The Simplest Math Problem No One Can Solve - Collatz Conjecture

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Veritasium

Veritasium

11 aylar önce

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 brilliant.org/veritasium 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.

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References:
Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. - ve42.co/Lagarias2006

Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963-1999). The ultimate challenge: the 3x, 1, 267-341. - ve42.co/Lagarias2003

Tao, T (2020). The Notorious Collatz Conjecture - ve42.co/Tao2020

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. - ve42.co/Tao2019

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. - ve42.co/Conway1987

The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1) [Computer software]. www.manim.community/

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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

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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 - ve42.co/3DCoral
Coral visualisation by Algoritmarte - ve42.co/Coral

YORUMLAR: 69 268
Pranav Pandey
Pranav Pandey
Your way of Explaining through Graphics is beautiful sir.
Demens Clay
Demens Clay
A big shoutout ot the graphics department for making this 100% more understandable!
Patrick Cooper
Patrick Cooper
As someone who goes to Syracuse university, totally caught me off guard when you mentioned it’s also known as the Syracuse problem. But I was more shocked it wasn’t a coincidence, looks like the math department here has spent a bit of time on the problem and picked up the name. I think they’ve given up on the problem because I hadn’t heard of it lol
Eray X
Eray X 28 gün önce
Hahaha the part
Claudio Aguilera
Claudio Aguilera
for the ones who want to play with this, here it's a code of python so you can try:
Quazi Rahman
Quazi Rahman
For negative numbers, the equation should be 3x - 1, and you'll get the same results. (@
Dabo Life
Dabo Life
Math problem no one can solve: Exists
julz z
julz z
the thing about the coral: it looks like coral that's actually exactly how nature works! it works on fractal math, because that's the simplest way to gain infinite complexity by just starting with a small rule like this
Victor Martinez
Victor Martinez
I actually did the 27,114,424 step by step on my phone calculator and it took ages but I felt so accomplished 😭
Omgdodogamer
Omgdodogamer Gün önce
15:33
Sergiu Stefan
Sergiu Stefan
Wish I had had one of you guys as my math teacher. Would have made class a lot more interesting.
STEREO Freq
STEREO Freq 21 gün önce
Someone should try graphing the relationships between the digital roots of the target numbers. The thing I noticed right off is that in the base 10 system (0 - 9), the "+1" in the algorithm never allows the target numbers to have a digital root of 3, 6, or 9. I.E. if you start with 7 (putting the digital roots in parenthesis), it would look like this:
Cosmic Nomad
Cosmic Nomad
I absolutely love how mathematicians always find the most random things to debate over!
Brian M
Brian M
Fascinating to see the correlation between the randomization of this equation and the patterns in nature and beyond, which should really be the focus in my opinion becasue the equation or problem itself doesn't seem to be a problem at all. I mean take replace 3 with 4 or with 5 and see what happens. There is always a pattern. It just so happens that the pattern of 3x+1 will always result in a sequence of dividing by 2 that will eventually overcome the multiplication of 3+1 reducing it to the 4-2-1 loop. I consider it solved, the solution which was presented in the video. Again, the real intriguing aspect is how that particular problem replicates randomness in nature, and well even other facets of this world including the stockmarket...hmmm..can anyone say matrix lol..perhaps this demonstrates that if you know the starting numerical value of anything, you can see how it will grow and perhaps when it will decline..ooops crazy conspiracy stuff leaking out now.That all being said, great job on the video!
John Hirano
John Hirano 14 saatler önce
There’s actually a simple way to prove that a divergent series can be balanced by a convergent series due to the combined functions, but it’s too much of a hassle to explain.
Infinity Plus 1
Infinity Plus 1 Gün önce
The more I know about math and science, the more I realize how much we don’t know
Raphat
Raphat
What an amazing video. I have learned so much from just the side ways you took the explanation.
Daniel Hed
Daniel Hed
Im sure someone has tried this already but my first instinct to solve this would be to try to prove that all prime numbers terminate in 4,2,1. If all prime numbers do than that implies every number reduces to 4,2,1.
shadyceddy
shadyceddy
Fun fact: We are not mathematicians but we got interested by this.
Puraskar Chakrabarti
Puraskar Chakrabarti
What a presentation! If I could pick one video that explains the topic, this would most surely be it.
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