The Simplest Math Problem No One Can Solve - Collatz Conjecture

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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.

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

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

čas přidán


30. 07. 2021





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Komentáře 53 757
Retarded fish
Retarded fish Před minutou
South Boston
South Boston Před 7 minutami
"Pick a number, any number..." Me: 7 "Seven, good choice.." Me: (0_0)
Summer Pinguin
Summer Pinguin Před 13 minutami
Isn't it because each time you add 1 it makes it easy to get a even number so you devide it which makes it less but because deviding by 2 is a big step that mostly if done once it will get lower eacht ime because the half of ×3 is × 1,5 which makes it go just a little but up each time and their for their is a +1 so it gets even and so devide it again by 2 which wit all numbers is possible because they have the law that ×1,5 makes it un even whatever the number so you add +1 and which makes it even which gets you to number 20 10 5 16 8 4 2 1. I don't know why people are stuck with this bc it's just simpe math rules. also if people don't know why the formula is not making sence it's because it has no logical rules.
Tomas Contreras
Tomas Contreras Před 16 minutami
He said "and) before a decimal.
Tomahawkfromscandinavia Před 17 minutami
Why do so many people use so long time with this? If we somehow solve this riddle, it is not like, it’s gonna cure cancer
K M Před 19 minutami
Why is this even a problem?
Kaspa969 Mapping
Kaspa969 Mapping Před 24 minutami
We don't know what is x, thats why it's imposible LOL
Sean Clarkson
Sean Clarkson Před 28 minutami
the anser is 7
Fehraz Az
Fehraz Az Před 32 minutami
okay okay i get it. this is some endlevel math. buuuuut i dont get the problem here...
Jelly Beans
Jelly Beans Před 36 minutami
and whats the purpose of this. Its cool but does it actually do something helpful
SoZiAlShMaRoTzA ™
SoZiAlShMaRoTzA ™ Před 40 minutami
Ever thought about "it is how it is" ?
A-Mech Studios-Skitlz
A-Mech Studios-Skitlz Před 41 minutou
BDSlawski Před 55 minutami
Why 3x+1? Why not infinitive number of potentional....everything...?
Alex Před hodinou
Step 1 : collecting Underwear. Step 2: ? Step 3: Profit.
Janis Magone
Janis Magone Před hodinou
Is calculator always right tho?
Pogboy Před hodinou
It’s 4
Not JellyBean Official
4 😳
Sarbi Momud
Sarbi Momud Před hodinou
you deserve a like just for the insane quality of video editing
LIL SCOOT Před hodinou
3. Perfectly Done
seren richards
seren richards Před hodinou
There is no way I just watched a 22 minute video about maths voluntarily
Mike Lewis
Mike Lewis Před hodinou
So...... Every positive integer has a bacon number
Hyperezil Před 2 hodinami
It's quite simple really. What goes up. Must come down. There we go solved, Nobel Peace Prize please. Thanks.
DaroMC Před 2 hodinami
Haha 3x+1 = 4x
Danijel Gombač
Danijel Gombač Před 2 hodinami
Interesting. Just do not see why its a problem? Its just it... let it be. And no problem at all. There- my very own Solomon judgement.
insanax Před 2 hodinami
Moore Koubel
Moore Koubel Před 2 hodinami
What problem?? its a sequence of instructions............ who cares?!
John Reez
John Reez Před 2 hodinami
..wow i really thought of 7 how comes?
Nathaniel Pina
Nathaniel Pina Před 2 hodinami
3x+1 is 4
SamXBeast Před 3 hodinami
X is Unknown if there is 2 without x that will be 7
Spectec Před 3 hodinami
(2)x 3 + 1=7???
Dbozz Před 3 hodinami
Maybe I am just stupid. But I do not understand this problem. I mean you make it hard for yourself, because if you say: yes 3*x + 1 is the calculation and if the number is odd you multiply it in the calculation. But if it is equal it is called divided by 2. Since two is a number that takes up half of all numbers, so every other number is divisible by 2, it is logical that if you multiply an odd number by 3 and then add 1 that it is very likely that if you divide it by two that it will come back to 1 in the end since every other number is in the family tree of 2. And if by dividing by two an odd number comes out, you repeat the process as if you WANT to end up with a 2. (For example, the calculation 3*x + 1 results at some point in the result = 2048, which you can divide by 2 until it is just 1. Do I understand there something wrong or does that sound logical? Please clarify xD
Dbozz Před 3 hodinami
Or if you look at it with imagination it is the calculation to the big bang if you understand what I mean. lmao
Johndth Před 3 hodinami
Pop7 Games HD
Pop7 Games HD Před 3 hodinami
this alwys 17
Liham_ Před 3 hodinami
Just type in a calculator “3X+1” and you get 1
Minecraft Cruise
Minecraft Cruise Před 3 hodinami
the answer to the thumbnail is 12
Mark Aitken Guitar
Mark Aitken Guitar Před 3 hodinami
I hate movies that don’t have a definitive ending… except this one! Outstanding presentation of a problem I didn’t know existed. Bravo!
Grayson Burr
Grayson Burr Před 3 hodinami
Òut of curiosity, has anyone made an algorithm where the computer is only trying to solve for a number on the tree? The computer would just have to know every number on the tree and the moment you reach a number on the tree, regardless of where you start, it will know that it continues to 1. Then, instead of doing a full sequence, the computer is just trying to find the closest point of contact to the tree. The path that number took then gets added to the tree and if a number later intersects, the computer knows to stop and start the next number.
Elisabeth Delignies calderon
no number can shoot off to infinity cuz infinit isn’t a number
UnrealOG Před 4 hodinami
I'm writing a program to solve this in python. My approach is to start with an array filled with known working numbers. If, at any point, the number being tested becomes less than or equal to a number in the known working array, add every number that was used to that array. At every calculation, check if the number is in that array. If it is, you can skip it. I think this would be an efficient way to calculate it, using memoization, but it also takes a lot of space and I'm not sure how well python handles arrays that are millions of values. I don't know if this is realistically provable by brute force. It might need to be number theory. If we can assume that every number below the max in the array works, then we don't need to have a super massive array. Also, if there is one counterexample found, there are also infinite counterexamples found, due to 2n repeatedly dividing those numbers.
Roger Bryant
Roger Bryant Před 4 hodinami
x = i² The mathematical Theory of the existance of Imagination "Land", or a contemporary of Freud whom had "my grain head aches"? Well, nothing to write home about the answer is 3(i²) + 1 Order of operations. . . . -1 + 1
cool couch potato
cool couch potato Před 4 hodinami
Pick a number Me; 7 Video: Seven? Good choice! Me: Tha- wait *holdup*
Sly Marbo
Sly Marbo Před 4 hodinami
Why do I need to see a reverse shot of your smug face when a person is telling me the information I came for?
Helliosq Před 4 hodinami
Okay but why?
mister fox
mister fox Před 5 hodinami
why you can't use a minus (for example -7 × 3 + 1, I think it's interesting)
Yara Před 5 hodinami
I don't understand a thing but I'm waiting for something to impress my math teacher
Cezar Torescu
Cezar Torescu Před 6 hodinami
This cannot be proven because we're talking about total radomness in an infinity conjunction. It's like trying to prove the Universe is infinite. We know it is infinite but there is no proof of that ...
Jelly Bean
Jelly Bean Před 6 hodinami
I call this the alt-coin value simulator function, some give the illusion of going up, but they all end up crashing to nothing eventually
is yk It
is yk It Před 6 hodinami
It is dangerous.
Cooper Cassidy
Cooper Cassidy Před 7 hodinami
I have to do stuff like this
Redemption Lost
Redemption Lost Před 7 hodinami
I have a question if they have used negative and positive numbers for this equation have, they used the number 0? If they have used the number 0, why doesn't it work?
Josh Guo
Josh Guo Před 7 hodinami
The Gospel: We sin against God and for our sins we deserve hell. We fall short of God’s perfect standard for heaven. But the good news is we have a way to be forgiven, that way is through Jesus. Because he loved the world, he came, lived a sinless life then died on the cross for our sins, paying the price for them which is death. He was buried and rose again on the third day. Because Jesus did this for us the gift of eternal life from God is offered to everyone. All we must do to be saved is put our faith in Jesus ✝️❤️.
Adrian Zarmaty
Adrian Zarmaty Před 7 hodinami
I think it’s 3 because 3 x positive 1
Oscar the better player
Oscar the better player Před 7 hodinami
Why don’t they just add another rule?
Bobbit Worm
Bobbit Worm Před 7 hodinami
No one can solve. Yet they had us do it in high school al the time. I had this equation in 3 different high schools as part of everyday math. High school math is dumb I guess.
Daniel Duntavs Saunders
Daniel Duntavs Saunders Před 7 hodinami
It’s just beautiful!
_Blaze Před 7 hodinami
why not just use 0, I mean it will always end at 0 and be 0. edit: also, i just wanted to point out that the negative numbers have different loops well isnt +1 to a negative number just -1 to a positive number.
matt Před 7 hodinami
Ok but WHY?
Aiden Haines
Aiden Haines Před 8 hodinami
Brew Jitsu
Brew Jitsu Před 8 hodinami
What is there to solve?
NoLove Jones
NoLove Jones Před 8 hodinami
You can't slove it because you don't believe in God 7 is forced its has a reminder you not using the reminder that's why you can't slove it their are only 8 numbers everything's else is a repect 9 or ten doesn't exist because irs just a repeat of 0 6
karateplayer 12
karateplayer 12 Před 8 hodinami
ayo bro if the smartest person in the world cant answer question is the smartest person in the world
The Webmaster
The Webmaster Před 8 hodinami
This is because the number zero has no substance, and only exists since some centuries, and before that as a line or dot in Sumeria and Egypt, but that base 9 is the true Math, and that there is no such thing as Zero, making all our formulas, seem to be true, but in truth, they are wrong. 9 controls 6 and 3, and these in turn control the rest. double or halve 9 as many times as you want and add up the cyphers and it will always be 9. There is more to it than that, and you can try doubling and halving 3 and 6 too, and see what happens. 9 + 1 = xxxxxxxxxx,, and 9 minus 1 = xxxxxxxxx. But You cannot make something from nothing, and Zero represents nothing. There is no such thing as nothing. Only 1, and minus 1, but nothing between. either you have more than 5 apples in your basket or one less, but otherwise, the only zero there, is having neither one extra, or one missing. Which leaves the value unchanged, and no math to be done. ONly when we realize that zero is not to be used with numbers, our math will start to reveal what we have not yet seen
Peter Newton
Peter Newton Před 9 hodinami
I’m putting my money on them finding an independent circle of number before they find one that goes to infinity. I have no evidence, expertise or real reason to believe this so it’s just a guess
Willyboy Ï
Willyboy Ï Před 10 hodinami
Daniel Nordhorn
Daniel Nordhorn Před 11 hodinami
This is so useless and childish.
Chardonnay Benson
Chardonnay Benson Před 11 hodinami
the answer is 8
Tywan Horton
Tywan Horton Před 11 hodinami
Takes a new meaning to all roads lead to Rome.
Dr Bean
Dr Bean Před 11 hodinami
It’s 3
Saddy Před 12 hodinami
he read my mind damn
Jayrobiot Před 12 hodinami
If no one can solve it, it’s hard
ceoung Před 12 hodinami
3x+1=3 tho
ceoung Před 12 hodinami
Mike V
Mike V Před 12 hodinami
GreenCup, BlueCup
GreenCup, BlueCup Před 13 hodinami
What's the problem?
Naythlamer _
Naythlamer _ Před 13 hodinami
My first impression on thumbnail: 3x+1=0 ? => x = -1/3
king james488
king james488 Před 13 hodinami
the nature of infinity means you'll eventually come to a larger number that will evenly divide back to 1, as the number one is the unit all numbers are based upon. 1000 is 1000 1s. it's all 1. it's like asking if there's a number you can multiply by 1 that won't remain the same.
Herman Klinge Paredes
Herman Klinge Paredes Před 13 hodinami
Is this a true mathematical problem? To me it seems that the prediction has a flaw. It rules only even or uneven numbers. Therefore as infint can't be even or uneven cause its unknown the result is also unknown. You dont need to search a number that doesnt fit this criteria cause, there is only two options, that its even or uneven, therefor this always will loop you in the result. Its flaw in the proposition of the problem and that is why in my opinion no could solve it yet. If you found a number that didnt meet this criteria then it was not uneven or even and could not be used in this equations cause it doesent fit this premise. Greetings ;)
Herman Klinge Paredes
Herman Klinge Paredes Před 12 hodinami
Try for exaple to fit Pi in the equation.
Devarshi Dave
Devarshi Dave Před 13 hodinami
I have a question, what was the expected outcome here if let's say we didn't encounter the 4-2-1 loop? If you directly choose the number 4 you're there in the loop already...so what's the point of choosing any greater number because the formula is designed such way to eventually decrease the output. Another thing I think is, that if we encounter number 4, our system should stop there and return 4.
Jacob traupman
Jacob traupman Před 13 hodinami
Wonder if this is task for quantum computer
Scot Chatterson
Scot Chatterson Před 14 hodinami
The "+1" assures that the odd numbers become even, and even numbers divided by 2 eventually arrive at 1. The frequent changing of digits assures it will eventually arrive at a number well-divisible by 2. The 4-2-1 loop is simply by nature of the problem. Add 3, divide by 2 twice. I don't see what the problem is, exactly.
lucky mmez
lucky mmez Před 14 hodinami
yall niggas slow x = -1/3
lucky mmez
lucky mmez Před 14 hodinami
Tomas Favetto
Tomas Favetto Před 14 hodinami
im not a mathematician, so can soneone enlighten me on my people spend so much time making up equations like this. what practicality comes from equations like these
Patrick Munger
Patrick Munger Před 14 hodinami
Loved this! First thought was that it feels like an animation, a marble bouncing down a hill and sucked into a perpetual tide pool. 3x+1/2 is a bully to odd numbers. Instead of explaining why/how it functions, I'd like to know what added function could be placed to have the 421 loop react in some way. Thanks! Really appreciate your work.
Sav Před 14 hodinami
Anyone else do the whole thing for 27 on their phone? lol
Thomas Eubank
Thomas Eubank Před 14 hodinami
Okay okay, what about 295,147,905,179,352,825,857? Has that number been tested?
Pasya Alfaridzi
Pasya Alfaridzi Před 15 hodinami
3x+1 3x-+1=0 3x=-1 x=-0.33
I am ze MEDIC!
I am ze MEDIC! Před 15 hodinami
I'm getting dizzy listening and watching this
Roger Matar
Roger Matar Před 15 hodinami
What about the trinity 1+1+1=1 🤔
SL I SenorLambo
SL I SenorLambo Před 15 hodinami
You cant call it simple if not the majority cant solve it 🤷
J Modified
J Modified Před 14 hodinami
The problem is simple. The solution may be simple but hard to find, but probably not.
PurpleFlame_YT Před 15 hodinami
the answers 12 o-o
Tyler Elmy
Tyler Elmy Před 15 hodinami
If X has no given value. It assumes the value of 1
Luis Lam
Luis Lam Před 16 hodinami
But why
Is using decimals against the rules or do they still work Edit: nvm I forgot decimals can’t count as odd or even so they can’t be used
Collin Arthur
Collin Arthur Před 16 hodinami
ix+1 haha
Adam Smith
Adam Smith Před 16 hodinami
the real question, why do you go past the first question?
nethernman e
nethernman e Před 16 hodinami
The Bobaz
The Bobaz Před 16 hodinami
I got 4
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