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Explore a fascinating 53-minute lecture that delves into the world of counterintuitive mathematical objects, beginning with Karl Weierstrass' infamous continuous curve lacking tangents - a discovery that horrified Henri Poincare. Journey through the mathematical landscape as De Lellis examines how these peculiar objects emerge from layering 'appropriate waves' at progressively smaller scales. Learn about groundbreaking constructions from mathematical giants John Nash and Stephen Smale from the 1950s and 1960s, discover Mikhael Gromov's influential contributions, and understand recent breakthroughs in incompressible fluid dynamics equations. Gain insights into how these seemingly monstrous mathematical constructs share common characteristics and continue to challenge our understanding of mathematical principles.
