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There is an entire branch of math simply devoted to knots – and it has changed the world. We’ll rope you in. Head to to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.

Special thanks to our Patreon supporters! Join the community to help us keep our videos free, forever:


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Huge thanks to Prof. Colin Adams for his excellent help guiding us through the world of knots.
Many thanks to Prof. Doug Smith, Dorian Raymer, Prof. David Leigh, and Prof. Dorothy Buck for helping us understand applications of knot theory.
Many thanks to Prof. Dan Silver & Prof. Jim Hoste for speaking with us about the history and tabulation of knots.

If you want to learn more about knots and play with them yourself, check out:
The amazing KnotPlot tool — . Thanks to Rob Scharein for providing technical help as well!
A table of knots and all their invariants —
The Knot Atlas for general info on knots —

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Knot Theory Video References –

Images & Video:
Alexander Cutting the Gordian Knot by Donato Creti via Fine Art America -
Indus Valley tablet via Quora -
Pages from the Book of Kells via National Trust of Scotland -
Medieval Celtic designs from @thebookofkellsofficial via Instagram -
Chinese knotwork by YWang9174 via Wikimedia Commons -
Quipu cords by Pi3.124 via Wikimedia Commons -
Borromeo heraldry via Terre Borromeo -
Birman/Jones letter via Celebratio Mathematica -
Molecular trefoil knot by M stone via Wikimedia Commons -
X-ray structure of trefoil knot by Ll0103 via Wikimedia Commons -
Bacteria animation from Your Body's Molecular Machines by Drew Berry via the Walter and Eliza Hall Institute of Medical Research -
Topoisomerase and knots from Orlandini et al. Synergy of topoisomerase. PNAS, vol. 116, no. 17, 2019, pp. 8149–8154. –
KnotProt 2.0: A database of proteins with knots and slipknots -

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Special thanks to our Patreon supporters:
Anton Ragin, Balkrishna Heroor, Bernard McGee, Bill Linder, Burt Humburg, Dave Kircher, Diffbot, Evgeny Skvortsov, Gnare, Jesse Brandsoy, John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Mario Bottion, MaxPal, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures

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Directed by Emily Zhang
Written by Emily Zhang and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Ivy Tello, Jakub Misiek, and Mike Radjabov
Filmed by Derek Muller, Raquel Nuno, and Emily Zhang
Produced by Emily Zhang, Han Evans, and Derek Muller

Thumbnail by Ignat Berbeci and Mike Radjabov
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

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