Goldstein, Catherine

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

Goldstein, Catherine - The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae, ebook


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ISBN: 9783540347200
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Table of contents

Part I. A Book’s History

1. A Book in Search of a Discipline (1801–1860)
Catherine Goldstein, Norbert Schappacher

2. Several Disciplines and a Book (1860–1901)
Catherine Goldstein, Norbert Schappacher

Part II. Algebraic Equations, Quadratic Forms, Higher Congruences: Key Mathematical Techniques of the Disquisitiones Arithmeticae

3. The Disquisitiones Arithmeticae and the Theory of Equations
Olaf Neumann

4. Composition of Binary Quadratic Forms and the Foundations of Mathematics
Harold M. Edwards

5. Composition of Quadratic Forms: An Algebraic Perspective
Della D. Fenster, Joachim Schwermer

6. The Unpublished Section Eight: On the Way to Function Fields over a Finite Field
Günther Frei

Part III. The German Reception of the Disquisitiones Arithmeticae: Institutions and Ideas

7. A Network of Scientific Philanthropy: Humboldt’s Relations with Number Theorists
Herbert Pieper

8. ‘O T?ò?’ A???µ??í???: The Rise of Pure Mathematics as Arithmetic with Gauss
José Ferreirós

Part IV. Complex Numbers and Complex Functions in Arithmetic

9. From Reciprocity Laws to Ideal Numbers: An (Un)Known Manuscript by E.E. Kummer
Reinhard Bölling

10. Elliptic Functions and Arithmetic
Christian Houzel

Part V. Numbers as Model Objects of Mathematics

11. The Concept of Number from Gauss to Kronecker
Jacqueline Boniface

12. On Arithmetization
Birgit Petri, Norbert Schappacher

Part VI. Number Theory and the Disquisitiones in France after 1850

13. The Hermitian Form of Reading the Disquisitiones
Catherine Goldstein

14. Number Theory at the Association française pour l’avancement des sciences
Anne-Marie Décaillot

Part VII. Spotlighting Some Later Reactions

15. An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae
Aldo Brigaglia

16. Zolotarev’s Theory of Algebraic Numbers
Paola Piazza

17. Gauss Goes West: The Reception of the Disquisitiones Arithmeticae in the USA
Della Fenster

Part VIII. Gauss’s Theorems in the Long Run: Three Case Studies

18. Reduction Theory of Quadratic Forms: Towards Räumliche Anschauung in Minkowski’s Early Work
Joachim Schwermer

19. Gauss Sums
Samuel James Patterson

20. The Development of the Principal Genus Theorem
Franz Lemmermeyer


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Keywords: MATHEMATICS / General MAT000000

Publication year
Natural Sciences

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