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Publisher:

Springer

Publication Date:

2014

Number of Pages:

484

Format:

Hardcover

Series:

Contributions in Mathematical and Computational Sciences 5

Price:

149.00

ISBN:

9783034807142

Category:

Monograph

[Reviewed by , on ]

Fernando Q. Gouvêa

07/14/2014

Some years ago, I wrote a review of *Emil Artin and Helmut Hasse: Their Correspondence 1923-1934*, edited by Peter Roquette and Günther Frei. This book is essentially an expanded second edition of that one. The most important change is the one responsible for the addition of Franz Lemmermeyer to the list of editors: the letters and commentary have been translated into English. In addition, several more letters are included, extending the range all the way to 1958. One new letter dated 1932, from Hasse to Artin, has been found and is included in that section. (As noted in the previous review, Hasse kept all the letters he received, but Artin did not, with the result that there are more letters *by Artin* in this volume, so a new letter from Hasse is a valuable find.)

The letters up to 1934 are the ones with the most mathematical interest. This was the period when Artin was working on class field theory, culminating in the proof of what is now called the Artin Reciprocity Theorem. At the same time, Hasse was working on a two-volume “report on class field theory.” So there was a great deal to talk about. There is extensive mathematical and biographical commentary accompanying the letters, making it possible to follow the discussion without having to be familiar with class field theory and its history.

After 1933, things clearly got much more difficult, The letters from 1937 and 1938 deal with Artin’s decision to emigrate. His wife Natasha was Jewish, and it was no longer safe for him to be in Germany. Hasse seems to have tried to find safer work conditions for Artin, but clearly that would not have been possible. Artin ended up in the United States, and there seem to be no letters from the following decade. Artin settled in Princeton until the mid-1950s. The correspondence with Hasse resume briefly in the 1950s, mostly as a result of Artin’s decision to return to Germany. They are friendly letters rather than letters of scientific collaboration.

For anyone interested in the history of number theory in the 20th century, this book is a must-have.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.

See the table of contents in pdf format.

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