Reverse Mathematics - by John Stillwell (Paperback)

About the Book

This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.

Book Synopsis

The first book surveying the history and ideas behind reverse mathematics

Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

From the Back Cover

"Reverse mathematics is the mathematical logician's version of zoology or botany, a classification of mathematical theorems in terms of the strength of the axioms needed to prove them. Stillwell carefully situates the field in the broader context of the history of mathematics and its foundations, and does a fine job of making the whole endeavor accessible to a general mathematical audience."--Jeremy Avigad, Carnegie Mellon University

"Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study. It provides a context for the questions investigated by reverse mathematics and makes an extended argument for their significance within contemporary mathematical practice."--Denis Hirschfeldt, University of Chicago

"Reverse mathematics is a major research direction in the foundations of mathematics and mathematical logic, and the insights obtained from reverse mathematics will interest a wide mathematically minded audience. Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. I heartily commend this very readable and accessible book."--Stephen Simpson, Vanderbilt University

Review Quotes

"Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study."--Denis Hirschfeldt, University of Chicago

"Stillwell carefully situates the field in the broader context of the history of mathematics and its foundations, and does a fine job of making the whole endeavor accessible to a general mathematical audience."--Jeremy Avigad, Carnegie Mellon University

"Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. I heartily commend this very readable and accessible book."--Stephen Simpson, Vanderbilt University

"The field has been due for a general treatment accessible to undergraduates and to mathematicians in other areas. . . . With Reverse Mathematics, John Stillwell provides exactly that kind of introduction."--Carl Mummert, Notices of the American Mathematical Society

About the Author

John Stillwell is professor of mathematics at the University of San Francisco and an affiliate of the School of Mathematical Sciences at Monash University, Australia. His many books include Mathematics and Its History and Elements of Mathematics (Princeton).