The Oxford Handbook of Generality in Mathematics and the Sciences

The Oxford Handbook of Generality in Mathematics and the Sciences

Author: Karine Chemla

Publisher: Oxford University Press

Published: 2016-07-07

Total Pages: 529

ISBN-13: 0191083054

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Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments. The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity", "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.


The Oxford Handbook of Generality in Mathematics and the Sciences

The Oxford Handbook of Generality in Mathematics and the Sciences

Author: Karine Chemla

Publisher: Oxford University Press

Published: 2016

Total Pages: 529

ISBN-13: 0198777264

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This collection of original essays aims to inquire into the diversity of Generality. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts.


Mastering the History of Pure and Applied Mathematics

Mastering the History of Pure and Applied Mathematics

Author: Toke Knudsen

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-06-04

Total Pages: 358

ISBN-13: 3110770075

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The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.


The Richness of the History of Mathematics

The Richness of the History of Mathematics

Author: Karine Chemla

Publisher: Springer Nature

Published: 2023-11-27

Total Pages: 702

ISBN-13: 3031408551

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This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.


Osiris, Volume 38

Osiris, Volume 38

Author: James Evans

Publisher: University of Chicago Press

Published: 2023-07-18

Total Pages: 419

ISBN-13: 0226827887

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Perceptively explores the shifting intersections between algorithmic systems and human practices in the modern era. How have algorithmic systems and human practices developed in tandem since 1800? This volume of Osiris deftly addresses the question, dispelling along the way the traditional notion of algorithmic “code” and human “craft” as natural opposites. Instead, algorithms and humans have always acted in concert, depending on each other to advance new knowledge and produce social consequences. By shining light on alternative computational imaginaries, Beyond Craft and Code opens fresh space in which to understand algorithmic diversity, its governance, and even its conservation. The volume contains essays by experts in fields extending from early modern arithmetic to contemporary robotics. Traversing a range of cases and arguments that connect politics, historical epistemology, aesthetics, and artificial intelligence, the contributors collectively propose a novel vocabulary of concepts with which to think about how the history of science can contribute to understanding today’s world. Ultimately, Beyond Craft and Code reconfigures the historiography of science and technology to suggest a new way to approach the questions posed by an algorithmic culture—not only improving our understanding of algorithmic pasts and futures but also unlocking our ability to better govern our present.


Mathematical Communities in the Reconstruction After the Great War 1918–1928

Mathematical Communities in the Reconstruction After the Great War 1918–1928

Author: Laurent Mazliak

Publisher: Springer Nature

Published: 2021-03-27

Total Pages: 373

ISBN-13: 3030616835

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This book is a consequence of the international meeting organized in Marseilles in November 2018 devoted to the aftermath of the Great War for mathematical communities. It features selected original research presented at the meeting offering a new perspective on a period, the 1920s, not extensively considered by historiography. After 1918, new countries were created, and borders of several others were modified. Territories were annexed while some countries lost entire regions. These territorial changes bear witness to the massive and varied upheavals with which European societies were confronted in the aftermath of the Great War. The reconfiguration of political Europe was accompanied by new alliances and a redistribution of trade – commercial, intellectual, artistic, military, and so on – which largely shaped international life during the interwar period. These changes also had an enormous impact on scientific life, not only in practice, but also in its organization and communication strategies. The mathematical sciences, which from the late 19th century to the 1920s experienced a deep disciplinary evolution, were thus facing a double movement, internal and external, which led to a sustainable restructuring of research and teaching. Concomitantly, various areas such as topology, functional analysis, abstract algebra, logic or probability, among others, experienced exceptional development. This was accompanied by an explosion of new international or national associations of mathematicians with for instance the founding, in 1918, of the International Mathematical Union and the controversial creation of the International Research Council. Therefore, the central idea for the articulation of the various chapters of the book is to present case studies illustrating how in the aftermath of the war, many mathematicians had to organize their personal trajectories taking into account the evolution of the political, social and scientific environment which had taken place at the end of the conflict.


Development Of Mathematics Between The World Wars, The: Case Studies, Examples And Analyses

Development Of Mathematics Between The World Wars, The: Case Studies, Examples And Analyses

Author: Martina Becvarova

Publisher: World Scientific

Published: 2021-05-14

Total Pages: 623

ISBN-13: 1786349329

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The Development of Mathematics Between the World Wars traces the transformation of scientific life within mathematical communities during the interwar period in Central and Eastern Europe, specifically in Germany, Russia, Poland, Hungary, and Czechoslovakia. Throughout the book, in-depth mathematical analyses and examples are included for the benefit of the reader.World War I heavily affected academic life. In European countries, many talented researchers and students were killed in action and scientific activities were halted to resume only in the postwar years. However, this inhibition turned out to be a catalyst for the birth of a new generation of mathematicians, for the emergence of new ideas and theories and for the surprising creation of new and outstanding scientific schools.The final four chapters are not restricted to Central and Eastern Europe and deal with the development of mathematics between World War I and World War II. After describing the general state of mathematics at the end of the 19th century and the first third of the 20th century, three case studies dealing with selected mathematical disciplines are presented (set theory, potential theory, combinatorics), in a way accessible to a broad audience of mathematicians as well as historians of mathematics.


Duality in 19th and 20th Century Mathematical Thinking

Duality in 19th and 20th Century Mathematical Thinking

Author: Ralf Krömer

Publisher: Springer Nature

Published: 2024

Total Pages: 962

ISBN-13: 3031597974

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This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.