The turn of the century

Abstract

In this chapter one finds a presentation of the work of Hilbert, who in his report on algebraic numbers summarized the state of their theory at the end of the nineteenth century, as well of Hensel, who created p-adic and adic numbers, which turned out to be an indispensable tool in future research. In the last part of the chapter the first steps towards creation of the class-field theory, characterizing Abelian extensions of algebraic number fields, are described.