Author: Georges Gonthier E-mail:gonthier@microsoft.com Title: The Four Color Theorem in Coq Abstract: This fall we completed a fully formal proof of the famous Four Color Theorem, using the Coq proof assistant, thus bringing a 5-year old side project to a close. In this talk we will review the main obstacles of this formal proof, and present the main techniques that were used to overcome them, in particular a general and pervasive use of computational reflection, and a simple tactic "shell" that very effectively simplifies proof context management.