Explore the philosophical and mathematical concept of shadows in this 36-minute lecture by renowned mathematician Mikhail Gromov at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the historical progression of shadow theory from Plato's allegory of the cave to René Thom's catastrophe theory, examining how these ideas have shaped our understanding of reality, perception, and mathematical modeling. Gain insights into the interconnections between philosophy, mathematics, and physics as Gromov illuminates the profound implications of shadow theory across various disciplines.