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Hilbert’s Tenth Problem: An Introduction to Logic, Number Theory, and Computability

M. Ram Murty Queen’s University, Kingston, ON, Canada
Brandon Fodden Carleton University, Ottawa, ON, Canada
Available Formats:
Softcover ISBN: 978-1-4704-4399-3
Product Code: STML/88
List Price: $55.00 Individual Price:$44.00
MAA Member Price: $44.00 Electronic ISBN: 978-1-4704-5261-2 Product Code: STML/88.E List Price:$55.00
Individual Price: $44.00 MAA Member Price:$44.00
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List Price: $82.50 MAA Member Price:$66.00
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Hilbert’s Tenth Problem: An Introduction to Logic, Number Theory, and Computability
M. Ram Murty Queen’s University, Kingston, ON, Canada
Brandon Fodden Carleton University, Ottawa, ON, Canada
Available Formats:
 Softcover ISBN: 978-1-4704-4399-3 Product Code: STML/88
 List Price: $55.00 Individual Price:$44.00 MAA Member Price: $44.00  Electronic ISBN: 978-1-4704-5261-2 Product Code: STML/88.E  List Price:$55.00 Individual Price: $44.00 MAA Member Price:$44.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
 List Price: $82.50 MAA Member Price:$66.00
• Book Details

Student Mathematical Library
Volume: 882019; 239 pp
MSC: Primary 11; 12;

Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists.

This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems.

Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.

Cover image by Jesse Jacobs.

Undergraduate and graduate students and researchers interested in number theory and logic.

• Chapters
• Introduction
• Cantor and infinity
• Axiomatic set theory
• Elementary number theory
• Computability and provability
• Hilbert’s tenth problem
• Applications of Hilbert’s tenth problem
• Hilbert’s tenth problem over number fields
• Background material

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 882019; 239 pp
MSC: Primary 11; 12;

Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists.

This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems.

Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.

Cover image by Jesse Jacobs.

Undergraduate and graduate students and researchers interested in number theory and logic.

• Chapters
• Introduction
• Cantor and infinity
• Axiomatic set theory
• Elementary number theory
• Computability and provability
• Hilbert’s tenth problem
• Applications of Hilbert’s tenth problem
• Hilbert’s tenth problem over number fields
• Background material
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.