7th Estonian Winter School in Computer Science (EWSCS)
VII Eesti Arvutiteaduse Talvekool (EATTK)
Palmse, Estonia
March 3 - 8, 2002
Prof. Yuri Matiyasevich
Steklov Institute of Mathematics (POMI)
St. Petersburg, RUSSIA
Hilbert's tenth problem
Abstract
A Diophantine equation is an equation of the form
D(x1,...,xm) = 0 ,
where D is a polynomial with integer coefficients. These equations were named after the Greek mathematician Diophantus who lived in the 3rd century A.D.
Hilbert's Tenth problem can be stated as follows:
Determination of the Solvability of a Diophantine Equation. Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients, devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.
Course materials
Yu. Matiyasevich. Hilbert's Tenth Problem. V. 1. of Pacific Inst. for the Math. Sciences Distinguished Lecture Series. Pacific Inst. for the Math. Sciences, 2000. *Reproduced with permission.*
Yu. Matiyasevich. My collaboration with Julia Robinson. The Mathematical Intelligencer, v. 14, n. 4, pp. 38-45, 1992.
Sect. 10.2. from Yu. Matiyasevich. Hilbert's 10th Problem. Foundations of Computing Series. The MIT Press, 1993.
About the Speaker
E-mail: yumat@pdmi.ras.ru
URL: http://logic.pdmi.ras.ru/~yumat/