Acknowledgments Introduction Babbage and French Ideologie: 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 uber 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.
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..