Hilbert's tenth problem

Yuri V. Matiyasevich ; with a foreword by Martin Davis

At the 1900 International Congress of Mathematicians, held that year in Paris, the German mathematician David Hilbert put forth a list of 23 unsolved problems that he saw as being the greatest challenges for twentieth-century mathematics. Hilbert's 10th problem, to find a method (what we now call an algorithm) for deciding whether a Diophantine equation has an integral solution, was solved by Yuri Matiyasevich in 1970. Proving the undecidability of Hilbert's 10th problem is clearly one of the great mathematical results of the century.This book presents the full, self-contained negative solution of Hilbert's 10th problem. In addition it contains a number of diverse, often striking applications of the technique developed for that solution (scattered previously in journals), describes the many improvements and modifications of the original proof - since the problem was "unsolved" 20 years ago, and adds several new, previously unpublished proofs.Included are numerous exercises that range in difficulty from the elementary to small research problems, open questions,and unsolved problems. Each chapter concludes with a commentary providing a historical view of its contents. And an extensive bibliography contains references to all of the main publications directed to the negative solution of Hilbert's 10th problem as well as the majority of the publications dealing with applications of the solution.Intended for young mathematicians, Hilbert's 10th Problem requires only a modest mathematical background. A few less well known number-theoretical results are presented in the appendixes. No knowledge of recursion theory is presupposed. All necessary notions are introduced and defined in the book, making it suitable for the first acquaintance with this fascinating subject.Yuri Matiyasevich is Head of the Laboratory of Mathematical Logic, Steklov Institute of Mathematics, Russian Academy of Sciences, Saint Petersburg.

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書名 Hilbert's tenth problem
著作者等 Matii︠a︡sevich, I︠U︡. V.
Davis Martin
Putnam Hilary
Matiyasevich Yuri
書名別名 Desi︠a︡tai︠a︡ problema Gilʹberta
シリーズ名 MIT Press series in the foundations of computing
出版元 MIT Press
刊行年月 c1993
ページ数 xxii, 264 p.
大きさ 24 cm
ISBN 9780262132954
NCID BA21148397
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言語 英語
原文言語 ロシア語
出版国 アメリカ合衆国