Explore a thought-provoking lecture on optimization problems in calculus of variations and their applications in economic theory. Delve into the limitations of traditional optimal solutions and discover why a new approach is necessary. Learn about the introduction of an innovative concept of solution, leading to an implicit ordinary differential equation (ODE) in the sense of René Thom. Join Ivar Ekeland from CEREMADE, Université Paris-Dauphine, and Paris-Sciences-Lettres as he bridges the gap between Frank Ramsey's work and René Thom's contributions, pushing the boundaries of optimization theory.