In this talk we will attempt to state and then give a rough outline of the proof of G\"{o}del's first incompleteness theorem. We will explore the notions of G\"{o}del numbers and recursive functions and relations, along with explanations of basic concepts in mathematical logic as needed. We will then state without proof some key theorems and outline the proof of G\"{o}del's incompleteness. This talk will follow notes written by Dr. Don Monk.
Godel's First Incompleteness Theorem