The Simplest Math Problem No One Can Solve - Collatz Conjecture
39,773,087
Published 2021-07-30
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 Ivy 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
All Comments (21)
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Everyone here: "...but just a maaaaybe I'll be the one to solve it."
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“Pick a number” Me:Fou- “Seven? Good choice” Me:but I-
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I love how he makes us think that he is the world's greatest mathematician by showing us his picture when saying that, but then shows the other half of the picture.
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Certainly one of the finest mathematical videos on YouTube.
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This math problem is actually like my trading portfolio, I can start with any number but end at $ 1
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Teacher: Why did you not answer the questions on your test. Me: Because the Math is not ripe enough for me to answer these questions
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Here because I have the Collatz Conjecture in a Brilliant coding question. I have found Brilliant the easiest to jump back into when I have time. Great loop back Veritasium.
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When negative numbers have 3 different loops, it makes me wonder if I change not only the seed sign but the operand. And turned out that if I apply 3n-1 for negatives (likewise changing the sign of the objectvie function on the concavity on linear programming), the graphical representation is a mirrored one of the positives. This way the whole set can apply the same rules for positives on 3n+1 including a single loop (-4, -2, -1)
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Whoever created all those graph animations is an absolute master in after effects expressions
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Me: Where should we eat? Girlfriend: Mathematics is not yet ripe enough for such question
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I’m glad I found this channel. Amazing quality content ❤️🙌
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You can accelerate the conversion by allowing division by 3 beside 2. I noticed that in my own limited search. Fascinating stuff.
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I absolutely love how mathematicians always find the most random things to debate over!
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Pretty much every subject in school is really interesting if I’m not forced to learn it
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I’ve always wondered why mathematicians only look at the patterns of the ’hailstone integers’ with this problem. Maybe the pattern is found in the numbers that are skipped after doing the equation either with 1 number or after a million numbers
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Consider the following. 1. there are an infinite number of 2^n numbers. 2. Consider an algorithm that selects a random number and tests it against whether it is a 2^n number. And if so applies the second half of the 3n+1 problem, in which case it will always collapse to the 4 -2-1 sequence. 3. What is the probability that the random number generator will never hit on one of the 2^n numbers. 4. I contend that the probability is zero.
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Me : "That's interesting puzzle, maybe I can solve it" Me 22 minutes later : "oh."
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The animation is everything here.
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“Pick a number, any number” Uhh… 7? “7? Good choice!”
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I wanna know who edit his videos.... The hard work ❤ ! We appreciate you bro !!
