Publisher Description

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.

Notes

The cultural historian Theodore Merz called it "that great book with seven seals," the mathematician Leopold Kronecker, "the book of all books." Already one century after its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) had acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organization and theory building; and as a source of mathematical inspiration. Various readings of the Disquisitiones Arithmeticae have left their mark on developments as different as Galois's theory of algebraic equations, Lucas's primality tests, and Dedekind's theory of ideals. In this volume, eighteen authors--mathematicians, historians, and philosophers among them-- assess the impact of the Disquisitiones since its publication.

Table of Contents

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Quadratic Forms and the Foundations of Mathematics.- Composition of Quadratic Forms: An Algebraic Perspective.- The Unpublished Section Eight: On the Way to Function Fields over a Finite Field.- The German Reception of the Disquisitiones Arithmeticae: Institutions and Ideas.- A Network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.

Review

From the reviews:"A book that traces the profound effect Gauss's masterpiece has had on mathematics over the past two centuries. … The shaping of arithmetic is a major accomplishment, one which will stand as an important reference work on the history of number theory for many years. … The editors and authors deserve our thanks for their efforts." (Victor J. Katz, Mathematical Reviews, Issue 2008 h)"It's a big book, with eighteen authors and almost six hundred pages, and it mixes the work of well-established scholars with that of recent Ph.D.'s. … This volume deserves a wide audience, both among the mathematically able and among historians of nineteenth-century science." (Thomas Archibald, Institute for Science and International Security, Vol. 102 (2), June, 2011)

Long Description

In 1998, the editors convinced themselves that it was the right time to take stock of recent research concerning the modern history of number theory, and to evaluate in its light our comprehension of the development of this discipline as a whole. One issue at stake was to bring together historiographical results coming from different disciplines and linguistic domains which, we felt, had remained too often unaware of each other. We organized two meetings at theMathematisches Forschungsinstitut Oberw- fach: ?rstasmallRIP-workshopheldJune14-19,1999,amonghistoriansofnumber theoryandhistoriansofrelatedtopics, andthenalargerconferencewhichtookplace June 17-23, 2001, two hundred years after the publication of Carl Friedrich Gauss's DisquisitionesArithmeticae. Thelatterbroughttogetherhistoriansandphilosophers of mathematics with number theorists interested in the recent history of their ?eld. Two further meetings, organized by one of us in Vienna and Z

Review Quote

From the reviews:"A book that traces the profound effect Gauss's masterpiece has had on mathematics over the past two centuries. … The shaping of arithmetic is a major accomplishment, one which will stand as an important reference work on the history of number theory for many years. … The editors and authors deserve our thanks for their efforts." (Victor J. Katz, Mathematical Reviews, Issue 2008 h)It's a big book, with eighteen authors and almost six hundred pages, and it mixes the work of well-established scholars with that of recent Ph.D.'s. … This volume deserves a wide audience, both among the mathematically able and among historians of nineteenth-century science. (Thomas Archibald, Institute for Science and International Security, Vol. 102 (2), June, 2011)

Feature

Assesses the impact of the Disquisitiones, in the 200 years since its publication Focuses on responses of specific mathematicians Explores the influence of the Disquisitiones as a source of mathematical inspiration Contributors include mathematicians, historians, philosophers

Description for Sales People

The cultural historian Theodore Merz called it "that great book with seven seals," the mathematician Leopold Kronecker, "the book of all books." Already one century after its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) had acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organization and theory building; and as a source of mathematical inspiration. Various readings of the Disquisitiones Arithmeticae have left their mark on developments as different as Galois's theory of algebraic equations, Lucas's primality tests, and Dedekind's theory of ideals. In this volume, eighteen authors--mathematicians, historians, and philosophers among them-- assess the impact of the Disquisitiones since its publication.

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