What's the story behind the five axioms of Euclidean geometry - and how is post-Euclidean geometry linked to modern physics? Watch the Q&A with Yang-Hui He here: https://www.youtube.com/watch?v=taB75bCk8J0 Subscribe for regular science videos: http://bit.ly/RiSubscRibe From geometry’s classical beginnings, via the Renaissance and the Enlightenment, to the present day, Yang-Hui He takes us on a journey through time and space, culminating in our understanding of spacetime itself. In the 19th century, mathematicians such as Carl Gauss and Bernhard Riemann considered what would happen if we relaxed Euclid’s axioms. The result was the explosion of post-Euclidean geometry, which paved the way for Einstein’s theory of relativity and the birth of modern physics. -- This Discourse was filmed at the Ri on 24 February 2023, in partnership with the London Institute for Mathematical Sciences (LIMS). Discourses are one of the Ri’s oldest and most prestigious series of talks. Since 1825, audiences in the theatre have witnessed countless mind-expanding moments, including the first public liquefaction of air by James Dewar, the announcement of the electron by JJ Thomson and over 100 lectures by Michael Faraday. In more recent times, we have had Nobel laureates, Fields medal winners, scientists, authors and artists – all from the cutting-edge of their field. Discourses are an opportunity for the best and brightest to share their work with the world. Steeped in nearly two centuries of tradition, a Discourse is more than just a lecture. To keep the focus on the topic, presenters begin sharply at 7:30pm without introduction and we lock the speaker into a room ten minutes ahead of the start (legend has it that a speaker once tried to escape!). Some of our guests and speakers dress smartly for our Discourse events to add to this sense of occasion. -- Prof. Yang-Hui He is a Fellow at the London Institute, Professor of Mathematics at City, University of London, Tutor in mathematics at Merton College, Oxford, and Chang-Jiang Chair of physics at Nankai University in China. He obtained his BA at Princeton, where he graduated summa cum laude and was awarded the Shenstone Prize and Kusaka Prize. He did his MA at Cambridge (Distinction, Tripos) and earned his PhD at MIT. After a postdoc at the University of Pennsylvania, Yang joined Oxford University as the FitzJames Fellow and an STFC Advanced Fellow. He works at the interface of string theory, algebraic and combinatorial geometry, and machine learning. -- A very special thank you to our Patreon supporters who help make these videos happen, especially: modsiw, Anton Ragin, Edward Unthank, Robert L Winer, Andy Carpenter, William Hudson Don McLaughlin, efkinel lo, Martin Paull, Ben Wynne-Simmons, Ivo Danihelka, Kevin Winoto, Jonathan Killin, Stephan Giersche, William Billy Robillard, Jeffrey Schweitzer, Frances Dunne, jonas.app, Tim Karr, Alan Latteri, David Crowner, Matt Townsend, THOMAS N TAMADA, Andrew McGhee, Paul Brown, David Schick, Dave Ostler, Osian Gwyn Williams, David Lindo, Roger Baker, Rebecca Pan -- The Ri is on Patreon: https://www.patreon.com/TheRoyalInstitution and Twitter: http://twitter.com/ri_science and Facebook: http://www.facebook.com/royalinstitution and TikTok: https://www.tiktok.com/@ri_science Listen to the Ri podcast: https://anchor.fm/ri-science-podcast Our editorial policy: https://www.rigb.org/editing-ri-talks-and-moderating-comments Subscribe for the latest science videos: http://bit.ly/RiNewsletter Product links on this page may be affiliate links which means it won't cost you any extra but we may earn a small commission if you decide to purchase through the link.