Statistical mechanics, non linear physics and mathematics have often progressed hand in hand, mutually enriching themselves by exchanging key questions and methods. This summer school will be organized around these interactions, with the aim of deepening them and extending them to current research questions. We have identified four active and quickly advancing topics : Random interfaces, Disordered landscapes and AI, Long-range interactions, and Active matter. Each one will be addressed simultaneously by two internationally renowned lecturers, a physicist and a mathematician. This original set-up for the summer school organization will provide two different points of view on the same topic and the tools to bridge them. We aim to bring together attendees from physics and mathematics, to provide them with opportunities to broaden their perspectives, from experimental physics to theoretical physics and mathematics, and to expand their scientific network.