Hilbert's tenth problem is one of the famous problems posed by mathematician David Hilbert in 1900. It asks whether there is a general algorithm that can determine if a given polynomial equation with integer coefficients has a solution in integers. In simpler terms, it questions if we can create a method to always find integer solutions for these types of equations. In 1970, mathematicians Julia Robinson, Martin Davis, and Hilary Putnam proved that no such algorithm exists. This result means that while some polynomial equations can be solved with integers, there is no universal procedure to determine the solvability for all such equations.