Classical Theorems in Reverse Mathematics and Higher Recursion Theory

Ph.DDOCTOR OF PHILOSOPH

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Correspondence of Leonhard Euler with Christian Goldbach

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