Today was the last day of the topology class I’ve been teaching. I decided to devote the day to the Poincaré conjecture. I started by telling the students a little about the history of the problem. Then I showed them three videos.
The first video was an excellent 50-minute lecture by Fields medalist Curt McMullen from October 11th, 2006. It is part of the Science Center Research Lecture Series at Harvard. It was intended for a general audience. I highly recommend watching this.