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The correspondence Emil Artin – Helmut Hasse (1937/38 and 1953 to 1958). The friendship of two scholars in its historical context. (Der Briefwechsel Emil Artin – Helmut Hasse (1937/38 und 1953 bis 1958). Die Freundschaft der beiden Gelehrten im historischen Kontext.) (German) Zbl 1403.01002

EAGLE 103. Leipzig: Edition am Gutenbergplatz Leipzig (EAGLE) (ISBN 978-3-95922-103-0/pbk). 254 p. (2018).
Emil Artin (1898–1962) and Helmut Hasse (1898–1979) were among the most influential mathematicians of the twentieth century, mainly through their various contributions to algebraic number theory and abstract algebra. Their close mathematical collaboration between 1923 and 1937, that is before Emil Artin emigrated to the United States of America, is not only reflected by common publications on supplementary results toward a general reciprocity law for certain number fields, but also by an intensive correspondence through letters during those years. In fact, 49 letters from Artin to Hasse in the course of this period have been edited (and commented) by G. Frei (ed.) and P. Roquette (ed.) in [Emil Artin und Helmut Hasse. Die Korrespondenz 1923–1934. Göttingen: Universitätsverlag Göttingen (2008; Zbl 1161.01002)], where especially Artin’s new construction of \(L\)-functions is thoroughly explained by him.
The book under review focuses on the remaining correspondence 1937/38 and between 1953 and 1958, hence before Emil Artin’s definitive return to Hamburg, Germany, where he became H. Hasse’s direct colleague again.
Although those letters are already available in book form [G. Frei (ed.) et al., Emil Artin and Helmut Hasse. The correspondence 1923–1958. Translated from the German by Franz Lemmermeyer. Basel: Springer (2014; Zbl 1294.01004), 73 letters], the present book provides much more than just those historical documents. Namely the author thoroughly analyzes the very different curricula vitae, the varied mathematical careers, the differing political and social attitudes, and the particular circumstances of the lives of the two outstanding mathematical scholars. Numerous copies of official documents, citations of statements of colleagues, friends, opponents, and family members provide new and additional information about the long, untroubled friendship of these two distinct mathematical personalities. Many of these valuable sources appear here for the first time, and in this way the comprehensive analysis of the historical context of a remarkable, utmost productive friendship between two towering mathematical figures of the twentieth century leads to a significantly deeper understanding of their overall mathematical impact.
The highly interesting and enlightening text is enhanced by five appendices, a carefully collected register of persons made reference to, and by a just as complete bibliography.
All in all, this book is a very useful and valuable source for both historians of mathematics and researchers in algebraic number theory likewise.

MSC:

01-02 Research exposition (monographs, survey articles) pertaining to history and biography
01A75 Collected or selected works; reprintings or translations of classics
01A60 History of mathematics in the 20th century
11-03 History of number theory
11R54 Other algebras and orders, and their zeta and \(L\)-functions

Biographic References:

Artin, Emil; Hasse, Helmut
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