Revolutions in Mathematics: A Critical Examination of Conceptual Change in Mathematical History by Donald Gillies

Introduction

Does mathematics undergo revolutions, much like the natural sciences? In Revolutions in Mathematics, editor Donald Gillies brings together a fascinating collection of essays that probe this very question. This book is an essential read for anyone interested in the philosophy and history of mathematics, offering a rigorous yet accessible exploration of how mathematical knowledge evolves. Whether you are a student, teacher, or researcher, this volume will challenge your understanding of what mathematics truly is.

Book Overview

Published by OUP Oxford, this hardcover edition is the first comprehensive examination of the concept of revolution as applied to mathematics. It reprints the seminal papers from the 1970s debate on mathematical revolutions, alongside fresh contributions from nine eminent historians of mathematics. Each chapter examines a pivotal episode in the history of mathematics—from the discovery of irrational numbers to the rise of non-Euclidean geometry—and asks whether it qualifies as a revolution. The book balances both supporting and opposing viewpoints, making it a balanced and thought-provoking resource.

Key Highlights

• First-ever comprehensive study of revolutions in mathematics
• Includes original papers from the 1970s debate plus updated perspectives
• Features contributions from nine leading experts in the history of mathematics
• Examines key episodes such as the calculus controversy, the birth of set theory, and the development of algebra
• Bridges philosophy, history, and mathematics in a single volume

Inside the Book

The book is divided into three parts. Part One reprints the foundational papers by Michael Crowe, Joseph Dauben, and others that sparked the original debate. Part Two presents new essays from these scholars, reflecting on how their views have evolved. Part Three contains nine original case studies, each analysing a specific historical turning point. The chapters are richly detailed yet written in clear, non-technical language, making them accessible even to readers without a deep background in mathematics.

Key Topics

• The nature of mathematical progress: cumulative or revolutionary?
• The discovery of irrational numbers and its impact on Greek mathematics
• The development of non-Euclidean geometries
• The rise of abstract algebra and set theory
• The role of social and cultural factors in mathematical change
• Comparison between revolutions in science and mathematics

Reader Benefits

• Gain a deeper understanding of how mathematical ideas evolve over time
• Learn to critically evaluate the concept of revolution in different fields
• Explore fascinating historical episodes that shaped modern mathematics
• Enhance your ability to think philosophically about knowledge and change
• Perfect for preparing academic papers, debates, or classroom discussions

Learning Outcomes

After reading this book, you will be able to: articulate the arguments for and against mathematical revolutions; identify key turning points in the history of mathematics; analyse the influence of external factors on mathematical development; and engage with contemporary debates in the philosophy of mathematics. The book also sharpens your critical thinking and historical awareness—skills that are valuable far beyond mathematics.

Who Should Read

• Mathematics students and teachers curious about the history of their subject
• Philosophers of science and mathematics
• Historians of science and intellectual history
• Researchers in science and technology studies
• General readers with an interest in how knowledge changes

About the Author

Donald Gillies is a renowned philosopher of science and mathematics, currently Professor at University College London. His research focuses on the philosophy of statistics, causality, and the history of mathematics. He has authored several influential books, including Philosophical Theories of Probability and Artificial Intelligence and Scientific Method. His editorial work on this volume has been praised for bringing clarity and depth to a complex debate.

About the Publisher

OUP Oxford (Oxford University Press) is one of the oldest and most respected academic publishers in the world. With a legacy spanning over five centuries, OUP is known for its rigorous editorial standards and commitment to scholarly excellence. This hardcover edition is produced to the highest quality, making it a durable addition to any library.

Conclusion

Revolutions in Mathematics is a landmark work that will change the way you think about mathematics. It is not merely a history book—it is an invitation to question the very foundations of a discipline we often take for granted. Whether you are a seasoned mathematician or a curious student, this book offers a rewarding intellectual journey. Add it to your collection today and discover the revolutionary ideas that have shaped the mathematical world.