Hilbert's famous 10th problem asks whether there is a general algorithm to decide whether a polynomial in many variables has a solution. I will explain how Robinson, Davis, Putnam, and Matijasevic answered the question in the negative by proving a much more interesting theorem: that any listable set can be listed using a polynomial equation. I'll also give some awesome mind-blowing consequences of this theorem, such as prime-producing polynomials! No background in anything will be required.