Ranging from the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, this book points out that human beings everywhere have been capable of advanced and innovative mathematical thinking. It shows us the deep influence that the Egyptians and Babylonians had on the Greeks.

Preface to the Third Edition xi Preface to the First Edition xxiii Chapter One: 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 Two: Mathematics from Bones, Strings, and Standing Stones 30 Beginnings: The Ishango Bone 30 Native Americans and Their Mathematics 45 The Emergence of Written Number Systems: A Digression 58 Mayan Numeration 66 Chapter Three: The Beginnings of Written Mathematics: Egypt 79 The Urban Revolution and Its African Origins 79 Sources of Egyptian Mathematics 81 Number Recording among the Egyptians 84 Egyptian Arithmetic 88 Egyptian Algebra: The Beginnings of Rhetorical Algebra 102 Egyptian Geometry 109 Egyptian Mathematics: A General Assessment 119 Chapter Four: The Beginnings of Written Mathematics: Mesopotamia 125 Fleshing Out the History 125 Sources of Mesopotamian Mathematics 132 The Mesopotamian Number System 136 Babylonian Algebra 150 Babylonian Geometry 159 Chapter Five: Egyptian and Mesopotamian Mathematics: An Assessment 177 Changing Perceptions 178 Neglect of Egyptian and Mesopotamian Mathematics 181 The Babylonian-Egyptian-Greek Nexus: A Seamless Story or Three Separate Episodes? 184 Chapter Six: Ancient Chinese Mathematics 188 Background and Sources 188 The Development of Chinese Numerals 198 Chinese Magic Squares (and Other Designs) 206 Mathematics from the Jiu Zhang (Suan Shu) 215 Chapter Seven: Special Topics in Chinese Mathematics 246 The "Piling-Up of Rectangles": The Pythagorean Theorem in China 248 Estimation of p 261 Solution of Higher-Order Equations and Pascal's Triangle 270 Indeterminate Analysis in China 282 The Influence of Chinese Mathematics 296 Chinese Mathematics: A Final Assessment 301 Chapter Eight: Ancient Indian Mathematics 311 A Restatement of Intent and a Brief Historical Sketch 311 Math from Bricks: Evidence from the Harappan Culture 317 Mathematics from the Vedas 323 Early Indian Numerals and Their Development 338 Jaina Mathematics 349 Mathematics on the Eve of the Classical Period 356 Chapter Nine: Indian Mathematics: The Classical Period and After 372 Major Indian Mathematician-Astronomers 373 Indian Algebra 380 Indian Trigonometry 392 Other Notable Contributions 403 Chapter Ten: A Passage to Infinity: The Kerala Episode 418 The Actors 418 Transmission of Kerala Mathematics 435 Chapter Eleven: Prelude to Modern Mathematics: The Islamic Contribution 450 Historical Background 450 Major Medieval Islamic Mathematicians 455 Medieval Islam's Role in the Rise and Spread of Indian Numerals 461 Arithmetic in the Islamic World 466 Algebra in the Islamic World 475 Islamic Algebra and Its Influence on Europe 486 Geometry in the Islamic World 487 Trigonometry in the Islamic World 496 Mathematics from Related Sources 503 The Islamic Contribution: A Final Assessment 508 References 521 Name Index 543 Subject Index 549

Praise for Princeton's previous editions: "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 Praise for Princeton's previous editions: "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."--Times Literary Supplement