The present issue contains two articles which are related to number theory, namely Anne-Marie Aubert’s survey article entitled “Around the Langlands Program” and under the rubric “Classics revisited” Franz Lemmermeyer’s review of David Hilbert’s work “Die Theorie der algebraischen Zahlkörper” which has been published in the Jahresbericht of the DMV in 1897.

In 1967, the Canadian mathematician Robert P. Langlands wrote a letter to the French mathematician André Weil, in which he made a number of groundbreaking conjectures. This was the starting point of a development which is nowadays called Langlands program and which seeks to build bridges between number theory and other fields of mathematics such as representation theory, algebraic geometry and automorphic forms. Enthusiastically it is sometimes called “a kind of grand unified theory of mathematics”. Langlands became professor in Princeton in 1972 and has received many awards, such as the Wolf prize in 1996, the Nemmers prize in 2006, and the Shaw prize in 2007. Anne-Marie Aubert gives an introduction to the multiple facets of the Langlands program.

In 1893 the DMV invited Hilbert and Minkowski to write reports on the theory of numbers. Minkowski eventually gave up writing his report, while Hilbert’s report about algebraic number theory appeared four years later. It was the textbook on algebraic number theory for the next decades and the next generations of number theorists learned from this textbook. Franz Lemmermeyer’s review not only describes the mathematics before and after the “Zahlbericht”, but also explains how André Weil is involved in this story, too.

We hope that you enjoy reading this issue.