The story of proof : logic and the history of mathematics

This book includes bibliographical references and index.

"The proof is one of the most significant and defining features of mathematical thought. Many of the most significant advances in mathematics have been advances in the concept of proof, and in many ways, the history of mathematics can be viewed as a history of the proof. Yet proof itself is not considered an interesting topic by many mathematicians. In the United States, proof is not deemed an essential part of mathematics education until the upper-undergraduate level. In The Story of Proof, John Stillwell argues that the proof is an important object of study in itself. He provides insight into the history, theory, and practice of proof in order to shed light on the way that mathematics works at its most fundamental levels. The book begins with the proof of one of mathematics' most foundational theorems, the Pythagorean Theorem. The book then proceeds to look at the role of proof in the various fields of mathematics, including geometry and number theory, algebra, algebraic geometry, and calculus. By examining the history of the proof, Stillwell sheds new light on age-old questions in mathematics, including how logic, computation, and abstraction are connected with one another and with the rest of mathematics"--