S. Restivo

Mathematics in Society and History (eBook, PDF)

Sociological Inquiries

• Format: PDF

Produktbeschreibung

This 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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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 202
• Erscheinungstermin: 1. Dezember 2013
• Englisch
• ISBN-13: 9789401129442
• Artikelnr.: 44171762

Inhaltsangabe

Prologue. Part I: Introduction. 1. Mathematics and Culture. An introduction
to Oswald Spengler's pioneering work on `numbers and culture' in The
Decline of the West. This is the source of a `weak' sociology of
mathematical traditions, and a `strong' sociology of mathematics as a
social world (mathematics as social relations and worldview). The `weak'
perspective guides the discussion in Part II, the `strong' perspective
guides the discussion in Part III. 2. Mathematics from the Ground Up. The
Social activities of everyday life in ancient societies give rise to
arithmetic and geometry, the classical forms of mathematical work. Part II:
Mathematical Traditions. 3. The Mathematics of Survival in China. From the
legend of Yu the Great and the Lo River tortoise to the `golden age' in
T'ang. 4. Mathematics in Context: The Arabic-Islamic Golden Age. A `golden
age of mathematics' (700-1400 in the Arabic-Islamic world) is sketched with
an emphasis on historical conditions and cultural settings. 5. Indian
Mathematics: A History of Episodes. Sociological highlights from the
history of Indian mathematics. 6. Mathematics and Renaissance in Japan. The
seventeenth century `renaissance' makes Japan a center of oriental
mathematical work; the mathematical revolution ends abruptly with the
consolidation of power by the Tokugawa shoguns. 7. Conflict, Social Change,
and Mathematics in Europe. `Scandals' are shown to reflect transitions to
new conditions of competition and conflict: the cases of Cardan and
Tartaglia (1540s), Newton and Leibniz (1670-1730), and Cauchy, Abel, and
Galois (1826-1832) represent key transitional scandals from the `robber
baron' era. The Cantor-Kronecker case (late nineteenth century) represents
a transition from the robber baron era to the era of `saintly politicians'
who emphasize the collective side of science in an era of competition
between `schools' of mathematics. The group of mathematicians known as
Bourbaki is a key example. Appendix 1: African Mathematics and the Problem
of Ethnoscience. Appendix 2: On Modes of Thought. Appendix 3: Mathematics
and God. Part III: Math Worlds. 8. Mathematics as Representation. Survey of
a wide range of issues, examples, and conjectures in the sociology of
mathematics that bear on the problem of representation. 9. Foundations of
the Sociology of Pure Mathematics. The sociological conditions behind
experiencing and labeling mental states and products as `pure'. 10. The
Social Relations of Pure Mathematics. Includes a sociological reading of
Boole's `laws of thought' and of Kleene's `metamathematics'. Bibliographic
Epilogue. References. Index.

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I. Introduction.- 1: Mathematics and Culture.- 2: Mathematics from the Ground Up.- II. Mathematical Traditions.- 3: The Mathematics of Survival in China.- 4: Mathematics in Context: The Arabic-Islamic Golden Age.- 5: Indian Mathematics: A History of Episodes.- 6: Mathematics and Renaissance in Japan.- 7: Conflict, Social Change, and Mathematics in Europe.- III: Math Worlds.- 8: Mathematics as Representation.- 9: Foundations of the Sociology of Pure Mathematics.- 10: The Social Relations of Pure Mathematics.- Bibliographic Epilogue.- Notes To Chapter 7.- Name Index.