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.

Readership

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