The Simplest Math Problem No One Can Solve

The Simplest Math Problem No One Can Solve

The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via get 20% off a yearly subscription.

Special thanks to Prof. Alex Kontorovich for introducing us to this topic, filming the interview, and consulting on the script and earlier drafts of this video.

Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. —

Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963–1999). The ultimate challenge: the 3x, 1, 267-341. —

Tao, T (2020). The Notorious Collatz Conjecture —

A. Kontorovich and Y. Sinai, Structure Theorem for (d,g,h)-Maps, Bulletin of the Brazilian Mathematical Society, New Series 33(2), 2002, pp. 213-224.

A. Kontorovich and S. Miller Benford’s Law, values of L-functions and the 3x+1 Problem, Acta Arithmetica 120 (2005), 269-297.

A. Kontorovich and J. Lagarias Stochastic Models for the 3x + 1 and 5x + 1 Problems, in “The Ultimate Challenge: The 3x+1 Problem,” AMS 2010.

Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. arXiv preprint arXiv:1909.03562. —

Conway, J. H. (1987). Fractran: A simple universal programming language for arithmetic. In Open problems in Communication and Computation (pp. 4-26). Springer, New York, NY. —

Special thanks to Patreon supporters: Alvaro Naranjo, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy ‘kkm’ K’Nelson, Sam Lutfi, Ron Neal

Written by Derek Muller, Alex Kontorovich and Petr Lebedev
Animation by Iván Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
Filmed by Derek Muller and Emily Zhang
Edited by Derek Muller
SFX by Shaun Clifford
Additional video supplied by Getty Images
Produced by Derek Muller, Petr Lebedev and Emily Zhang

3d Coral by Vasilis Triantafyllou and Niklas Rosenstein —
Coral visualisation by Algoritmarte —

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44 Responses

  1. Dabo Life says:

    Math problem no one can solve: Exists
    Me: Finally I’m not the only one who is bad at math.

  2. Dr. Trefor Bazett says:

    This is a delightful exploration of the Collatz Conjecture, thank you! I particularly liked just how pretty the visualizations become when you play with adding rotations for evens and odds.

    • Anti Matters Too says:

      @The Chosen one lol 🙂

    • Frankkey says:

      Out of curiosity and I’m in not means a mathematician here, just an IT… I actually failed Math over and over again. But, with that in mind, is there any ways to test the Collatz conjecture with other units such as octal or hexadecimal units?

    • Naughty Spicy Corner says:

      @:p Ofcourse I understand because I am looking at U from 9th. And I am not building limitations around me but the around the ppl here in comment section. 😉

    • Anti Matters Too says:

      @Frankkey what difference would that make? It is just a different way to express numbers (not units).

    • Chandan Kumar says:

      Wow, @Trefor Bazett , I have been huge fan of yours as well and Veratasium , 3B1b, numberphile, you guys are simply revolutionizing the STEM learning. The world thanks you all.
      I wish I could be part of any one of you. May be in some parallel universe 😀

  3. MIMIK says:

    “Ok, little Gauss”, should have said the teacher to his annoyingly smart student, “what about 3x + 1?”.

  4. Hannah says:

    Imagine the stock market actually follows this and we’re just on one of the early upswings headed to 1

  5. Optimus Prime says:

    Honestly maths should just grow up and solve its own problems

  6. Jason Crittenden says:

    Mathematicians: “don’t publish stuff on this. It’s useless.”
    This guy: “how bout I do tho?”

  7. Jai Singh Bisht says:

    “one that young mathematicians are warned not to waste their time on”
    Me: instantly closes the video

  8. Kenan Ehmedov says:

    That’s not a mathematical problem, that’s just a typical *cryptocurrency graphic* after I buy them

  9. Greco Cabanero says:

    The humuor when Derek was saying “one of the world’s greatest living mathematicians” with his picture then shows his co-selfie Terrence Tao when he finally mentions his name.

  10. Make Build Modify says:

    After, “pick a number” I immediately wrote a program to go through the first million integers. When it looped “4,2,14,2,1,4,2,1” I thought I had bug. Nope.

    • TheAcidicMolotov says:

      @ceiling light the theory is not a good one if there is two options. Either your theory works or doesnt. If the only other option is the theory doesnt work, it isnt secure enough.

    • Feronanthus says:

      @ceiling light I hate to burst your bubble, but you aren’t going to casually propose an “obvious” proof of “just do it in reverse” in a youtube comment. Erdos wasn’t a slouch. Neither are any of the people who have seriously looked at this before.

    • ceiling light says:

      @TheAcidicMolotov ok

    • ceiling light says:

      @Feronanthus that’s way it was casual it’s just idea

    • redwall1521 says:

      @ceiling light the issue was that you’re claiming that any even number is or can get to the power of 2. You need to prove this step. And if you think about it, this is the crux of the problem since and odd number going through the formula will become even.

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