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. |
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 Yü 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 |
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Common terms and phrases
Abbasid abstract academies al-Ma'mun algebra Arabic Arabic-Islamic argues arithmetic astronomical autonomy Baghdad become Bloor Boole Bourbaki Brahmagupta calculus Cantor Cardan Cauchy century chapter China Chinese mathematics claims Classical collective competition concept conjecture cultural Durkheim equations established everyday example experience fact formal functions G.H. Hardy Galois geometry Greek mathematics history of mathematics ideas Indian mathematics individual intellectual Islamic Japanese mathematical Johann Bernoulli Kleene knowledge Kronecker Leibniz logic material mathe mathematical activity mathematical community mathematical objects mathematical workers mathematicians mathematics of survival maticians matics method modern naive realism nature networks Newton notation organizational period philosophy political problems professional proofs propositions pure mathematics reality reflected relationship representations Restivo robber baron roots scientific scientists social construction social interests social practice society sociology of mathematics sociology of science solution Spengler structure Suan symbols Tartaglia theorem theory thought tion traditional translated truth University York