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 approaches" by Abel Laureate Sir Andrew Wiles, University of Oxford 2. "Andrew Wiles' marvelous proof" by professor Henri Darmon, McGill University 3. "What is the Birch--Swinnerton-Dyer Conjecture, and what is known about it?" by professor Manjul Bhargava, Princeton University 4. "From Fermat's Last Theorem to Homer's Last Theorem" - a popular lecture by Simon Singh, author of Fermat's Last Theorem among other achievements. This lecture will never be published because the presentation contained material protected by intellectual property.