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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 ...
Franzén introduces Hilbert's tenth problem and the MRDP theorem (Matiyasevich-Robinson-Davis-Putnam theorem) which states that "no algorithm exists which can decide whether or not a Diophantine equation has any solution at all". MRDP uses the undecidability proof of Turing: "... the set of solvable Diophantine equations is an example of a ...
His work on Hilbert's tenth problem led to the MRDP theorem. He also advanced the Post–Turing model and co-developed the Davis–Putnam–Logemann–Loveland (DPLL) algorithm, which is foundational for Boolean satisfiability solvers. Davis won the Leroy P. Steele Prize, the Chauvenet Prize (with Reuben Hersh), and the Lester R. Ford Award.
The Entscheidungsproblem is related to Hilbert's tenth problem, which asks for an algorithm to decide whether Diophantine equations have a solution. The non-existence of such an algorithm, established by the work of Yuri Matiyasevich , Julia Robinson , Martin Davis , and Hilary Putnam , with the final piece of the proof in 1970, also implies a ...
Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. Her work on Hilbert's tenth problem (now known as Matiyasevich's theorem or the MRDP theorem) played a crucial ...
In 1963-1964 he completed 10th grade at the Moscow State University physics and mathematics boarding school No. 18 named after A. N. Kolmogorov. [ 1 ] [ 2 ] In 1964, he won a gold medal at the International Mathematical Olympiad [ 3 ] and was enrolled in the Mathematics and Mechanics Department of St. Petersburg State University without exams.
Jan Denef. Jan Denef (born 4 September 1951) is a Belgian mathematician.He is an Emeritus Professor of Mathematics at the Katholieke Universiteit Leuven (KU Leuven). [1]Denef obtained his PhD from KU Leuven in 1975 with a thesis on Hilbert's tenth problem; his advisors were Louis Philippe Bouckaert and Willem Kuijk.
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