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

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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

30. 07. 2021

Můj playlist

Přehrát později

Retarded fish Před minutou

4x

South Boston Před 7 minutami

"Pick a number, any number..." Me: 7 "Seven, good choice.." Me: (0_0)

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 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 Před 24 minutami

We don't know what is x, thats why it's imposible LOL

Sean Clarkson Před 28 minutami

the anser is 7

Fehraz Az Před 32 minutami

okay okay i get it. this is some endlevel math. buuuuut i dont get the problem here...

Jelly Beans Před 36 minutami

and whats the purpose of this. Its cool but does it actually do something helpful

SoZiAlShMaRoTzA ™ Před 40 minutami

Ever thought about "it is how it is" ?

A-Mech Studios-Skitlz Před 41 minutou

4x

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 Před hodinou

Is calculator always right tho?

Pogboy Před hodinou

It’s 4

Not JellyBean Official Před hodinou

4 😳

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 Před hodinou

There is no way I just watched a 22 minute video about maths voluntarily

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 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

Facts

Moore Koubel Před 2 hodinami

What problem?? its a sequence of instructions............ who cares?!

John Reez Před 2 hodinami

..wow i really thought of 7 how comes?

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

1

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 Před 3 hodinami

the answer to the thumbnail is 12

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 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 Před 4 hodinami

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 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 Před 4 hodinami

Pick a number Me; 7 Video: Seven? Good choice! Me: Tha- wait *holdup*

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 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 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 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 Před 6 hodinami

It is dangerous.

Cooper Cassidy Před 7 hodinami

I have to do stuff like this

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 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 Před 7 hodinami

I think it’s 3 because 3 x positive 1

Oscar the better player Před 7 hodinami

Why don’t they just add another rule?

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 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 Před 8 hodinami

2x

Brew Jitsu Před 8 hodinami

What is there to solve?

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 Před 8 hodinami

ayo bro if the smartest person in the world cant answer question is the smartest person in the world

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 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 Před 10 hodinami

Wow

Daniel Nordhorn Před 11 hodinami

This is so useless and childish.

Chardonnay Benson Před 11 hodinami

the answer is 8

Tywan Horton Před 11 hodinami

Takes a new meaning to all roads lead to Rome.

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

Nvm

Mike V Před 12 hodinami

0

GreenCup, BlueCup Před 13 hodinami

What's the problem?

Naythlamer _ Před 13 hodinami

My first impression on thumbnail: 3x+1=0 ? => x = -1/3

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 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 Před 12 hodinami

Try for exaple to fit Pi in the equation.

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 Před 13 hodinami

Wonder if this is task for quantum computer

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 Před 14 hodinami

yall niggas slow x = -1/3

lucky mmez Před 14 hodinami

nvm

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 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 Před 14 hodinami

Okay okay, what about 295,147,905,179,352,825,857? Has that number been tested?

Pasya Alfaridzi Před 15 hodinami

3x+1 3x-+1=0 3x=-1 x=-0.33

I am ze MEDIC! Před 15 hodinami

I'm getting dizzy listening and watching this

Roger Matar Před 15 hodinami

What about the trinity 1+1+1=1 🤔

SL I SenorLambo Před 15 hodinami

You cant call it simple if not the majority cant solve it 🤷

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 Před 15 hodinami

If X has no given value. It assumes the value of 1

Luis Lam Před 16 hodinami

But why

IMPRECISEWORDSDREEEEEEEEEEEEEEAAAAAAAAAAAAAAMMMM Před 16 hodinami

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 Před 16 hodinami

ix+1 haha

Adam Smith Před 16 hodinami

the real question, why do you go past the first question?

nethernman e Před 16 hodinami

4x

The Bobaz Před 16 hodinami

I got 4

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