History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
An expanded narrative of the rich, unique history of the University of Chicago. One of the most influential institutions of higher learning in the world, the University of Chicago has a powerful and distinct identity, and its name is synonymous with intellectual rigor. With nearly 170,000 alumni living and working in more than one hundred and fifty countries, its impact is far-reaching and long-lasting. With The University of Chicago: A History, John W. Boyer, Dean of the College from 1992 to 2023, thoroughly engages with the history and the lived politics of the university. Boyer presents a history of a complex academic community, focusing on the nature of its academic culture and curricula, the experience of its students, its engagement with Chicago’s civic community, and the resources and conditions that have enabled the university to sustain itself through decades of change. He has mined the archives, exploring the school’s complex and sometimes controversial past to set myth and hearsay apart from fact. Boyer’s extensive research shows that the University of Chicago’s identity is profoundly interwoven with its history, and that history is unique in the annals of American higher education. After a little-known false start in the mid-nineteenth century, it achieved remarkable early successes, yet in the 1950s it faced a collapse of undergraduate enrollment, which proved fiscally debilitating for decades. Throughout, the university retained its fierce commitment to a distinctive, intense academic culture marked by intellectual merit and free debate, allowing it to rise to international acclaim. Today it maintains a strong obligation to serve the larger community through its connections to alumni, to the city of Chicago, and increasingly to its global community. Boyer’s tale is filled with larger-than-life characters—John D. Rockefeller, Robert Maynard Hutchins, and many other famous figures among them—and episodes that reveal the establishment and rise of today’s institution. Newly updated, this edition extends through the presidency of Robert Zimmer, whose long tenure was marked by significant developments and controversies over subjects as varied as free speech, medical inequity, and community relations.
Sophie Germain taught herself mathematics by candlelight, huddled in her bedclothes. Ada Byron Lovelace anticipated aspects of general-purpose digital computing by more than a century. Cora Ratto de Sadosky advanced messages of tolerance and equality while sharing her mathematical talents with generations of students. This captivating book gives voice to women mathematicians from the late eighteenth century through to the present day. It documents the complex nature of the conditions women around the world have faced--and continue to face--while pursuing their careers in mathematics. The stories of the three women above and those of many more appear here, each one enlightening and inspiring. The earlier parts of the book provide historical context and perspective, beginning with excursions into the lives of fifteen women born before 1920. Included are histories of collective efforts to improve women's opportunities in research mathematics. In addition, a photo essay puts a human face on the subject as it illustrates women's contributions in professional associations. More than eighty women from academe, government, and the private sector provide a rich mélange of insights and strategies for creating workable career paths while maintaining rewarding personal lives. The book discusses related social and cultural issues, and includes a summary of recent comparative data relating to women and men in mathematics and women from other sciences. First-person accounts provide explicit how-tos; many narratives demonstrate great determination and perseverance. Talented women vividly portray their pleasure in discovering new mathematics. The senior among them speak out candidly, interweaving their mathematics with autobiographical detail. At the beginning of a new century, women at all stages of their careers share their outlooks and experiences. Clear, engaging, and meticulously researched, Complexities will inspire young women who are contemplating careers in mathematics and will speak to women in many fields of endeavor and walks of life.
This book examines the historically unique conditions under which the International Congress of Mathematicians took place in Oslo in 1936. This Congress was the only one on this level to be held during the period of the Nazi regime in Germany (1933–1945) and after the wave of emigrations from it. Relying heavily on unpublished archival sources, the authors consider the different goals of the various participants in the Congress, most notably those of the Norwegian organizers, and the Nazi-led German delegation. They also investigate the reasons for the absence of the proposed Soviet and Italian delegations. In addition, aiming to shed light onto the mathematical dimension of the Congress, the authors provide overviews of the nineteen plenary presentations, as well as their planning and development. Biographical information about each of the plenary speakers rounds off the picture. The Oslo Congress, the first at which Fields Medals were awarded, is used as a lens through which the reader of this book can view the state of the art of mathematics in the mid-1930s.
A remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval. At age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel's famous 1931 paper "On Formally Undecidable Propositions" appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton's famous Institute for Advanced Study, called him "the greatest logician since Aristotle." He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of the human mind, and beset by personal demons of anxiety and paranoid delusions that would ultimately lead to his tragic end from self-starvation. Drawing on previously unpublished letters, diaries, and medical records, Journey to the Edge of Reason offers the most complete portrait yet of the life of one of the 20th century's greatest thinkers. Stephen Budiansky's account brings to life the remarkable world of philosophical and mathematical creativity of pre-war Vienna, and documents how it was barbarically extinguished by the Nazis. He charts Gödel's own hair's-breadth escape from Nazi Germany to the scholarly idyll of Princeton; and the complex, gently humorous, sensitive, and tormented inner life of this iconic but previously enigmatic giant of modern science. Weaving together Gödel's public and private lives, this is a tale of creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval.