Axiomatics: Mathematical Thought and High Modernism

Alma Steingart's book "The Modernist Impulse in American Mathematics" explores the rise of abstraction and axiomatics in postwar mathematics, highlighting their significance in American intellectual thought. It argues that the expansion of mathematics in this period was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence. The book demonstrates how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences, and how the meaning of mathematization changed as mathematics changed.

Format: Paperback / softback
Length: 272 pages
Publication date: 10 January 2023
Publisher: The University of Chicago Press

The first history of postwar mathematics, offering a fresh interpretation of the rise of abstraction and axiomatics in the twentieth century, is presented here.

Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In reclaiming the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought.

The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics.

For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization.

Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar era.

Dimension: 229 x 152 x 18 (mm)
ISBN-13: 9780226824208
Edition number: 1