Catalogue


Conflicts between generalization, rigor, and intuition : number concepts underlying the development of analysis in 17-19th century France and Germany /
Gert Schubring.
imprint
New York : Springer, c2005.
description
xiv, 678 p.
ISBN
0387228365 (acid-free paper)
format(s)
Book
Holdings
More Details
imprint
New York : Springer, c2005.
isbn
0387228365 (acid-free paper)
catalogue key
5436575
 
Includes bibliographical references and index.
A Look Inside
Reviews
Review Quotes
From the reviews: "This is a very ambitious book, both in its methodology and in the amount of material it addresses. a? The topic is of major interest, focusing on two concepts that extended the idea of what was meant by a'numbera? a? . this book remains a major contribution. The rich and detailed account of textbooks and educational institutions, and the key passages and events Schubring highlights a? add greatly to our understanding of the history of mathematics in one of its most exciting periods." (Judith V. Grabiner, SIAM Review, Vol. 48 (2), 2006) "The present book is a voluminous and detailed study of the conceptual developments of negative numbers and infinitesimals from the prehistory of the calculus to the end of the nineteenth century. ... It stands out as special by treating many primary mathematical sources that are rarely subjected to historical study a? . this volume presents an important new contextualised perspective on the history of negative numbers and infinitesimals. It includes a rich variety of institutional and philosophical discussions a? ." (Henrik Kragh S'renson, Zentralblatt MATH, Vol. 1086, 2006) "This deep and important epistemological study analyses the evolution of concepts fundamental to mathematical analysis up to the nineteenth century. a? The author examines how concepts were generalized and differentiated and pays particular attention to the role of symbolism. He critically reviews the work of other authors who have treated the same historical periods." (E. J. Barbeau, Mathematical Reviews, Issue 2006 d)
From the reviews:"This is a very ambitious book, both in its methodology and in the amount of material it addresses. … The topic is of major interest, focusing on two concepts that extended the idea of what was meant by 'number' … . this book remains a major contribution. The rich and detailed account of textbooks and educational institutions, and the key passages and events Schubring highlights … add greatly to our understanding of the history of mathematics in one of its most exciting periods." (Judith V. Grabiner, SIAM Review, Vol. 48 (2), 2006)"The present book is a voluminous and detailed study of the conceptual developments of negative numbers and infinitesimals from the prehistory of the calculus to the end of the nineteenth century. ... It stands out as special by treating many primary mathematical sources that are rarely subjected to historical study … . this volume presents an important new contextualised perspective on the history of negative numbers and infinitesimals. It includes a rich variety of institutional and philosophical discussions … ." (Henrik Kragh Sørenson, Zentralblatt MATH, Vol. 1086, 2006)"This deep and important epistemological study analyses the evolution of concepts fundamental to mathematical analysis up to the nineteenth century. … The author examines how concepts were generalized and differentiated and pays particular attention to the role of symbolism. He critically reviews the work of other authors who have treated the same historical periods." (E. J. Barbeau, Mathematical Reviews, Issue 2006 d)
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Summaries
Main Description
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.
Back Cover Copy
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.
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 refoulè
Le Retour du Refoule: 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
Table of Contents provided by Publisher. All Rights Reserved.

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