Topic summary
MRDP theorem
Extracted from the Wikipedia article Diophantine set.
Matiyasevich's completion of the MRDP theorem settled Hilbert's tenth problem. Hilbert's tenth problem was to find a general algorithm that can decide whether a given Diophantine equation has a solution among the integers. While Hilbert's tenth problem is not a formal mathematical statement as such, the nearly universal acceptance of the (philosophical) identification of a decision algorithm with a total computable predicate allows the MRDP theorem to be used to conclude that the tenth problem is unsolvable.