A Concise History of Mathematics for Philosophers

by John Stillwell

Overview

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.

Product Details

ISBN-13:	9781108456234
Publisher:	Cambridge University Press
Publication date:	06/06/2019
Series:	Elements in the Philosophy of Mathematics
Pages:	75
Sales rank:	736,675
Product dimensions:	5.91(w) x 9.06(h) x 0.20(d)

Table of Contents

Preface; 1. Irrational numbers and geometry; 2. Infinity in Greek mathematics; 3. Imaginary numbers; 4. Calculus and infinitesimals; 5. Continuous functions and real numbers; 6. From non-Euclidean geometry to arithmetic; 7. Set theory and its paradoxes; 8. Formal systems; 9. Unsolvability and incompleteness.