The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is Idea #13, "Geometry and Topology." Yes that's two ideas, and furthermore they're from math more than from science, but we'll put them to good use. In particular we look at Riemannian (non-Euclidean) geometry, and a kind of topological invariants called "homotopy groups." My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/podcast The Biggest Ideas playlist: https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX Blog posts for the series: http://www.preposterousuniverse.com/blog/category/biggest-ideas-in-the-universe/ Background image by RyoThorn at DeviantArt: https://www.deviantart.com/ryothorn/art/Steamworks-to-my-own-oblivion-147929840 #science #physics #ideas #universe #learning #cosmology #philosophy #math #geometry #topology