Uploaded August 2026 | Updated September 2026, 2 weeks ago
00:00 I/ Introduction and welcome
00:49 I/ Why study knots: history and everyday presence
01:53 I/ Knots in nature, from microbes to solar flares
03:29 I/ Helmholtz, vortex rings, and the birth of knot science
04:34 I/ Lord Kelvin, Peter Tait, and the founding of knot theory
05:56 I/ What is a knot? The mathematical definition
07:06 I/ Ambient isotopy: when two knots are "the same"
09:13 I/ Beyond knots: braids and links
10:40 I/ Knot diagrams and the crossing number
13:53 I/ Reidemeister moves: proving knots are equal
17:00 I/ Chirality: mirror images and the figure-eight knot
17:45 I/ Composing knots: the arithmetic of knots
20:01 I/ Prime knots and the fundamental theorem
22:15 I/ Classifying knots by crossing number
25:00 I/ Modern knot tables: billions of knots
27:02 I/ Unknotting number and the Gordian Knot problem
33:59 I/ DNA topology and the enzymes that untangle it
38:16 I/ Transposons, gel electrophoresis, and ideal knots
45:42 I/ Umbilical cord knots: how and when they form
52:54 I/ Conclusion: knot theory's reach across science
Watch the Q&A session here: youtu.be/DeYwOh9rCgc
Knots are ubiquitous in the world around us, appearing as tangled cords, shoelaces, or the complex structures of DNA. Far from being nuisances, knots have profound and beautiful mathematical properties with tentacular connections to geometry, topology, physics, and biology. This lecture introduces the fascinating world of knot theory, exploring how the mathematical study of knots helps us understand and predict their formation, stability, and behaviour.
This lecture was recorded by Alain Goriely on 9th May 2026 at Barnard's Inn Hall, London.
Professor Alain Goriely FRS is Gresham Professor of Geometry.
He is also a mathematician known for dynamical systems, mathematical biology, and mechanics. He developed the mathematical theory of biological growth and is Director of the Oxford Centre for Industrial and Applied Mathematics. His work spans plant tendrils, seashells, umbilical cords, brain modelling, and applied mathematics outreach.
The transcript and downloadable versions of the lecture are available from the Gresham College website: gresham.ac.uk/watch-now/shape-knots
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: gresham.ac.uk/support
Website: gresham.ac.uk
Twitter: twitter.com/greshamcollege
Facebook: facebook.com/greshamcollege
Instagram: instagram.com/greshamcollege
00:00 I/ Introduction and welcome
00:49 I/ Why study knots: history and everyday presence
01:53 I/ Knots in nature, from microbes to solar flares
03:29 I/ Helmholtz, vortex rings, and the birth of knot science
04:34 I/ Lord Kelvin, Peter Tait, and the founding of knot theory
05:56 I/ What is a knot? The mathematical definition
07:06 I/ Ambient isotopy: when two knots are "the same"
09:13 I/ Beyond knots: braids and links
10:40 I/ Knot diagrams and the crossing number
13:53 I/ Reidemeister moves: proving knots are equal
17:00 I/ Chirality: mirror images and the figure-eight knot
17:45 I/ Composing knots: the arithmetic of knots
20:01 I/ Prime knots and the fundamental theorem
22:15 I/ Classifying knots by crossing number
25:00 I/ Modern knot tables: billions of knots
27:02 I/ Unknotting number and the Gordian Knot problem
33:59 I/ DNA topology and the enzymes that untangle it
38:16 I/ Transposons, gel electrophoresis, and ideal knots
45:42 I/ Umbilical cord knots: how and when they form
52:54 I/ Conclusion: knot theory's reach across science
Watch the Q&A session here: youtu.be/DeYwOh9rCgc
Knots are ubiquitous in the world around us, appearing as tangled cords, shoelaces, or the complex structures of DNA. Far from being nuisances, knots have profound and beautiful mathematical properties with tentacular connections to geometry, topology, physics, and biology. This lecture introduces the fascinating world of knot theory, exploring how the mathematical study of knots helps us understand and predict their formation, stability, and behaviour.
This lecture was recorded by Alain Goriely on 9th May 2026 at Barnard's Inn Hall, London.
Professor Alain Goriely FRS is Gresham Professor of Geometry.
He is also a mathematician known for dynamical systems, mathematical biology, and mechanics. He developed the mathematical theory of biological growth and is Director of the Oxford Centre for Industrial and Applied Mathematics. His work spans plant tendrils, seashells, umbilical cords, brain modelling, and applied mathematics outreach.
The transcript and downloadable versions of the lecture are available from the Gresham College website: gresham.ac.uk/watch-now/shape-knots
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: gresham.ac.uk/support
Website: gresham.ac.uk
Twitter: twitter.com/greshamcollege
Facebook: facebook.com/greshamcollege
Instagram: instagram.com/greshamcollege
