1
1. Curious Beginnings 3
2. Certain Ancient Number Systems 10
3. Silk and Royal Roads 26
4. The Indian Gift 35
5. Arrival in Europe 51
6. The Arab Gift 60
7. Liber Abbaci 64
8. Refuting Origins 73
Part 2 Algebra 81
9. Sans Symbols 85
10. Diophantus’s Arithmetica 93
11. The Great Art 109
12. Symbol Infancy 116
13. The Timid Symbol 127
14. Hierarchies of Dignity 133
15. Vowels and Consonants 141
16. The Explosion 150
17. A Catalogue of Symbols 160
18. The Symbol Master 165
19. The Last of the Magicians 169
Part 3 The Power of Symbols 177
20. Rendezvous in the Mind 179
21. The Good Symbol 189
22. Invisible Gorillas 192
23. Mental Pictures 210
24. Conclusion 216
Appendix A Leibniz’s Notation 221
Appendix B Newton’s Fluxion of xn 223
Appendix C Experiment 224
Appendix D Visualizing Complex Numbers 228
Appendix E Quaternions 230
Acknowledgments 233
Notes 235
Index 269

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)