Cover -- Copyright page -- Title page -- Introduction -- Contents -- 1 The Ancient World -- 1.1 Prehistory -- 1.2 Egypt -- 1.2.1 Egyptian Mathematics -- 1.2.2 The New Kingdom -- 1.3 Mesopotamia -- 1.3.1 Positional Notation -- 1.3.2 Babylon -- 1.3.3 The Iron Empires -- For Further Reading -- 2 The Classical World -- 2.1 The Greeks -- 2.1.1 Thales and Pythagoras -- 2.1.2 The Wars of Greece -- 2.1.3 Mathematicians of the Golden Age -- 2.1.4 Mathematicians and the Academy -- 2.1.5 The Hellenistic Kingdoms -- 2.2 The Romans -- 2.2.1 Archimedes -- 2.2.2 The Fall of the Republic -- 2.2.3 The Return to Order -- 2.2.4 Decline and Fall -- For Further Reading -- 3 China and India -- 3.1 China -- 3.1.1 Positional Numeration -- 3.1.2 The Rise of Imperial China -- 3.1.3 Partition and Unification -- 3.1.4 The Mongols -- 3.2 India -- 3.2.1 The Sulbasutras -- 3.2.2 Early India -- 3.2.3 Aryabhata -- 3.2.4 Varahamihira -- 3.2.5 Brahmagupta -- 3.2.6 Southern India -- 3.3 The Importance of Proof -- For Further Reading -- 4 The Islamic World -- 4.1 Early Islam -- 4.1.1 Umayyads and Abbasids -- 4.1.2 Al Khwarizmı -- 4.1.3 The Biblical Value of pi -- 4.2 The Rise and Fall of Dynasties -- 4.2.1 Translating and Transcending -- 4.2.2 The Geometers of the Buyid Court -- 4.2.3 Decimal Notation -- 4.2.4 The Seljuqs -- 4.2.5 Al-Khayyamı -- 4.3 The Age of Invasion -- 4.3.1 Al-Samaw'al -- 4.3.2 The Mongol Era -- 4.4 Andalusia -- 4.4.1 The Mathematicians of the Party Kings -- 4.4.2 The Mathematical Diaspora -- For Further Reading -- 5 The Middle Ages -- 5.1 Norman Sicily -- 5.1.1 Adelard of Bath -- 5.1.2 The Hohenstaufens -- 5.1.3 Leonardo of Pisa -- 5.1.4 The Translators -- 5.2 Early Medieval France -- 5.2.1 Gerbert of Aurillac -- 5.2.2 The University of Paris -- 5.2.3 Paladins, Troubadours, and Translators -- 5.2.4 Architecture -- 5.2.5 Jordanus Nemorarius.

5.2.6 The Encyclopedists -- 5.3 High Medieval France -- 5.3.1 Exiles and Captives -- 5.3.2 Plague and War -- 5.3.3 Oresme -- 5.3.4 Chuquet -- For Further Reading -- 6 Renaissance and Reformation -- 6.1 The Italian Peninsula -- 6.1.1 Mathematics and the Liberal Arts -- 6.1.2 The Secret of Solving the Cubic -- 6.2 Central Europe -- 6.2.1 Peuerbach and Regiomontanus -- 6.2.2 Albrecht Dürer -- 6.2.3 The Lutheran Reformation -- 6.2.4 German Arithmeticians -- 6.2.5 Trigonometry -- For Further Reading -- 7 Early Modern Europe -- 7.1 France -- 7.1.1 Viète -- 7.1.2 The Age of Fermat and Pascal -- 7.2 The Low Countries -- 7.2.1 Simon Stevin -- 7.2.2 The Changing Battlefield -- 7.2.3 Descartes -- 7.2.4 The Dutch Masters -- 7.2.5 Leibniz -- 7.2.6 The Great Northern War -- 7.3 Great Britain -- 7.3.1 Robert Recorde -- 7.3.2 Elizabeth -- 7.3.3 Gerardus Mercator -- 7.3.4 Thomas Harriot -- 7.3.5 Scotland -- 7.3.6 Royalists and Parliamentarians -- 7.3.7 The Restoration -- 7.3.8 The Glorious Revolution -- For Further Reading -- 8 The Eighteenth Century -- 8.1 Great Britain -- 8.1.1 Probability -- 8.1.2 The Theory of the Moon -- 8.1.3 Expatriates in Venice -- 8.1.4 Maclaurin -- 8.1.5 Mathematics and Coffee -- 8.2 Central and Eastern Europe -- 8.2.1 The Bernoullis -- 8.2.2 Leonhard Euler -- 8.2.3 Maria Agnesi -- 8.2.4 Berlin -- 8.3 France -- 8.3.1 D'Alembert -- 8.3.2 The Stability of the Solar System -- 8.3.3 The Revolution -- 8.3.4 Napoleon and his Mathematicians -- 8.3.5 Gauss -- 8.3.6 Germain -- 8.3.7 Projective Geometry -- For Further Reading -- 9 The Nineteenth Century -- 9.1 France -- 9.1.1 The Revolution of 1830 -- 9.1.2 Railroads and Computers -- 9.1.3 Fermat's Last Theorem -- 9.1.4 The Second Empire -- 9.2 Great Britain -- 9.3 Italy -- 9.4 Germany -- 9.4.1 Jacobi -- 9.4.2 Gottingen and Berlin -- 9.4.3 Bismarck and von Moltke -- 9.4.4 Klein and Lie.

9.4.5 The Birth of Three Nations -- For Further Reading -- 10 The United States -- 10.1 From Colony to Country -- 10.1.1 Benjamin Banneker -- 10.1.2 Nathaniel Bowditch -- 10.1.3 Robert Adrain -- 10.1.4 William Rowan Hamilton -- 10.1.5 Benjamin Peirce -- 10.1.6 The Civil War -- 10.1.7 Vectors Victorious -- 10.1.8 The Howland Will -- 10.2 The Gilded Age -- 10.2.1 The Rise of American Mathematics -- 10.2.2 Oil -- 10.2.3 Chicago -- 10.2.4 Progressivists and Imperialists -- 10.2.5 Princeton and the Presidency -- For Further Reading -- 11 The Modern World -- 11.1 Before the Great War -- 11.1.1 Kovalevskaya -- 11.1.2 The Stockholm Prizes -- 11.1.3 Mathematicians and Antisemitism -- 11.1.4 Cape Colony -- 11.2 The Era of the Great War -- 11.2.1 Ballistics -- 11.2.2 Suffrage -- 11.2.3 Painlevé and Borel -- 11.2.4 Noether and Courant -- 11.2.5 The Black Chamber -- 11.3 The Depression Era -- 11.3.1 Gertrude Blanch -- 11.3.2 Poland -- 11.3.3 Austria and Germany -- 11.3.4 The Soviet Union -- 11.4 World War Two -- 11.4.1 Applied Mathematics -- 11.4.2 Science Fiction -- 11.4.3 Appeasement and War -- 11.4.4 The Two Enigmas -- 11.4.5 The United States -- For Further Reading -- Epilog -- Bibliography -- Figure Citations -- Index -- About the Author.