Table of Contents

Acknowledgements xi Preface to the First Edition xii Preface to the Second Edition xvii Chapter 1: The History of Mathematics: Alternative Perspectives 1 A Justification for This Book 1 The Development of Mathematical Knowledge 3 Mathematical Signposts and Transmissions Across the Ages 12 Chapter 2: Mathematics from Bones, Strings and Standing Stones 23 Beginnings: The Ishango Bone 23 Knotted Strings from South America: The Inca Quipu 28 The Emergence of Written Number Systems: A Digression 41 Mayan Numeration 49 Chapter 3 The Beginnings of Written Mathematics: Egypt 57 The Urban Revolution and its African Origins 57 Sources of Egyptian Mathematics 59 Number Recording Among the Egyptians 61 Egyptian Arithmetic 63 Egyptian Algebra: The Beginnings of Rhetorical Algebra 76 Egyptian Geometry 81 Chapter 4 The Beginnings of Written Mathematics: Babylonia 91 Sources of Babylonian Mathematics 95 The Babylonian Number System 96 Babylonian Algebra 108 Babylonian Geometry 113 Chapter 5 Egyptian and Babylonian Mathematics: An Assessment 125 Chapter 6 Ancient Chinese Mathematics 130 Background and Sources 130 The Development of Chinese Numerals 140 Chinese Magic Squares (and Other Designs) 148 Mathematics from the Chiu Chang 156 Chapter 7 Special Topics in Chinese Mathematics 178 The 'Piling-up of Rectangles': The Pythagorean Theorem in China 180 Estimation of tt 188 Solution of Higher-order Equations and Pascal's Triangle 197 Indeterminate Analysis in China 205 Chinese Mathematics: A Final Assessment 211 Chapter 8 Ancient Indian Mathematics 215 A Restatement of Intent and a Brief Historical Sketch 215 Maths from Bricks: Evidence from the Harappan Culture 221 Mathematics from the Vedas 224 Early Indian Numerals and Their Development 239 Jaina Mathematics 249 Mathematics on the Eve of the Classical Period 256 Chapter 9 Indian Mathematics: The Classical Period and After 264 Major Indian Mathematician-Astronomers 265 Indian Algebra 272 Indian Trigonometry 280 Kerala Mathematics 286 Other Notable Contributions 294 Chapter 10 Prelude to Modern Mathematics: The Arab Contribution 301 Historical Background 301 Major Arab Mathematicians 304 The Arab Role in the Rise and Spread of Indian Numerals 311 Arab Arithmetic 316 Arab Algebra 324 Arab Geometry 333 Arab Trigonometry 338 The Arab Conhibution: A Final Assessment 344 Reflections 349 The History of Mathematics: Alternative Perspectives 349 Mathematics from Bones, Strings and Standing Stones 357 The Beginnings of Written Mathematics: Egypt 369 The Beginnings of Written Mathematics: Babylonia 377 Ancient Chinese Mathematics 385 Special Topics in Chinese Mathematics 389 Ancient Indian Mathematics 395 Indian Mathematics: The Classical Period and After 406 Prelude to Modem Mathematics: The Arab Contribution 417 Bibliography 425 Name Index 441 Subject Index 447

About the Author

George Gheverghese Joseph was born in Kerala, southern India, and lived in India for nine years. His family then moved to Mombassa in Kenya, where he received his schooling. He studied at the University of Leicester, and later at the University of Manchester, where he completed his postgraduate studies. He has worked in various occupations that have taken him to places all over the world, including East and Central Africa, India, Papua New Guinea, and South East Asia.

Reviews

Enthralling... After reading it, we cannot see the past in the same comforting haze of age-old stories, faithfully and uncritically retold from teacher to pupil down the years... Invaluable for mathematics teachers at all levels. New Scientist What is valuable here is the unified approach that Joseph brings ... and the non-technical clarity that the attempt to reorder historical priorities and educate his readers out of their European prejudices requires. The Times Literary Supplement A magnificent contribution... The conventional wisdom being challenged is that there is one mathematics, largely invented by Europeans. Joseph demonstrates convincingly that the conventional wisdom is false... A rich and fascinating canvas. Race & Class If only this book had been available when I was a student!... This book will carry you to a deeper place: an appreciation of the many non-European roots of mathematics. -- Jerry Lenz Mathematics Teacher