What is a hole?

An introduction to the fundamental group, a key concept in algebraic topology. This video is sponsored by Brilliant. To try it out for free for 30 days, head to https://brilliant.org/Aleph0/. The first 200 people to sign up will get 20% off a yearly subscription. Help fund future projects: https://www.patreon.com/aleph0. An equally valuable form of support is to simply share the videos. A HUGE thank you to Waleed Qaisar for working with me to make the script and storyboard for this video. You rock Waleed! And thank you to Davide Radaelli for patiently listening to the script and offering helpful feedback! CORRECTIONS: At the start of the video, I said that Poincare’s paper Analysis Situs was published in 1985. This is a typo - the paper was published in 1895. Thanks to those who spotted the error. SOURCES and REFERENCES for Further Reading: This video is a quick-and-dirty introduction to the fundamental group. But as with any quick introduction, there are details that I gloss over for the sake of brevity. To learn these details rigorously, I've listed a few resources down below. (a) Video Lectures by Pierre Albin: https://www.youtube.com/playlist?list=PLpRLWqLFLVTCL15U6N3o35g4uhMSBVA2b (b) “Algebraic Topology” by Allen Hatcher: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html Follow me! Twitter: @00aleph00 ___ MUSIC CREDITS: Music: https://www.purple-planet.com Song: Thinking Ahead