How The Most Useless Branch of Math Could Save Your Life

6,725,458
0
Published 2023-09-03
There is an entire branch of math simply devoted to knots – and it has changed the world. We’ll rope you in. Head to brilliant.org/veritasium 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:
ve42.co/PatreonDEB

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

▀▀▀
Knot Theory Video References – ve42.co/KnotTheoryRefs

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

▀▀▀
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

▀▀▀
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

All Comments (21)
  • @veritasium
    Have any lingering questions about knots? Want to hear more knot stories that didn’t make the cut? Derek and Emily (the writer/director of this video) will be hosting a livestream for our Patreons next week! Join our Patreon for more info and a link to the stream - ve42.co/VePatreon
  • @zebatov
    My earphones discover all 352,152,252 knots half a second after entering my pocket.
  • Veritasium's graphic designer would have become a physicist by now. It must take a lot of understanding on their part to learn the concept first and then visualize how to demonstrate it. It is just mind-blowing.
  • @the_Spartan_117
    The mathematicians missed the opportunity to name it 'Notknot'.
  • @persona2grata
    Although I wouldn't in a hundred years choose to study knots, it never fails to inspire me how people take up these causes, pushing esoteric fields forward for nothing more than a pure love of the game until eventually their discoveries can be tied to other fields to make important scientific advances. Science really is humanities most collaborative sport.
  • @smoov22_sonic
    There is a certain demographic that I hope never finds this extended tribute to knots
  • @logankennedy7082
    As a Ph.D. student in algebraic topology, I am glad to see that different areas of topology are finally getting the attention they deserve.
  • @rmorell28
    "Not knot" "Who's there?" The Unknot
  • @peterbigblock
    I don’t think I’ve ever watched a video that I completely understood while, at the same time, I had no idea what you were talking about. It’s like a miracle. Fascinating subject!
  • @chriscrossx
    I'm in awe at someone having the patience and skill to visually tie thousands of knots and distinguish duplicates. Thanks for another great story wonderfully told.
  • @AuxiliaryHillman
    Math is so incredible. People just study a phenomenon and it reveals a language that describes the world in ways we didn't know of before. Wonder what fields of maths exist that we have yet to study
  • I've started to lace my shoes like this ~2 years ago when I realized its symetry and aesthetism, but never paid attention to its tightness. Thank you for this great video, as always !
  • @rozygcf6611
    Fun fact: making sure you're doing a square knot instead of a granny knot is also very important in surgery. They are taught to alternate the way they secure off the suture.
  • @Haeze
    When it comes to avoiding knots in headphones, my easy way that I have used for years is to simply not allow the endpoints into the storage case. If it is a zippered pouch, just leave the earbuds and the plug hanging outside the zipper. You can just grab the entire length of cable and shove it in the zipper pouch as a massive wad if you want, just leave the ends outside the zipper, and you will have no knots. Same story if you put them in your pocket. Just leave the ends sticking out of the pocket and you get no knots.
  • @pomegranate3601
    i love that I never know in which rabbit hole I am going to fall into when I watch your videos but it`s always incredibly fascinating! Thank you for your valuable content!
  • @cliffperry
    Many of your videos i watch and enjoy your explanations yet only begin to grasp the concepts. Some I’m still clueless yet i love to know how much i don’t know about the world. Thank you for them all.
  • @espygaming5101
    Just to avoid potential confusion for those folks moving to a squar knot for tying their shoes, its actually isnt just clockwise or counter clock wise, it depends on how the first overhand knot you make is tied, whether its the left side going over then under or vice versa. It also depends on if you make the loop on the left or right side. So check to look if it actually appears like a squar knot to confirm.
  • @michaeljohn8905
    This is amazing Im so glad I watched this till the end to see what it could be used for. It’s a lot to digest and I have a certain problem concentrating but I made it. Thank you for posting.