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When Leonhard Euler first arrived at the Russian Academy of Sciences, at the age of 20, his career was supported and promoted by the Academy's secretary, the Prussian jurist and amateur mathematician Christian Goldbach (1690-1764). Their encounter would grow into a lifelong friendship, as evinced by nearly 200 letters sent over 35 years. This exchange - Euler's most substantial long-term correspondence - has now been edited for the first time with an English translation, ample commentary and documentary indices. These present an overview of 18th-century number theory, its sources and repercussions, many details of the protagonists' biographies, and a wealth of insights into academic life in St. Petersburg and Berlin between 1725 and 1765. Part I includes an introduction and the original texts of the Euler-Goldbach letters, while Part II presents the English translations and documentary indices.

Table of Contents

Preface.- Introduction.- 1 Historical and biographical setting.- 1.1. Christian Goldbach: A short biography.- 1.2. Goldbach and Euler.- 1.3. The Euler-Goldbach correspondence – chronology and statistics.- 2 Main subjects of the correspondence.- 2.1. Number theory.- 2.2. Analytic tools in number theory.- 2.3. Algebra: roots of polynomials and transcendence.- 2.4. Analysis.- 2.5. Geometry, topology, combinatorics.- 2.6. Natural science.- 2.7. Professional life: Academies, prizes, publications.- 2.8. Personal life: family, travel, health.- 3 Editing the Euler-Goldbach correspondence.- 3.1. Description of the manuscript sources.- 3.2. Prior editions.- 3.3. Editorial principles.- Correspondence with Christian Goldbach. Original Texts.- Translations.- Indices: Synoptic Table.- Bibliography.- Systematic Subject Index.- Name Index.

Review

"The present volume is the second part of Lemmermeyer and Mattmüller's edition of the correspondence between Euler and Goldbach. … This edition of the Euler-Goldbach correspondence published in two volumes will soon be the indispensable reference. It is a pearl in the literature concerning history of mathematics and history of number theory in particular." (Thomas Sonar, zbMATH 1361.01009, 2017)

Review Quote

"The present volume is the second part of Lemmermeyer and Mattmller's edition of the correspondence between Euler and Goldbach. ... This edition of the Euler-Goldbach correspondence published in two volumes will soon be the indispensable reference. It is a pearl in the literature concerning history of mathematics and history of number theory in particular." (Thomas Sonar, zbMATH 1361.01009, 2017)

Feature

Features the first modern-language translation of Leonhard Euler's most substantial long-term correspondence Documents the development of many of Euler's most significant scientific achievements, particularly in number theory, including the Four Squares Theorem, the Pentagonal Number Theorem, Fermat's Last Theorem, the Goldbach Conjecture, the Euler Formula on complex logarithms and the Polyhedron Formula Presents a wealth of insights into the protagonists' biographies and into academic life in St. Petersburg and Berlin between 1725 and 1765 Provides an ample documentary index featuring hard-to-find biographic and bibliographic information

Details