Episodes in the history of modern algebra (1800-1950) / Jeremy J. Gray and Karen Hunger Parshall, editors.

Format:

Book

Contributor:

Gray, Jeremy, 1947- editor.

Parshall, Karen Hunger, 1955- editor.

Series:

History of mathematics ; Volume 32.

History of Mathematics ; Volume 32

Language:

English

Subjects (All):

Algebra--History.

Algebra.

Physical Description:

1 online resource (337 pages) : illustrations, tables.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island ; London, England : American Mathematical Society : The London Mathematical Society, 2007.

Summary:

Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.

Contents:

Cover

Half Title

Title Page

Contents

Acknowledgments

Introduction

Babbage and French Idéologie: Functional equations, language, and the analytical method

"Very full of symbols": Duncan F. Gregory, the calculus of operations, and the Cambridge Mathematical Journal

Divisibility theories in the early history of commutative algebra and the foundations of algebraic geometry

Kronecker's fundamental theorem of general arithmetic

Developments in the theory of algebras over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory

Minkowski, Hensel, and Hasse: On the beginnings of the local-global principle

Research in algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert

Emmy Noether's 1932 ICM lecture on noncommutative methods in algebraic number theory

From Algebra (1895) to Moderne Algebra (1930): Changing conceptions of a discipline-A guided tour using the Jahrbuch über die Fortschritte der Mathematik

A historical sketch of B. L. van der Waerden's work in algebraic geometry: 1926-1946

On the arithmetization of algebraic geometry

The rising sea: Grothendieck on simplicity and generality

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1808-8