Geometry podcasts

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.

Hosted by Janna Levin, Steven Strogatz

Lauren Williams introduces the positive Grassmannian and the surprising connections it creates across mathematics and physics. She explains links to waves, traffic and particle scattering, and discusses how research-level mathematical problems can help assess what artificial intelligence is capable of proving.

Hosted by Steven Strogatz

Zhouli Xu explains the Kervaire invariant problem and the role of unusual geometric objects in high-dimensional topology. He describes the long route towards resolving the problem in dimension 126, including the collaborative and technical challenges behind the proof. The conversation was recorded during the Isaac Newton Institute programme on equivariant homotopy theory.

Yang-Hui He joins Steven Strogatz to trace geometry from ancient measurement and Euclid to curved spaces, general relativity, and string theory. They discuss why geometry provides a shared language for mathematics and physics, how rigorous proof interacts with physical intuition, and how artificial intelligence might change mathematical discovery. The conversation also contrasts broad conceptual views with concentrated work on individual problems.

Hosted by Steven Strogatz, Janna Levin

Steven Strogatz talks with mathematicians Colin Adams and Lisa Piccirillo about knot theory and why it matters across mathematics and science. They explore how mathematicians distinguish knots, connections with the geometry of three-dimensional and higher-dimensional spaces, and applications involving DNA, materials and theoretical physics.

Hosted by Steven Strogatz