Signup for your free trial to The Great Courses Plus here: http://ow.ly/b5wA30hIviV (sponsor) More links & stuff in full description below ↓↓↓ James Grime on a proof involving Pythagorean Triples. James Grime: http://singingbanana.com/ (book him for a talk) More on the proof: https://www.cs.utexas.edu/~marijn/ptn/ Preprint of the paper: https://arxiv.org/abs/1605.00723 Ron Graham videos: http://bit.ly/Ron_Graham Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: null The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US, UK, and Australian markets. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally.