## Mathematics in Society and History: Sociological InquiriesThis is the first book by a sociologist devoted exclusively to a general sociology of mathematics. The author provides examples of different ways of thinking about mathematics sociologically. The survey of mathematical traditions covers ancient China, the Arabic-Islamic world, India, and Europe. Following the leads of classical social theorists such as Emile Durkheim, Restivo develops the idea that mathematical concepts and ideas are collective representations, and that it is mathematical communities that create mathematics, not individual mathematicians. The implications of the sociology of mathematics, and especially of pure mathematics, for a sociology of mind are also explored. In general, the author's objective is to explore, conjecture, suggest, and stimulate in order to introduce the sociological perspective on mathematics, and to broaden and deepen the still narrow, shallow path that today carries the sociology of mathematics. This book will interest specialists in the philosophy, history, and sociology of mathematics, persons interested in mathematics education, students of science and society, and people interested in current developments in the social and cultural analysis of science and mathematics. |

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### Contents

Mathematics and Culture | 3 |

An introduction to Oswald Spenglers pioneering work on numbers | 9 |

The Mathematics of Survival in China | 23 |

From the legend of Yu the Great and the Lo River tortoise to the golden age | 30 |

Indian Mathematics A History of Episodes | 47 |

Mathematics and Renaissance in Japan | 55 |

Conflict Social Change and Mathematics in Europe | 61 |

African Mathematics and the Problem of Ethnos | 89 |

Mathematics as Representation | 99 |

Foundations of the Sociology of Pure Mathematics | 129 |

The Social Relations of Pure Mathematics | 149 |

BIBLIOGRAPHIC EPILOGUE | 177 |

NAME INDEX | 189 |

195 | |

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### Common terms and phrases

Abbasid abstract Academie al-Battani al-Khwarizmi al-Ma'mun algebra Arab ARABIC-ISLAMIC MATHEMATICS Archimedes argues arithmetic astronomical autonomy Baghdad Boole Brahmagupta calculus Caliphs Cantor Cardan Cauchy chapter China Chinese mathematics Chiu Chang Classical competition concept conjecture cultural equations established Euclid everyday example fact formal G.H. Hardy Galois geometry golden age Greek mathematics history of mathematics Hsiao-wu ideas Indian mathematics intellectual Islamic Japanese mathematical Kleene knowledge large numbers Leibniz logic Mahavira manuscripts mathe mathematical activity mathematical community mathematical objects mathematical workers mathematicians mathematics of survival maticians matics method Needham networks Newton notation organizational period political problems proofs pure mathematics Ramanujan relationship religious representations Restivo roots rules scholars scientific social construction social practice society sociology of mathematics sociology of science solution solving Spengler structure Suan Shu Suan-ching symbols Tartaglia tenth century theorem theory thought tion traditions translated University Western mathematics writing

### Popular passages

Page 199 - EPISTEME A SERIES IN THE FOUNDATIONAL, METHODOLOGICAL, PHILOSOPHICAL, PSYCHOLOGICAL, SOCIOLOGICAL AND POLITICAL ASPECTS OF THE SCIENCES, PURE AND APPLIED...