Overview
- Elucidates the relationship between mathematical practices and the philosophy of mathematics
- Presents an overview through time, from the origins of mathematics to contemporary mathematical practices
- Brings together experts from different fields to present a multifaceted view on the topic
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Table of contents (114 entries)
Keywords
- Origins
- Natural History
- Natural Philosophy
- Mathematician’s reflections
- Probability
- Constructing the reals
- Paradoxes and foundations
- Euclidean and non-Euclidean geometry
- Logic
- Proof
- Ontology
- Pluralism
- Experimental mathematics
- Views from other domains
- New perspectives
- Semiology of mathematical practice
- Reuben Hersh
- Yuri Manin
- Chandler Davis
- Influences in 20C and 21C mathematical practices
About this book
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, USAWilliam Byers, Concordia University, Canada
Carlo Cellucci, Sapienza University of Rome, ItalyChandler 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
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, of proof 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
Editors and Affiliations
About the editor
Bharath Sriraman is a Professor of Mathematics at the University of Montana-Missoula working in the areas of cognition, creativity, mathematics and philosophy. In 2016, he was named the University of Montana Distinguished Scholar. Prof. Sriraman has held 40+ visiting professorships at institutions in Norway, Iceland, Sweden, Germany, Turkey, Iran, Malaysia, South Korea, Canada, South Africa, Colombia, and Argentina, which include two US Fulbright awards. To date, Prof. Sriraman has published more than 330 journal articles, book chapters, proceedings papers, and reference work entries, and served as the Editor of 33 volumes, in his areas of interest. He is the founder and Editor-in-Chief of The Mathematics Enthusiast, an independent, peer-reviewed, open-access international journal. In addition to editing and curating the Handbook of the History and Philosophy of Mathematical Practice, he previously served as the Editor-in-Chief of the Handbook of the Mathematics of the Arts and Sciences (Springer, 2021). In keeping with the adage Omne Trium Perfectum, his third Major Springer Reference Works Project is the Handbook of Visual, Experimental and Computational Mathematics: Bridges through Data in preparation for release in 2027. In his spare time, he is an amateur arborist.
Bibliographic Information
Book Title: Handbook of the History and Philosophy of Mathematical Practice
Editors: Bharath Sriraman
DOI: https://doi.org/10.1007/978-3-030-19071-2
Publisher: Springer Cham
eBook Packages: Springer Reference Mathematics, Reference Module Computer Science and Engineering
eBook ISBN: 978-3-030-19071-2Due: 09 June 2024
Number of Pages: XV, 3200
Topics: History of Mathematical Sciences, Philosophy of Mathematics, Mathematical Logic and Foundations