## A History of Mathematics: From Mesopotamia to ModernityA History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader. |

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### Contents

Introduction | 1 |

Babylonian mathematics | 14 |

Greeks and origins | 33 |

Greeks practical and theoretical | 57 |

Chinese mathematics | 78 |

Islam neglect and discovery | 101 |

Understanding the scientific revolution | 133 |

The calculus | 161 |

Geometries and space | 189 |

Modernity and its anxieties | 213 |

A chaotic end? | 235 |

Conclusion | 260 |

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abu Kamil al-Biruni al-Kashi al-Khwarizmi al-Samaw'al al-Uqlidisi algebra ancient answer Appendix Arabic Archimedes argument axioms Babylonian Babylonian mathematics calculation called century Chinese mathematics circle classical consider construction counting rods cube curve decimal defined Descartes discovery equal equation Euclid Euclidean Euclidean geometry example fact Fauvel and Gray follows formula fractions give given Greek mathematics Hilbert historians history of mathematics idea important infinitely small Islamic mathematics language later Leibniz length machine mathematicians means method modern multiply Newton Nine Chapters non-Euclidean geometry notation particular period postulate practical problem proof proposition Ptolemy Qin Jiushao quadratic question radius ratio reader real numbers rectangle Reidemeister moves result revolution right angles rules scientific seems sexagesimals side simple solve space square root straight line subtract suppose symbol tangent textbook texts theorem theory tradition translation triangle writing