# History and Philosophy of Modern Mathematics

Volume XI

Publication Year: 1988

*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.

Published by: University of Minnesota Press

Series: Minnesota Studies in the Philosophy of Science

#### Cover

#### I: Logic and the Foundations of Mathematics

#### II: Reinterpretations in the History of Mathematics

#### Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics

Joseph W Dauben

...Historically, the dual concepts of infinitesimals and infinities have always been at the center of crises and foundations in mathematics, from the first "foundational crisis" that some, at least, have associated...

#### How Can Mathematicians and Mathematical Historians Help Each Other?

Richard Askey

...dropped, but I could argue both sides of that question. The present title presumes the optimistic answer, and while we all hope that this is the correct answer, the present time may not be the right one for this answer. The history of mathematics is not an easy field...

#### III: Case Studies in the History and Philosophy of Mathematics

#### Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth-Century Transformation of Mathematics

Howard Stein

...so profound that it is not too much to call it a second birth of the subject— its first birth having occurred among the ancient Greeks, say from the sixth through the fourth century...

#### Ten Misconceptions about Mathematics and Its History

Michael J. Crowe

...teaching, and writing history of mathematics. During those decades, I have become convinced that ten claims I formerly accepted concerning mathematics and its development are both seriously wrong and a hindrance to the historical study of...

#### Mathematics and the Sciences

Felix E. Browder

...interaction between mathematics and the sciences and to relate the trends to the historical development of mathematics as an intellectual discipline and of the sciences as they have developed since the seventeenth century. This story is interesting...

#### Mathematical Naturalism

Philip Kitcher

...century has been concerned with the enterprise of providing a foundation for mathematics. There is no doubt that this enterprise has often been mathematically fruitful. Indeed, the growth of logic as an important field within mathematics owes much to the pioneering...

#### IV: The Social Context of Modern Mathematics

#### Partisans and Critics of a New Science: The Case of Artificial Intelligence and Some Historical Parallels

Judith V Grabiner

...in mathematics courses—we see the presence of the computer. We are told that we are entering a new age, that of the Computer Revolution, and that the field known as Artificial Intelligence is at the forefront of that revolution. Its practitioners have...

#### The Emergence of Princeton as a World Center for Mathematical Research, 1896-1939

William Aspray

...University, reflecting its ambitions for graduate education and research. At the time, Princeton, like other American universities, was primarily a teaching institution that made few significant contributions...

#### Contributors

...Richard Askey, Professor of Mathematics, University of Wisconsin at Madison William Aspray, Associate Director, Charles Babbage Institute for the History of Information Processing, University of Minnesota M. K. Bennett, Professor of Mathematics, University of Massachusetts at Amherst...

E-ISBN-13: 9780816653058

E-ISBN-10: 0816653054

Print-ISBN-13: 9780816615674

Page Count: 396

Publication Year: 1988

Series Title: Minnesota Studies in the Philosophy of Science

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