When Reason Produces Monsters While It Is Wide Awake

“I turn with terror and horror from this lamentable scourge.” Henri Poincare uttered this sentence in response to Karl Weierstrass’ famous example of a continuous curve that has no tangent at any point.

In this lecture, Camillo De Lellis will argue that this terrifying curve is just the first of a long series of counterintuitive mathematical objects that all share common aspects. In particular, they all result from piling up ‘appropriate waves’ at smaller and smaller scales in a suitable way. He will touch upon famous constructions of John Nash and Stephen Smale in the ’50s and ’60s, celebrated subsequent works of Mikhael Gromov, and relatively recent discoveries pertaining to the most basic equations in incompressible fluid dynamics.