How did Emil Artin influence Bartel van der Waerden’s approach to algebra?

Emil Artin significantly influenced Bartel van der Waerden’s structural approach to algebra, particularly through his reformulation of Galois theory.1

Rather than focusing on the Galois group of a polynomial equation with coefficients in a specific field, Artin shifted the perspective to the group of automorphisms of the coefficients' splitting field. This approach allowed Galois theory to be understood as the study of interrelations between field extensions and the subgroups of the Galois group. By treating the solvability of equations as an application of a more general, abstract theory, Artin provided a model for the structural methodology that van der Waerden later codified in his influential 1930 textbook, Moderne Algebra.12

Van der Waerden, who attended Artin’s lectures in Hamburg, adopted this structural viewpoint, which prioritized the study of algebraic structures—such as groups, rings, and fields—over the manipulation of individual elements. This shift inverted the classical conceptual hierarchy of algebra, establishing the study of general structures as the discipline's primary focus.2