The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae [electronic resource] /
Goldstein, Catherine.editor.
Schappacher, Norbert.editor.
Schwermer, Joachim.editor.
Revisits successive periods in the reception of the Disquisitiones as it studies which parts were taken up and when, which themes were further explored. This work also focuses on how specific mathematicians reacted to Gauss' book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others.
Revisits successive periods in the reception of the Disquisitiones as it studies which parts were taken up and when, which themes were further explored. This work also focuses on how specific mathematicians reacted to Gauss' book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others.
Includes index.
A Book’s History -- A Book in Search of a Discipline (1801–1860) -- Several Disciplines and a Book (1860–1901) -- Algebraic Equations, Quadratic Forms, Higher Congruences: Key Mathematical Techniques of the Disquisitiones Arithmeticae -- The Disquisitiones Arithmeticae and the Theory of Equations -- Composition of Binary Quadratic Forms and the Foundations of Mathematics -- Composition of Quadratic Forms: An Algebraic Perspective -- The Unpublished Section Eight: On the Way to Function Fields over a Finite Field -- The German Reception of the Disquisitiones Arithmeticae: Institutions and Ideas -- A Network of Scientific Philanthropy: Humboldt’s Relations with Number Theorists -- ‘O ??ò?’ A??????í???: The Rise of Pure Mathematics as Arithmetic with Gauss -- Complex Numbers and Complex Functions in Arithmetic -- From Reciprocity Laws to Ideal Numbers: An (Un)Known Manuscript by E.E. Kummer -- Elliptic Functions and Arithmetic -- Numbers as Model Objects of Mathematics -- The Concept of Number from Gauss to Kronecker -- On Arithmetization -- Number Theory and the Disquisitiones in France after 1850 -- The Hermitian Form of Reading the Disquisitiones -- Number Theory at the Association française pour l’avancement des sciences -- Spotlighting Some Later Reactions -- An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae -- Zolotarev’s Theory of Algebraic Numbers -- Gauss Goes West: The Reception of the Disquisitiones Arithmeticae in the USA -- Gauss’s Theorems in the Long Run: Three Case Studies -- Reduction Theory of Quadratic Forms: Towards Räumliche Anschauung in Minkowski’s Early Work -- Gauss Sums -- The Development of the Principal Genus Theorem.
Gauss, Carl Friedrich, 1777-1855.
Number theory.
Algebra.
Mathematics.
History.
Number Theory.
Algebra.
History of Mathematical Sciences.