The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae

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Catherine Goldstein, Norbert Schappacher, Joachim Schwermer
Springer Science & Business Media, Feb 3, 2007 - Mathematics - 578 pages

Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.

 

Contents

A Books History
1
2 Several Disciplines and a Book 18601901 Catherine Goldstein Norbert Schappacher
67
x
119
2 Composition of Binary Quadratic Forms and
129
An Algebraic Perspective
145
On the Way to Function
159
The Rise of Pure Mathematics
235
Complex Numbers and Complex Functions in Arithmetic
269
Number Theory and the Disquisitiones in France after 1850
375
2 Number Theory at the Association française pour
411
Spotlighting Some Later Reactions 429
430
2 Zolotarevs Theory of Algebraic Numbers
453
The Reception of the Disquisitiones
463
Three Case Studies 481
482
2 Gauss Sums
505
3 The Development of the Principal Genus Theorem
529

2 Elliptic Functions and Arithmetic
291
Numbers as Model Objects of Mathematics
313
2 On Arithmetization
343
List of Illustrations
563
Authors Addresses
577
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About the author (2007)

Catherine Goldstein is Directrice de recherches du CNRS and works at the Institut de mathématiques de Jussieu (Paris, France). She is the author of "Un théorème de Fermat et ses lecteurs" (1995) and a coeditor of "Mathematical Europe: History, Myth, Identity"(1996). Her research aims at developing a social history of mathematical practices and results, combining close readings and a network analysis of texts. Her current projects include the study of mathematical sciences through World War I and of experimentation in XVII th-century number theory.

Norbert Schappacher is professor of mathematics at Université Louis Pasteur, Strasbourg.His mathematical interests relate to the arithmetic of elliptic curves.But his current research projects lie in the history of mathematics. Specifically, he focuses on the intertwinement of philosophical and political categories with major junctures in the development of mathematical disciplines in the XIX\up{th} and XX\up{th} centuries. Examples include number theory and algebraic geometry, but also medical statistics.

Joachim Schwermer is professor of mathematics at University of Vienna. In addition, he serves as scientific director at the Erwin-Schroedinger International Institute for Mathematical Physics, Vienna. His research interests lie in number theory and algebra, in particular, in questions arising in arithmetic algebraic geometry and the theory of automorphic forms. He takes a keen interest in the mathematical sciences in the XIX\up{th} and XX\up{th} centuries in their historical context.

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