The Simplest Math Problem No One Can Solve – Collatz Conjecture
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. —
The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.13.1) [Computer software].
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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 —
Coral visualisation by Algoritmarte —
Given these specific laws of composition and decomposition, the whole system should inevitably grind to the smallest possible decomposition since decomposition is stronger
The answer for the question in the thumbnail is 3
You can never find a counterexample that is climbing. I mean when do you stop. It will go on to infinity.The only way is to find a loop.
I think that the answer to this solution lies in the nature as it is the manifestation of all knowledge
Eventually we'll get caught in a power of two which crashes us down to 1.
what about the number 1.9702913456*10^362
if it always reaches 4 and loop, why dont they start backwards from 4?
Wenn Du die gleiche Regel im negativen Bereich anwendest hast Du eine ganz andere Perspektive. 3x+1 verhält sich negativ wie 3x-1 im positiven Bereich wäre. Du spiegelst die Achse.
Entsprechend hat 3x-1 die GLEICHEN Loops im Positiven wie die 3x+1 im Negativen.
Diesen Teil fand ich jetzt doch offensichtlich unsauber. Die Dimensionen stimmten überhaupt nicht überein.
The same rule of the positive dimension applied to the mirror of the negative dimension is not the same. The equivalent to 3x+1 in the negative realm (to "grow" the axis by 1) is 3x-1. Thus using 3x+1 in the negative realm creating those 3 loops is like using 3x-1 in the positive realm creating the same.
That part of the video was not well researched. Comparing different functions for their respective dimensions is not clean.
3^-2=1 quite easy
[3+1=4][(4/2)/2=1] The X's cancel out. There is your answer.
İngilizce bilmeyerek bir süre dinleyerek anlamaya çalıştıktan sonra ben: level up
Ah yes, the first result of me having a 🦆ing seziure and slamming my keyboard for searching “ù< ùñ% ~Nõ%⊫ ñ% ù öõq'yy `< ø⊫6'y't'6-“.
“But have you tried putting it into wolfram alpha?”
This kid one time went up to me and asked “are you good at math?” I said “yeah kinda” and he said “then what is 3x+1?” As a veritasium subscriber I knew he had no idea what he was talking about and just looked at the thimbnail 🤣
It is 4
GOD IS SOOOOO INTENTIONAL ✨️😉
This video does a poor job of explaining what the goal is? What are they trying to solve. It’s a chaotic pattern. So what? Are they trying to discover a pattern? Trying to find a number that it won’t work with? What’s the point of this video? This channel sucks.
hmm could the organic looking structures must be a result of the relatively arbitrary choice to use base 10? I wonder how those sorts of structures would change under different bases. Fascinating.
Zeroooo it's easy 🤣
In one dimension, the pattern is simply unsolvable. In two dimensions: that holds given that it after all boils back to one. However, in reality; space is complex. That is, multi-dimensional. Such that no object is immune to transformation. Brute force? NIL.
Does it ever make a Bell shape curve?
I am sorry you should start with why do I want to solve it not how I can solve it 10 min in and still I don’t care about the problem cuz I don’t know why I want to solve it in the first place
there is no problem
im confused on what the actual problem is, there is nothing to solve?
You go into fractions and you stop the loop.
Also interesting to do a *Collatzception*: start with whatever number, count the steps and enter the number of steps as a new number. All the tests I did came to 5. And 5 needs 5 steps to get to 1. 16 leads to 4.
What is the "problem" you're trying to "solve" that there might be one number that doesn't conform to the principle of 3x+1? What would the relevance of that be of you proved it either right or wrong?
Nothing is perfect! Like in nature, square root does not exist to infinity!
is it possible to use infinity as x?
I'm pretty sure it's always possible to get to one, because eventually, if you get an infinite number of chances for each number to get to one, than it's always possible.
1/3 is the answer
In this game, there’s more chance of hitting even than odd. Odd +50% even -50%. Even always follows odd. Odd or even can follow even.
There’s also a chance of hitting a geometric sequence of evens (64, 32, 16, 8, 4, 2).
I probably missed something important but that’s how I think about this.
Rules of the game are rigged in favour of evens always winning (eventually) and then getting trapped in 4-1 loop. The loop is just because of the +1 I think.
If I do solve it, what do I get? And how is this applied?
The answer is 10.
I solved it… Like legitimately
this is easy its 5
Where can I submit an answer?
The amount of intelligent people on the comment is staggering. While I'm here trying to light my wet zippo with a candle.
It's 6 i think
Im in my dads account
Is the answer 3
How about we put x=27.5 maybe it can work.
The narrator suggests that this is something that can't be brute-forced, but I'm struggling to understand why a supercomputer couldn't simply churn through numbers, checking them one by one? Given modern computing power, I'd think such a setup could surpass the current known limit relatively quickly.
31 There it's solved 😄