Conflicts between Generalization, Rigor, and Intuition Number Concepts Underlying the Development of Analysis in 17–19th Century France and Germany /

• Main Author: Schubring, Gert (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Series: Sources and Studies in the History of Mathematics and Physical Sciences
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; History.; History of Mathematical Sciences.; Analysis.

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 discus...

Table of Contents:

• Question and Method
• Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field
• Paths toward 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.