Axiomatics mathematical thought and high modernism
Steingart, Alma
Axiomatics mathematical thought and high modernism Alma Steingart - 291 Seiten Illustrationen
Includes bibliographical references and index
Pure abstraction: mathematics as modernism -- Applied abstraction: axiomatics and the meaning of mathematization -- Human abstraction: "The mathematics of man' and midcentury social sciences -- Creative abstraction: abstract art, pure mathematics, and Cold War ideology -- Unreasonable abstraction: the meaning of applicability, or the Miseducation of the applied mathematician -- Historical abstraction: Kuhn, Skinner, and the problem of the weekday platonist.
"The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. 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 recovering 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 development of mathematics band Cold War epistemology writ large. As Steingart's history ably demonstrates, mathematics is the social activity in which styles of truth-here, abstraction-become synonymous with ways of knowing. "--
9780226824185 cloth 9780226824208 paperback
2022026640
Mathematics--Philosophy--History--20th century
Mathematics--History--United States--20th century
Knowledge, Theory of--History--United States--20th century
Axiomatic set theory
MATHEMATICS / History & Philosophy
PHILOSOPHY / Epistemology
Fellow Berthold Leibinger Fellow Class of Fall 2022
QA8.4
Axiomatics mathematical thought and high modernism Alma Steingart - 291 Seiten Illustrationen
Includes bibliographical references and index
Pure abstraction: mathematics as modernism -- Applied abstraction: axiomatics and the meaning of mathematization -- Human abstraction: "The mathematics of man' and midcentury social sciences -- Creative abstraction: abstract art, pure mathematics, and Cold War ideology -- Unreasonable abstraction: the meaning of applicability, or the Miseducation of the applied mathematician -- Historical abstraction: Kuhn, Skinner, and the problem of the weekday platonist.
"The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. 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 recovering 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 development of mathematics band Cold War epistemology writ large. As Steingart's history ably demonstrates, mathematics is the social activity in which styles of truth-here, abstraction-become synonymous with ways of knowing. "--
9780226824185 cloth 9780226824208 paperback
2022026640
Mathematics--Philosophy--History--20th century
Mathematics--History--United States--20th century
Knowledge, Theory of--History--United States--20th century
Axiomatic set theory
MATHEMATICS / History & Philosophy
PHILOSOPHY / Epistemology
Fellow Berthold Leibinger Fellow Class of Fall 2022
QA8.4