Julia Robinson and Hilbert’s Tenth Problem

Hilbert’s Tenth Problem asks whether there is an algorithmic procedure to solve Diophantine equations (polynomial equations with integer coefficients) for integer solutions. This famous problem was shown to be unsolvable by Yuri Matiyasevič in 1970. In other words, there is no algorithm that can decide in general whether a given Diophantine equations has integer solutions or not. This negative solution builds on a long line of work by Martin Davis, Hilary Putnam, and importantly, Julia Robinson. In this article, we briefly describe the problem, its unsolvability, and Julia Robinson’s contribution.