2007

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

ISBN: 978-3-540-20441-1 (Print) 978-3-540-34720-0 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xi

  2. A Book’s History

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 2-65

      A Book in Search of a Discipline (1801–1860)

    3. No Access

      Book Chapter

      Pages 66-103

      Several Disciplines and a Book (1860–1901)

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

    1. Front Matter

      Pages 105-105

    2. No Access

      Book Chapter

      Pages 107-127

      The Disquisitiones Arithmeticae and the Theory of Equations

    3. No Access

      Book Chapter

      Pages 129-144

      Composition of Binary Quadratic Forms and the Foundations of Mathematics

    4. No Access

      Book Chapter

      Pages 145-158

      Composition of Quadratic Forms: An Algebraic Perspective

    5. No Access

      Book Chapter

      Pages 159-198

      The Unpublished Section Eight: On the Way to Function Fields over a Finite Field

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

    1. Front Matter

      Pages 199-199

    2. No Access

      Book Chapter

      Pages 201-233

      A Network of Scientific Philanthropy: Humboldt’s Relations with Number Theorists

    3. No Access

      Book Chapter

      Pages 234-268

      ‘O Θɛòζ’ Aριθμηίíξɛι: The Rise of Pure Mathematics as Arithmetic with Gauss

  5. Complex Numbers and Complex Functions in Arithmetic

    1. Front Matter

      Pages 269-269

    2. No Access

      Book Chapter

      Pages 270-290

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

    3. No Access

      Book Chapter

      Pages 291-312

      Elliptic Functions and Arithmetic

  6. Numbers as Model Objects of Mathematics

    1. Front Matter

      Pages 313-313

    2. No Access

      Book Chapter

      Pages 314-342

      The Concept of Number from Gauss to Kronecker

    3. No Access

      Book Chapter

      Pages 343-374

      On Arithmetization

  7. Number Theory and the Disquisitiones in France after 1850

    1. Front Matter

      Pages 375-375

    2. No Access

      Book Chapter

      Pages 376-410

      The Hermitian Form of Reading the Disquisitiones

    3. No Access

      Book Chapter

      Pages 411-427

      Number Theory at the Association française pour l’avancement des sciences

  8. Spotlighting Some Later Reactions

    1. Front Matter

      Pages 429-429

    2. No Access

      Book Chapter

      Pages 431-452

      An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae

    3. No Access

      Book Chapter

      Pages 453-462

      Zolotarev’s Theory of Algebraic Numbers

    4. No Access

      Book Chapter

      Pages 463-479

      Gauss Goes West: The Reception of the Disquisitiones Arithmeticae in the USA

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

    1. Front Matter

      Pages 481-481

    2. No Access

      Book Chapter

      Pages 483-504

      Reduction Theory of Quadratic Forms: Towards Räumliche Anschauung in Minkowski’s Early Work

    3. No Access

      Book Chapter

      Pages 505-528

      Gauss Sums

    4. No Access

      Book Chapter

      Pages 529-561

      The Development of the Principal Genus Theorem

  10. Back Matter

    Pages 563-578