Mathematics in Historical Context

What would Newton see if he looked out his bedroom window? This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected...

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What would Newton see if he looked out his bedroom window? This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.

Jeff Suzuki was born in California, and received his B.A. in mathematics and history from California State University at Fullerton, and M.A. and Ph.D. in mathematics from Boston University. His previous publications include A History of Mathematics (Prentice-Hall, 2002); A Brief History of Impossibility (Mathematics Magazine 81, 27–38); Lagrange’s Proof of the Fundamental Theor...

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Jeff Suzuki was born in California, and received his B.A. in mathematics and history from California State University at Fullerton, and M.A. and Ph.D. in mathematics from Boston University. His previous publications include A History of Mathematics (Prentice-Hall, 2002); A Brief History of Impossibility (Mathematics Magazine 81, 27–38); Lagrange’s Proof of the Fundamental Theorem of Algebra (American Mathematical Monthly, 113, 705–714); and The Lost Calculus: Tangency and Optimization Without Limits (Mathematics Magazine, 78, 339–353), for which he won the Carl B. Allendoerfer Award from the MAA for an article of expository excellence. He is an Associate Professor of Mathematics at Brooklyn College.

Introduction vii
1 The Ancient World 1
1.1 Prehistory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Egypt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Mesopotamia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 The Classical World 15
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Introduction vii
1 The Ancient World 1
1.1 Prehistory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Egypt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Mesopotamia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 The Classical World 15
2.1 The Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The Romans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 China and India 55
3.1 China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 The Importance of Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 The Islamic World 83
4.1 Early Islam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 The Rise and Fall of Dynasties . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3 The Age of Invasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4 Andalusia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5 The Middle Ages 119
5.1 Norman Sicily . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.2 Early Medieval France . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3 High Medieval France . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6 Renaissance and Reformation 157
6.1 The Italian Peninsula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.2 Central Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7 Early Modern Europe 185
7.1 France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.2 The Low Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
7.3 Great Britain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
8 The Eighteenth Century 231
8.1 Great Britain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
8.2 Central and Eastern Europe . . . . . . . . . . . . . . . . . . . . . . . . . . 242
8.3 France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9 The Nineteenth Century 277
9.1 France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
9.2 Great Britain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
9.3 Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
9.4 Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
10 The United States 311
10.1 From Colony to Country . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
10.2 The Gilded Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
11 The Modern World 337
11.1 Before the Great War . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
11.2 The Era of the Great War . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
11.3 The Depression Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
11.4 World War Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
Epilog 385
Bibliography 387
Figure Citations 395
Index 397
About the Author 409
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