Hardcover ISBN:  9780883855676 
Product Code:  SPEC/59 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614445050 
Product Code:  SPEC/59.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Hardcover ISBN:  9780883855676 
eBook: ISBN:  9781614445050 
Product Code:  SPEC/59.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 
Hardcover ISBN:  9780883855676 
Product Code:  SPEC/59 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614445050 
Product Code:  SPEC/59.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Hardcover ISBN:  9780883855676 
eBook ISBN:  9781614445050 
Product Code:  SPEC/59.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 

Book DetailsSpectrumVolume: 59; 2008; 346 pp
During the first 75 years of the twentieth century, almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics, such as "what is the nature of mathematical knowledge and of mathematical objects" and "how is mathematics related to science." Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, connections are made to issues relevant to the teaching of mathematics.

Table of Contents

Proof and How it is Changing

Chapter 1. Proof: Its Nature and Significance, Michael Detlefsen

Chapter 2. Implications of Experimental Mathematics for the Philosophy of Mathematics, Jonathan Borwein

Chapter 3. On the Roles of Proof in Mathematics, Joseph Auslander

Social Constructivist Views of Mathematics

Chapter 4. When Is a Problem Solved?, Philip J. Davis

Chapter 5. Mathematical Practice as a Scientific Problem, Reuben Hersh

Chapter 6. Mathematical Domains: Social Constructs?, Julian Cole

The Nature of Mathematical Objects and Mathematical Knowledge

Chapter 7. The Existence of Mathematical Objects, Charles Chihara

Chapter 8. Mathematical Objects, Stewart Shapiro

Chapter 9. Mathematical Platonism, Mark Balaguer

Chapter 10. The Nature of Mathematical Objects, Øystein Linnebo

Chapter 11. When is One Thing Equal to Some Other Thing?, Barry Mazur

The Nature of Mathematics and its Applications

Chapter 12. Extreme Science: Mathematics as the Science of Relations as Such, R. S. D. Thomas

Chapter 13. What is Mathematics? A Pedagogical Answer to a Philosophical Question, Guershon Harel

Chapter 14. What Will Count as Mathematics in 2100?, Keith Devlin

Chapter 15. Mathematics Applied: The Case of Addition, Mark Steiner

Chapter 16. Probability—A Philosophical Overview, Alan Hájek


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
During the first 75 years of the twentieth century, almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics, such as "what is the nature of mathematical knowledge and of mathematical objects" and "how is mathematics related to science." Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, connections are made to issues relevant to the teaching of mathematics.

Proof and How it is Changing

Chapter 1. Proof: Its Nature and Significance, Michael Detlefsen

Chapter 2. Implications of Experimental Mathematics for the Philosophy of Mathematics, Jonathan Borwein

Chapter 3. On the Roles of Proof in Mathematics, Joseph Auslander

Social Constructivist Views of Mathematics

Chapter 4. When Is a Problem Solved?, Philip J. Davis

Chapter 5. Mathematical Practice as a Scientific Problem, Reuben Hersh

Chapter 6. Mathematical Domains: Social Constructs?, Julian Cole

The Nature of Mathematical Objects and Mathematical Knowledge

Chapter 7. The Existence of Mathematical Objects, Charles Chihara

Chapter 8. Mathematical Objects, Stewart Shapiro

Chapter 9. Mathematical Platonism, Mark Balaguer

Chapter 10. The Nature of Mathematical Objects, Øystein Linnebo

Chapter 11. When is One Thing Equal to Some Other Thing?, Barry Mazur

The Nature of Mathematics and its Applications

Chapter 12. Extreme Science: Mathematics as the Science of Relations as Such, R. S. D. Thomas

Chapter 13. What is Mathematics? A Pedagogical Answer to a Philosophical Question, Guershon Harel

Chapter 14. What Will Count as Mathematics in 2100?, Keith Devlin

Chapter 15. Mathematics Applied: The Case of Addition, Mark Steiner

Chapter 16. Probability—A Philosophical Overview, Alan Hájek