# Episodes in the History of Modern Algebra (1800–1950)

### About this Title

**Jeremy J. Gray**, *The Open University, Milton Keynes, England* and **Karen Hunger Parshall**, *University of Virginia, Charlottesville, VA*, Editors

Publication: History of Mathematics

Publication Year:
2007; Volume 32

ISBNs: 978-0-8218-6904-8 (print); 978-1-4704-1808-3 (online)

DOI: https://doi.org/10.1090/hmath/032

MathSciNet review: MR2307989

MSC: Primary 00B25; Secondary 01A05, 01A55, 01A60, 01A70, 13-03

### Table of Contents

**Front/Back Matter**

**Chapters**

- 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