The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lecture 2016 1. "Fermat's Last Theorem: abelian and non-abelian