Hilbert's 10th Problem

Abstract

In 1900 German mathematician David Hilbert published a list of 23 open mathematical problems. Hilbert’s 10th problem asks for an algorithm which determines whether a polynomial with integer coefficients (and an arbitrary amount of variables) has a root in Z. We will explore and explain Matiyasevich’s proof and the necessary theory to understand it. Reading this thesis will guide you through both logic and number theory, with small parts hinting to theoretical computer science.