Handbook of the History and Philosophy of Mathematical Practice (Hardcover)

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 of Technology 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 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