Why was A Survey of Modern Algebra influential for mathematics students in the United States?

A Survey of Modern Algebra (1941), coauthored by Saunders Mac Lane and Garrett Birkhoff, was highly influential because it helped establish the structural approach to algebra within the United States.1

Following the precedent set by Bartel van der Waerden’s earlier work, Moderne Algebra (1930), the book played a fundamental role in shaping the education of several generations of American mathematicians. By focusing on the general algebraic structure of sets—such as matrices and vector spaces—rather than merely the rules for manipulating individual elements, the text aligned with the shift toward structural methods that became a dominant and dynamic force in 20th-century mathematics. Its widespread adoption as a textbook helped integrate these modern concepts into the standard curriculum, influencing how the discipline was taught and understood for decades.12