Synopses & Reviews
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics.
The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text.
Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.
Review
"The Mathematics of Egypt, Mesopotamia, China, India, and Islam is a wonderful collection, for which Victor Katz is to be commended. This book is a one-stop source for numerous original mathematical texts in translation. I cannot overemphasize how wonderful it is to have this large, exquisite selection of . . . mathematical texts together in one volume. . . . Every history of mathematics teacher will want a copy of this book in their personal library as well as in the library of their college or university."--James V. Rauff, Mathematics and Computer Education
Review
This pioneering work provides English translations of mathematical texts from each of these regions and cultures, and a better understanding of their contributions to mathematics. There are nuggets of information difficult to find elsewhere. The use of non-mathematical sources, particularly letters and administrative documents from Egypt and Mesopotamia, reveals the practical applications of mathematics and the scribes who composed and used the documents...An essential resource for anyone wishing to know more about how the mathematics of the different regions influenced and shaped the development of world mathematics. -- George Gheverghese Joseph, Nature We're aware that the ancient cultures were mathematically advanced. Now translations of early texts from five key regions are available together for the first time, and put into context by experts. -- Nature Physics The corrections to the Eurocentrism that understandably characterized Western assays of the intellectual history of the planet early on must inevitably be applied to the history of mathematics. Editor Katz and his scholarly coauthors have greatly advanced the process with this one-volume sourcebook...The introductory essays that precede each section are lucidly written, well within the reach of an undergraduate math major. Katz asks more or less rhetorically 'how much effect the mathematics of these civilizations had on what is now world mathematics of the twenty-first century.' This invaluable book will help significantly in formulating an answer. -- M. Schiff, Choice This book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom. -- L'Enseignement Mathematique The Mathematics of Egypt, Mesopotamia, China, India, and Islam is a wonderful collection, for which Victor Katz is to be commended. This book is a one-stop source for numerous original mathematical texts in translation. I cannot overemphasize how wonderful it is to have this large, exquisite selection of . . . mathematical texts together in one volume. . . . Every history of mathematics teacher will want a copy of this book in their personal library as well as in the library of their college or university. -- James V. Rauff, Mathematics and Computer Education What we have here is a useful selection, one that should be of interest to specialists in world history or in the history of the sciences in any of these culture areas and, in particular, to scholars who are engaged with the history of mathematics as specialists or because of its role as a tool. -- Tom Archibald, Isis [This] is the biggest sourcebook containing the newest fruit of historical research and that is why the book can replace older sources for the history of mathematics. -- EMS Newsletter
Review
"This pioneering work provides English translations of mathematical texts from each of these regions and cultures, and a better understanding of their contributions to mathematics. There are nuggets of information difficult to find elsewhere. The use of non-mathematical sources, particularly letters and administrative documents from Egypt and Mesopotamia, reveals the practical applications of mathematics and the scribes who composed and used the documents...An essential resource for anyone wishing to know more about how the mathematics of the different regions influenced and shaped the development of world mathematics."--George Gheverghese Joseph, Nature
Review
"We're aware that the ancient cultures were mathematically advanced. Now translations of early texts from five key regions are available together for the first time, and put into context by experts."--Nature Physics
Review
"The corrections to the Eurocentrism that understandably characterized Western assays of the intellectual history of the planet early on must inevitably be applied to the history of mathematics. Editor Katz and his scholarly coauthors have greatly advanced the process with this one-volume sourcebook...The introductory essays that precede each section are lucidly written, well within the reach of an undergraduate math major. Katz asks more or less rhetorically 'how much effect the mathematics of these civilizations had on what is now world mathematics of the twenty-first century.' This invaluable book will help significantly in formulating an answer."--M. Schiff, Choice
Review
"This book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom."--L'Enseignement Mathematique
Review
"What we have here is a useful selection, one that should be of interest to specialists in world history or in the history of the sciences in any of these culture areas and, in particular, to scholars who are engaged with the history of mathematics as specialists or because of its role as a tool."--Tom Archibald, Isis
Review
"[This] is the biggest sourcebook containing the newest fruit of historical research and that is why the book can replace older sources for the history of mathematics."--EMS Newsletter
Review
Joseph Warren Dauben, Winner of the 2012 Albert Leon Whiteman Memorial Prize, American Mathematical Society
Synopsis
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context.
The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics.
The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text.
Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.
Synopsis
"This is the first major sourcebook in English for the history of mathematics in Egypt, Mesopotamia, India, China, and the Middle East. It is notable for the wide variety of sources, which will challenge preconceptions everywhere, as well as for the clarity and force of the introductions to the mathematical cultures on display. The authors are leading authorities in their subjects, and the scholarship is of the highest order. This book will be an irreplaceable source for a general mathematical readership."
--Jeremy J. Gray, author of The History of Mathematics: A Reader and The Hilbert Challenge"Unique and timely, this book will enrich students' and general mathematical readers' understanding of the depth and power of non-Western mathematics for decades to come, and I will be first in line to buy it. It presents fuller portraits of the mathematical histories of these five non-Western cultures than are found in other books. One of the greatest strengths of the book is its scholarship. All of the authors are established or renowned scholars, and they have done a uniformly good job of selecting readings that give a cross-section of their subject."--Glen Van Brummelen, coeditor of Mathematics and the Historian's Craft
Synopsis
"This is the first major sourcebook in English for the history of mathematics in Egypt, Mesopotamia, India, China, and the Middle East. It is notable for the wide variety of sources, which will challenge preconceptions everywhere, as well as for the clarity and force of the introductions to the mathematical cultures on display. The authors are leading authorities in their subjects, and the scholarship is of the highest order. This book will be an irreplaceable source for a general mathematical readership."--Jeremy J. Gray, author of The History of Mathematics: A Reader and The Hilbert Challenge
"Unique and timely, this book will enrich students' and general mathematical readers' understanding of the depth and power of non-Western mathematics for decades to come, and I will be first in line to buy it. It presents fuller portraits of the mathematical histories of these five non-Western cultures than are found in other books. One of the greatest strengths of the book is its scholarship. All of the authors are established or renowned scholars, and they have done a uniformly good job of selecting readings that give a cross-section of their subject."--Glen Van Brummelen, coeditor of Mathematics and the Historian's Craft
Synopsis
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context.
The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics.
The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text.
Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.
Synopsis
"This is the first major sourcebook in English for the history of mathematics in Egypt, Mesopotamia, India, China, and the Middle East. It is notable for the wide variety of sources, which will challenge preconceptions everywhere, as well as for the clarity and force of the introductions to the mathematical cultures on display. The authors are leading authorities in their subjects, and the scholarship is of the highest order. This book will be an irreplaceable source for a general mathematical readership."--Jeremy J. Gray, author of
The History of Mathematics: A Reader and The Hilbert Challenge"Unique and timely, this book will enrich students' and general mathematical readers' understanding of the depth and power of non-Western mathematics for decades to come, and I will be first in line to buy it. It presents fuller portraits of the mathematical histories of these five non-Western cultures than are found in other books. One of the greatest strengths of the book is its scholarship. All of the authors are established or renowned scholars, and they have done a uniformly good job of selecting readings that give a cross-section of their subject."--Glen Van Brummelen, coeditor of Mathematics and the Historian's Craft
About the Author
Victor J. Katz is professor emeritus of mathematics at the University of the District of Columbia. His many books include the textbook, "A History of Mathematics: An Introduction, 2nd ed." (Addison-Wesley). He is the coeditor of "Historical Modules for the Teaching and Learning of Mathematics".
Table of Contents
Preface ix
Permissions xi
Introduction 1
Chapter 1: Egyptian Mathematics
Annette Imhausen
Preliminary Remarks 7
I. Introduction 9
a. Invention of writing and number systems 13
b. Arithmetic 14
c.Metrology 17
II. Hieratic Mathematical Texts 17
a. Table texts 18
b. Problem texts 24
III. Mathematics in Administrative Texts 40
a. Middle Kingdom texts: The Reisner papyri 40
b. New Kingdom texts: Ostraca from Deir el Medina 44
IV. Mathematics in the Graeco-Roman Period 46
a. Context 46
b. Table texts 47
c. Problem texts 48
V. Appendices 52
a. Glossary of Egyptian terms 52
b. Sources 52
c. References 54
Chapter 2: Mesopotamian Mathematics
Eleanor Robson
I. Introduction 58
a. Mesopotamian mathematics through Western eyes 58
b.Mathematics and scribal culture in ancient Iraq 62
c. From tablet to translation 65
d. Explananda 68
II. The Long Third Millennium, c. 3200-2000 BCE 73
a. Uruk in the late fourth millennium 73
b. Shuruppag in the mid-third millennium 74
c. Nippur and Girsu in the twenty-fourth century BCE 76
d. Umma and Girsu in the twenty-first century BCE 78
III. The Old Babylonian Period, c. 2000-1600 BCE 82
a. Arithmetical and metrological tables 82
b. Mathematical problems 92
c. Rough work and reference lists 142
IV. Later Mesopotamia, c. 1400-150 BCE 154
V. Appendices 180
a. Sources 180
b. References 181
Chapter 3: Chinese Mathematics
Joseph W. Dauben
Preliminary Remarks 187
I. China: The Historical and Social Context 187
II. Methods and Procedures: Counting Rods, The "Out-In" Principle 194
III. Recent Archaeological Discoveries: The Earliest Yet-Known Bamboo Text 201
IV. Mathematics and Astronomy: The Zhou bi suan jing and Right Triangles (The Gou-gu or "Pythagorean" Theorem) 213
V. The Chinese "Euclid", Liu Hui 226
a. The Nine Chapters 227
b. The Sea Island Mathematical Classic 288
VI. The "Ten Classics" of Ancient Chinese Mathematics 293
a. Numbers and arithmetic: The Mathematical Classic of Master Sun 295
b. The Mathematical Classic of Zhang Qiujian 302
VII. Outstanding Achievements of the Song and Yuan Dynasties
(960-1368 CE) 308
a. Qin Jiushao 309
b. Li Zhi (Li Ye) 323
c. Yang Hui 329
d. Zhu Shijie 343
VIII. Matteo Ricci and Xu Guangxi, "Prefaces" to the First Chinese
Edition of Euclid's Elements (1607) 366
IX. Conclusion 375
X. Appendices 379
a. Sources 379
b. Bibliographic guides 379
c. References 380
Chapter 4: Mathematics in India
Kim Plofker
I. Introduction: Origins of Indian Mathematics 385
II. Mathematical Texts in Ancient India 386
a. The Vedas 386
b. The S´ulbasutras 387
c. Mathematics in other ancient texts 393
d. Number systems and numerals 395
III. Evolution of Mathematics in Medieval India 398
a.Mathematics chapters in Siddhanta texts 398
b. Transmission of mathematical ideas to the Islamic world 434
c. Textbooks on mathematics as a separate subject 435
d. The audience for mathematics education 477
e. Specialized mathematics: Astronomical and
cosmological problems 478
IV. The Kerala School 480
a. Madhava, his work, and his school 480
b. Infinite series and the role of demonstrations 481
c. Other mathematical interests in the Kerala school 493
V. Continuity and Transition in the
Second Millennium 498
a. The ongoing development of Sanskrit mathematics 498
b. Scientific exchanges at the courts of Delhi and Jaipur 504
c. Assimilation of ideas from Islam; mathematical table texts 506
VI. Encounters with Modern Western Mathematics 507
a. Early exchanges with European mathematics 507
b. European versus "native" mathematics education in British India 508
c. Assimilation into modern global mathematics 510
VII. Appendices 511
a. Sources 511
b. References 512
Chapter 5: Mathematics in Medieval Islam
J. Lennart Berggren
I. Introduction 515
II. Appropriation of the Ancient Heritage 520
III. Arithmetic 525
IV. Algebra 542
V. Number Theory 560
VI. Geometry 564
a. Theoretical geometry 564
b. Practical geometry 610
VII. Trigonometry 621
VIII. Combinatorics 658
IX. On mathematics 666
X. Appendices 671
a. Sources 671
b. References 674
Contributors 677
Index 681