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:    / seancarroll  

Mindscape podcast: http://www.preposterousuniverse.com/p...

The Biggest Ideas playlist:    • The Biggest Ideas in the Universe!  

Blog posts for the series: http://www.preposterousuniverse.com/b...

Background image by RyoThorn at DeviantArt: https://www.deviantart.com/ryothorn/a...

#science #physics #ideas #universe #learning #cosmology #philosophy #math #geometry #topology