How The Most Useless Branch of Math Could Save Your Life

How The Most Useless Branch of Math Could Save Your Life

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.

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 —

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 –

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 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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29 Responses

  1. Veritasium says:

    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 –

  2. UY VŨ KIỀU says:

    This guy somehow finds a way to make videos like this. It is really complicated but he still finds these facts out.

  3. Logan Kennedy says:

    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.

    • Daniel Shauri says:

      So you deal with stuff like mobious strips, klein bottles and 4-D toruses

    • Charles Panigeo says:

      Very cool! I’m a graduate student in math learning algebraic topology. I’m working through Hatcher’s right now. Its interesting enough right now, so we’ll see if I end up focusing on algebraic topology.

    • Watcher says:

      As a non-Ph. D student in anything, topology and knot theory is, and has been, a very popular subject on science and mathematics themed channels for a very long time. It isn’t “finally” getting the attention the subject deserves – you have only just now discovered it, apparently. Those are two very different situations.

    • Logan Kennedy says:

      @Watcher I have not “just now discovered knot theory”, however, I was merely trying to say that I am happy people are presenting it to the general public so more people can learn about these fields of mathematics.

    • VWLZ says:

      ​@WatcherAs a non-phd student in anything, you should let them talk

  4. Ralph Xu says:

    I’m so glad that veritasium is making more and more math videos.

  5. William Arcor says:

    Derek has been killing it with the math videos lately

  6. francisco varela says:

    My initial reaction was “So what? I wear slip-on shoes.”. I then became slightly interested by the mathematics underlying knot theory and ended up floored by the practical applications of this area of study. An excellent video as always.

  7. jake peralta says:

    What I love so much about science is how even what might seem the most useless thing you can study can have so many useful applications

  8. Prakash Arora says:

    What a wonderful video! I gained tremendous respect for these people who worked just for their curiosity, when they could be doing the equivalent of watching Netflix on their couch and eating snacks. It’s because if their tireless efforts that we enjoy the discoveries and treatments that we do today. This is why going out of your boundaries and discovering the unknown matters, this is why exploring the cosmos and sending probes to the moon, sun, Mars, and beyond matters, even for developing countries. Well done Derek and team!! 👏

    • rogink says:

      Yes but a lot of these Victorian thinkers had independent income so could do this full time.

      But I was intrigued that Tait complained he didn’t have enough leisure time (and thanks Derek – I appreciate the pronunciation from British perspective). I wonder what he was doing for the rest of the time!

    • VWLZ says:

      ​@roginkresearchers like these dont earn enough for the work they put in, because their work rarely IMMEDIATELY becomes productive. In this capitalistic society, if ur work is not immediately productive, ur gunna struggle to find someone to pay u.

      Professors get by teaching students but for how many hours they work, their pay isnt that great. Its definitely a passion job.

    • rogink says:

      @VWLZ True the title ‘professor’ isn’t quite as prestigious as it once was. Of course it depends on which university employs you, and your discipline. Sure, the humble PhD student has to scrape by, but when you get to Prof status, in most Western universities you will have a comfortable salary, a job for life, and generous pension when you retire.

      Regardless, that has nothing to do with these Victorian thinkers. They weren’t employed by universities – or anyone else. They mostly had property and earned income from that.

  9. Devwardhan Kothari says:

    Phenomenal video! I was always intrigued by this field of math and you have shown me how hilariously pointless this theory seemed vs how imperative it has become. Absolutely love random yet super interesting stuff like this from you Derek and team!

  10. Derek Lush says:

    Its honestly incredible how much your videos have improved in recent years

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