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Other titles in the Sources and Studies in the History of Mathematics and Physic series:

Conflicts Between Generalization, Rigor, and Intuition

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Conflicts Between Generalization, Rigor, and Intuition Cover

 

Synopses & Reviews

Publisher Comments:

Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there. This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries, with a detailed analysis of Lazare Carnot's and A. L. Cauchy's foundational ideas. By researching the development of the concept of negative and infinitely small numbers, the book provides a productive unity to a large number of historical sources. This approach permits a nuanced analysis of the meaning of mathematical ideas as conceived of by 18th and 19th century scientists, while illustrating the authors' actions within the context of their respective cultural and scientific communities. The result is a highly readable study of conceptual history and a new model for the cultural history of mathematics.

Synopsis:

This book deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Schubring studies often overlooked texts, in particular German and French textbooks, and reveals a much richer history than previously thought while throwing new light on major figures, such as Cauchy.

Table of Contents

* Question and Method * Paths Towards Algebraization - Development until the 18th Century. The Number Field * The development of negative numbers * Paths towards algebraization--The field of limits: The development of infinitely small quantities * Culmination of Algebraization and retour du refoulé * Le Retour du Refoulé: From the Perspective of Mathematical Concepts * Cauchy's Compromise Concept * Development of Pure Mathematics in Prussia/Germany * Conflicts Between Confinement to Geometry and Algebraization in France * Summary and Outlook * References * Appendix

Product Details

ISBN:
9780387228365
Author:
Schubring, Gert
Publisher:
Springer
Subject:
History
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
History -- Philosophy.
Subject:
History of Mathematics
Subject:
Calculus -- History.
Subject:
Mathematical analysis -- History.
Subject:
Mathematics-Calculus
Subject:
History of Mathematical Sciences
Subject:
Analysis
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Sources and Studies in the History of Mathematics and Physical Sciences
Publication Date:
June 2005
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
692
Dimensions:
235 x 155 mm 2520 gr

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Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History

Conflicts Between Generalization, Rigor, and Intuition New Hardcover
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Product details 692 pages Springer - English 9780387228365 Reviews:
"Synopsis" by , This book deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Schubring studies often overlooked texts, in particular German and French textbooks, and reveals a much richer history than previously thought while throwing new light on major figures, such as Cauchy.
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