“Mathematics has undergone tremendous changes, especially during the twentieth century, when it pushed ever deeper into the realm of abstraction. This upheaval even involved a redefinition of the definition itself, as Steingart explains in Axiomatics. A historian of science, Steingart sees this revolution as central to the modernist movements that dominated the mid-twentieth century in the arts and social sciences, particularly in the United States.”

Nature

“Steingart provides a history of mathematical thinking over the twentieth century: a compelling review of the increased abstraction of mathematical thought as well as its embrace of deep exploration of alternative axiomatic systems.”

Public Books

“Steingart takes a wide-angle view on mid-twentieth-century mathematics, connecting the axiomatic movement with high abstraction in modern art, structuralism in the social sciences, the New Criticism in literary criticism, and the deep unease felt by many scientists and mathematicians in the wake of World War II as their research became ever more entangled with military applications. Unfailingly lucid and alert to sympathetic resonances between apparently disparate realms, Steingart positions modern mathematics squarely in the center of high modernism.”

Lorraine Daston, author of Rules: A Short History of What We Live By

“The push for axiomatic reasoning, so central to twentieth-century mathematics, extended by 1950 to elite social science. But the power of this abstract logic, never absolute, was in retreat by the 1990s. Although the most familiar of these challenges took form as a new cult of data, Steingart’s most engaging arguments explore a new fascination with mathematical historicism.”

Theodore M. Porter, author of Trust in Numbers: The Pursuit of Objectivity in Science and Public Life

"Alma Steingart’s Axiomatics: Mathematical Thought and High Modernism is an attempt to combine the story of abstraction with developments outside of mathematics. . . . she presents this material from a very interesting and well-informed perspective."

American Mathematical Monthly

"The mathematicians of the later period explored here (approximately 1945–70) were shaped by their wartime experiences, the postwar growth of the military-industrial complex, and anticommunism. For chapter themes, Steingart divides abstraction in mathematical research into six dimensions: pure, applied, human, creative, unreasonable, and historical. The last chapter provides a clear, thorough survey of the notorious1970s debates over mathematics historiography. Most of the discussion of mathematics is conceptual rather than technical, so the book is broadly accessible to an academic audience."

Choice