What Does the Fourth Dimension Actually Look Like?

Mathematician Maggie Miller of the University of Texas at Austin joins Janna Levin and Steven Strogatz to explore knots, surfaces and four-dimensional topology. They discuss why loops can untangle in four spatial dimensions while two-dimensional surfaces can remain knotted, how three-dimensional snapshots help visualize 4D spaces, and Miller and collaborators’ resolution of a knotted-surface question posed by Charles Livingston in 1982. The conversation also connects visual techniques from art with mathematical reasoning.