Overview

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.

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9780691196411

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Reviews

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 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 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 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 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 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

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 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 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

If you are not familiar with this relatively new research about the foundations and and minimal assumptions needed to develop the massive mathematical structure, this provides a good informal guideline. ---Adhemar Bultheel, European Mathematical Society 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 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

Author Information

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).

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