**History of Mathematics**

Volume: 30;
2006;
346 pp;
Softcover

MSC: Primary 01; 11;

Print ISBN: 978-0-8218-4172-3

Product Code: HMATH/30

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

**Electronic ISBN: 978-1-4704-3897-5
Product Code: HMATH/30.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

#### Supplemental Materials

# Exposition by Emil Artin: A Selection

Share this page *Edited by *
*Michael Rosen*

A co-publication of the AMS and the London Mathematical Society

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.”

This volume is one of an informal sequence of works within the
History of Mathematics series. Volumes in this subset,
“Sources”, are classical mathematical works that served as
cornerstones for modern mathematical thought.

#### Readership

Advanced undergraduates, graduate students, and research mathematicians interested in number theory and related topics, and in their history.

#### Reviews & Endorsements

The editor's excellent introduction to the present selection from Emil Artin's works provides both a biographical sketch of this great mathematician and an explanation of the books and papers included in the volume. All together, the entire collection reflects Emil Artin's mathematical thinking in very instructive a manner.

-- Werner Kleinert for Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Exposition by Emil Artin: A Selection

- Cover Cover11
- Title page iii4
- Contents v6
- Photos vi7
- Credits and acknowledgments ix10
- Introduction 112
- Books by Emil Artin 1122
- The Gamma Function 1324
- Galois Theory 6172
- Theory of Algebraic Numbers 109120
- Papers by Emil Artin 239250
- Axiomatic characterization of fields by the product formula for valuations 241252
- A note on axiomatic characterization of fields 265276
- A characterization of the field of real algebraic numbers 269280
- The algebraic construction of real fields 273284
- A characterization of real closed fields 285296
- The theory of braids 291302
- Theory of braids 299310
- On the theory of complex functions 325336
- A proof of the Krein-Milman theorem 335346
- The influence of J. H. M. Wedderburn on the development of modern algebra 339350
- Back Cover Back Cover1359