Full Description
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy - as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today - who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy.
Editorial Advisory Board
Andrew Aberdein, Florida Institute ofTechnology, USA
Jody Azzouni, Tufts University, USA
Otávio Bueno, University of Miami, USA
William Byers, Concordia University, Canada
Carlo Cellucci, Sapienza University of Rome, Italy
Chandler Davis, University of Toronto, Canada (1926-2022)
Paul Ernest, University of Exeter, UK
Michele Friend, George Washington University, USA
Reuben Hersh, University of New Mexico, USA (1927-2020)
Kyeong-Hwa Lee, Seoul National University, South Korea
Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023)
Athanase Papadopoulos, University of Strasbourg, France
Ulf Persson, Chalmers University of Technology, Sweden
John Stillwell, University of San Francisco, USA
David Tall, University of Warwick, UK (1941-2024)
This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin.
---Barry Mazur, Gerhard Gade University Professor, Harvard University
This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate.
---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize
Dedicating a volume to the memory of three mathematicians - Chandler Davis, Reuben Hersh, and Yuri Manin -, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration!
---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
Contents
Introduction to the Handbook of the History and Philosophy of Mathematical Practice.- From Origins to the Natural Historians/Philosophers.- Logic.- Practices in Euclidean and Non-Euclidean Geometry.- "Experimental" Mathematics.- Constructing the Reals; Paradoxes and Foundations.- Views from Other Domains.- Ontology.- Proof.- Pluralism.- New Perspectives.- Trends and Influences in 20th Century Mathematics. Mathematicians' Reflections on Practice and Working Philosophy of Mathematics. Practical, Historical, and Philosophical Instances of Probability.- Semiology of Mathematical Practice.
