E-grāmata: Axiomatics: Mathematical Thought and High Modernism

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 * "Alma Steingarts 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 194570) 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 * The book is well written, and employs many articles, speeches, memoranda, and national reports in which mathematicians were addressing the public at large, especially by those in charge of science policy decisions. This adds greatly to the value of the work. The discussion is kept accessible for a relatively large readership, avoiding any kind of technical details. Readers will come away with an enriched picture of the world of mathematics. * Notices of the American Mathematical Society * 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 This sophisticated and wide-ranging book examines mid-century American mathematics as a species of high modernism, both in its pure form and in applied mathematics. It looks at how it was supported, why it was advocated, how and why it was compared to contemporary abstract art, how the evolving ideas of abstraction played out in the Cold War, and how this even affected the writing of the history of mathematics. It is a major addition to and critique of the literature that presents modern mathematics as a species of modernism, and it should be read by every historian of modern science and indeed by anyone interested in how abstract ideas have shaped the modern world. -- Jeremy Gray, author of Platos Ghost: The Modernist Transformation of Mathematics American mathematics was in the midst of a puzzling contradiction at midcentury: applied mathematics appeared triumphant even as many mathematicians promoted abstraction and rejected the idea that utility was important. Steingarts brilliant book has finally resolved this puzzle. Far from standing in opposition, mathematics utility and idealism, its calculations and foundations, were historically intertwined with the concept of axiomatics. By masterfully weaving together the work of artists and mathematicians, mundane academic conference proceedings and philosophical treatises, Steingart has written an essential guide to the transformation of postwar mathematics. -- Christopher J. Phillips, author of The New Math: A Political History 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, Steingarts 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 "The book offers many thought-provoking questions about the role of mathematics, the relation between mathematics and art, and about the border between pure and applied mathematics. . . . recommended to all historians of modern science, as well as to working mathematicians who enjoy thinking about the nature of their subject." * zbMATH Open *