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Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.
Hilbert's tenth problem does not ask whether there exists an algorithm for deciding the solvability of Diophantine equations, but rather asks for the construction of such an algorithm: "to devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers". That this ...
"The problem of deciding whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic", a consequence of the MRDP theorem resolving Hilbert's tenth problem. [6] Determining the domain of a solution to an ordinary differential equation of the form
Hilbert's 2nd and 10th problems introduced the "Entscheidungsproblem" (the "decision problem"). In his 2nd problem he asked for a proof that "arithmetic" is " consistent ". Kurt Gödel would prove in 1931 that, within what he called "P" (nowadays called Peano Arithmetic ), "there exist undecidable sentences [propositions]". [ 4 ]
"Hilbert's Tenth Problem is Unsolvable". American Mathematical Monthly. 80 (3): 233– 269. doi:10.2307/2318447. ISSN 0002-9890. JSTOR 2318447. Zbl 0277.02008. Matiyasevich, Yuri V. (1993). Hilbert's 10th Problem. MIT Press Series in the Foundations of Computing. Foreword by Martin Davis and Hilary Putnam. Cambridge, MA: MIT Press. ISBN 0-262 ...
Hilbert's axioms Hilbert's problems Hilbert's program Einstein–Hilbert action Hilbert space Hilbert system Epsilon calculus: Spouse: Käthe Jerosch: Children: Franz (b. 1893) Awards: Lobachevsky Prize (1903) Bolyai Prize (1910) ForMemRS (1928) [1] Scientific career: Fields: Mathematics, Physics and Philosophy: Institutions: University of ...
In 1972, at the age of 25, he defended his doctoral dissertation on the unsolvability of Hilbert's tenth problem. [ 7 ] From 1974 Matiyasevich worked in scientific positions at LOMI, first as a senior researcher, in 1980 he headed the Laboratory of Mathematical Logic.
Pages in category "Hilbert's problems" The following 35 pages are in this category, out of 35 total. This list may not reflect recent changes. ...
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