Embark on a panoramic tour through combinatorial optimization in this 59-minute lecture by Michel Goemans, presented at the "Panorama of Mathematics" conference. Organized by the Hausdorff Center for Mathematics to celebrate their tenth year of excellence, this talk explores new trends, results, and challenges in mathematical sciences. Delve into the fascinating world of combinatorial optimization as Goemans guides you through its key concepts, recent developments, and future directions, providing valuable insights for mathematicians and researchers in related fields.