Exposition by Emil Artin: A Selection
About this Title
Michael Rosen, Brown University, Providence, RI, Editor
Publication: History of Mathematics
Publication Year: 2006; Volume 30
ISBNs: 978-0-8218-4172-3 (print); 978-1-4704-3897-5 (online)
MathSciNet review: MR2288274
MSC: Primary 01A75; Secondary 00B60, 11-06, 12-06
Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. He also discovered and proved the Artin reciprocity law, the culmination of over a century and a half of progress in algebraic number theory.
Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching and expository writing. In this volume we gather together in one place a selection of his writings wherein the reader can learn some beautiful mathematics as seen through the eyes of a true master.
The volume's Introduction provides a short biographical sketch of Emil Artin, followed by an introduction to the books and papers included in the volume. The reader will first find three of Artin's short books, titled The Gamma Function, Galois Theory, and Theory of Algebraic Numbers, respectively. These are followed by papers on algebra, algebraic number theory, real fields, braid groups, and complex and functional analysis. The three papers on real fields have been translated into English for the first time.
The flavor of these works is best captured by the following quote of Richard Brauer. “There are a number of books and sets of lecture notes by Emil Artin. Each of them presents a novel approach. There are always new ideas and new results. It was a compulsion for him to present each argument in its purest form, to replace computation by conceptual arguments, to strip the theory of unnecessary ballast. What was the decisive point for him was to show the beauty of the subject to the reader.”
Advanced undergraduates, graduate students, and research mathematicians interested in number theory and related topics, and in their history.
Table of Contents
Books by Emil Artin
Papers by Emil Artin
- Axiomatic characterization of fields by the product formula for valuations
- A note on axiomatic characterization of fields
- A characterization of the field of real algebraic numbers
- The algebraic construction of real fields
- A characterization of real closed fields
- The theory of braids
- Theory of braids
- On the theory of complex functions
- A proof of the Krein-Milman theorem
- The influence of J. H. M. Wedderburn on the development of modern algebra