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.
An Interview with Reuben Hersh.- Nine decades: A photographic passage .- Pluralism as modeling and as Confusion.- "Now" has an infinitesimal positive duration.- Review of How Humans Learn to Think Mathematically: Exploring the three worlds of mathematics..- Can You Say What Mathematics Is?.- The Exact Sciences and Non-Euclidean Logic.- XENOMATH!.- Cognitive Networks: Brains, Internet and Civilizations.- Reuben Hersh on the Growth of Mathematical Knowledge: Kant, Geometry and Number Theory.- Do Mathematicians have responsibilities?.- School Mathematics and "Real" Mathematics.- What is Mathematics and What Should it Be?.- Humanism about Abstract Objects.- Can something just happen to be true?.- The "Artificial Mathematician" Objection: Exploring the (im)possibility of automating mathematical understanding.- Wittgenstein, Mathematics and the Temporality of Technique.- Gödel's Legacy.- Varieties of Maverick Philosophy of Mathematics.- Does reason evolve? (Does the reasoning in mathematics evolve?).- Mathematical Theories as Models.- Mathematics for makers and mathematics for users.- Case Study in Hersh's Philosophy: Bézout's Theorem.- A gift to teachers.- The Philosophy of Reuben Hersh: a non-technical assessment.- Friends and Former Comrades.- On the nature of mathematical entities.