Humanizing Mathematics and its Philosophy: Essays Celebrating the 90th Birthday of Reuben Hersh

Bharath Sriraman

Birkhäuser, Nov 7, 2017 - Mathematics - 363 pages

This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume:

• Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians?
  

• Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing?
  

The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians.
With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

Contents

• An Interview with Reuben Hersh: 1
• Nine Decades: 11
• Pluralism as Modeling and as Confusion: 19
• Now Has an Infinitesimal Positive Duration: 30
• Exploring the Three Worlds of Mathematics: 39
• Can You Say What Mathematics Is?: 45
• The Exact Sciences and NonEuclidean Logic: 61
• Xenomath: 68
• Brains Internet and Civilizations: 85
• Kant Geometry and Number Theory: 97
• Do Mathematicians Have Responsibilities?: 115
• School Mathematics and Real Mathematics: 124
• What Is Mathematics and What Should It Be?: 139
• Humanism About Abstract Objects: 150
• Can Something Just Happen to Be True?: 167
• Exploring the Impossibility of Automating Mathematical Understanding: 173
• Wittgenstein Mathematics and the Temporality of Technique: 199
• Gödels Legacy: 214
• Varieties of Maverick Philosophy of Mathematics: 223
• Does Reason Evolve? Does the Reasoning in Mathematics Evolve?: 253
• Mathematical Theories as Models: 290
• Mathematics for Makers and Mathematics for Users: 309
• Bézouts Theorem: 328
• A Gift to Teachers: 347
• A Nontechnical Assessment: 350
• Friends and Former Comrades: 355
• On the Nature of Mathematical Entities: 360

About the author

Bharath Sriraman is a Professor of Mathematics at the University of Montana

Bibliographic information

• Title: Humanizing Mathematics and its Philosophy: Essays Celebrating the 90th Birthday of Reuben Hersh
• Editor: Bharath Sriraman
• Publisher: Birkhäuser, 2017
• ISBN: 331961231X, 9783319612317
• Length: 363 pages
• Subjects: Mathematics / Applied; Mathematics / General