The Insane Math Of Knot Theory

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

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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 — https://knotplot.com/. Thanks to Rob Scharein for providing technical help as well!
A table of knots and all their invariants — https://knotinfo.math.indiana.edu/
The Knot Atlas for general info on knots — http://katlas.org/wiki/Main_Page

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Knot Theory Video References – https://ve42.co/KnotTheoryRefs

Images & Video:
Alexander Cutting the Gordian Knot by Donato Creti via Fine Art America - https://ve42.co/GordianCut
Indus Valley tablet via Quora - https://ve42.co/IndusValley
Pages from the Book of Kells via National Trust of Scotland - https://ve42.co/BookOfKells
Medieval Celtic designs from @thebookofkellsofficial via Instagram - https://ve42.co/KellsInsta
Chinese knotwork by YWang9174 via Wikimedia Commons - https://ve42.co/Panchang
Quipu cords by Pi3.124 via Wikimedia Commons - https://ve42.co/Quipu
Borromeo heraldry via Terre Borromeo - https://ve42.co/Borromeo
Birman/Jones letter via Celebratio Mathematica - https://ve42.co/JonesBirman
Molecular trefoil knot by M stone via Wikimedia Commons - https://ve42.co/TrefoilMolecule
X-ray structure of trefoil knot by Ll0103 via Wikimedia Commons - https://ve42.co/XrayTrefoil
Bacteria animation from Your Body's Molecular Machines by Drew Berry via the Walter and Eliza Hall Institute of Medical Research - http://wehi.tv
Topoisomerase and knots from Orlandini et al. Synergy of topoisomerase. PNAS, vol. 116, no. 17, 2019, pp. 8149–8154. – https://ve42.co/Orlandini2019
KnotProt 2.0: A database of proteins with knots and slipknots - https://ve42.co/Knotprot

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Special thanks to our Patreon supporters:
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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