How geometry created modern physics – with Yang-Hui He

Published 2023-04-13
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:    • Q&A: How geometry created modern phys...  
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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.

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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.

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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.

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All Comments (21)
  • @theccieguy
    I am still amazed by the fact we get these great lectures for free, anywhere we want. Thank you RI.
  • This is one of the best Royal Institutions Lectures I have watched. Showing how mathematics has evolved over time - and consequently physics as well. For the first time I finally got to see how mathematics is the beautiful language of the universe. I loved the professor’s enthusiasm and his way of communicating these ideas. Beautiful video.
  • @TazPessle
    I remember in high school (about 14) we were all told to make a triangle out of paper, tear off each corner and place them on a line in our excercise book. It was the only math lesson that we used glue sticks, but something about that practical aspect allowed me to start manipulating geometric problems in my head to make the solution more apparent.
  • @RD-sk8cx
    Yang-Hui He is such a good communicator, would have loved to be in his class. This talk brought back what first kindled my interest in mathematics in school - Euclidean proofs. And then he builds up from there. Brilliant.
  • @muthukumaranl
    Thank you so much to Prof. Yang-Hui He and RI for this amazing lecture!
  • @brianlee9310
    I could watch these brilliant lectures all day and night long and I have . I AM
  • Linear algebra somehow clicked for me in a way calculus did not. Seeing R3xR really helped. I feel so lucky to see RI lectures like this.
  • @raphaelkaume
    What an amazing teacher! Such a joy to listen to! I mean these are fearsome topics for most but he had me smiling and laughing several times. His students are most fortunate and now so is the rest of the world able to access this. Thanks Yang-Hui He!!!😃
  • @primajump
    One of the most riveting experiences for me. Very interesting in deed! I am grateful that these talks are available for us. Thank you !
  • @mariavm9178
    What a phenomenal lecture! Thank you, Prof. Yang-Hui He and Ri. Looking forward to reading your books!
  • @photon434
    You create an infectious excitement in all your lectures. Amazing!
  • @tehdii
    I salute him for making "A compact history of infinity" by David Foster Wallace and making it digestible and clear in a 60 min lecture... Bravo!
  • @ktiwari31
    I loved it! It’s one of the best lectures I have found in a long long time! Yong-Hui is amazing!
  • @F_L_U_X
    I forgot how amazing Ri videos are. Been falling asleep to The History of the Universe lately. Daniel Tammet comes to mind when listening to this guy explain his passion. I would love to see them hang out.
  • @Danny-hb1zb
    Love whenever Yang-Hui He does a presentation it’s always brilliant 👏🏻
  • I absolutely loved this lecture. I struggle with being told what to do as opposed to what to think about which engages me.
  • @as-qh1qq
    Such a beautiful lecture, like a well written screenplay.
  • @freeheeler09
    I would have liked to take a course or seven from you! Your love of mathematics is inspiring!
  • @koenth2359
    The 5th axiom as given at 7:16 would only hold in 2 dimensions. Later, at 44:41 it is represented in a better way, using the word parallel, which is also valid in general for Euclidian spaces of higher dimension.