#### Am Vor 2 Monate

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

## KOMMENTARE

## Woody

Ok but like at the beggining, hpw u know what i picked

Vor 2 Minuten## Mike van Gaans

So the conclusion is that 3N+1 always result in 1… so that’s the conclusion, where’s the problem?

Vor 7 Minuten## mozziezapper

Seems pretty easy to me 😐

Vor 9 Minuten## a human

and then there's my math teacher,who's probably gonna solve this somehow, *without using a calculator* /j

Vor 21 Minute## Not Noob1234

idk what it is but my estimate is 4...

Vor 32 Minuten## look it up

3x+1 = 3x=-1 = x=-1/3

Vor 44 Minuten## look it up

if we keep going solving for the whole thing and not just the x: 3(-1/3)+1 3x3 cancels out so -1+1 which is equal to 0 youre welcome i solved the easiest problem no one can solve, i suppose im a genius

Vor 41 Minute## Jesse James

X=1/3

Vor 46 Minuten## E. M. C.

3x + 1 is simple math and I can solve it. 3x + 1.....divide both sides by 3... X is now alone and you have 1/3 so now its x + 1/3 which is literally 1/3x. X is whatever you want it to be so solve it with that. X is life. You can sit here and think this problem is hard but you can replace the variable white whatever you want. Look at life like that. You have a problem with one solution, make another solution. Have a good day yall

Vor 48 Minuten## Abbas Rayyan

3x+1 is 4

Vor Stunde## Mario Bircea

and all of this starts from an father game :))

Vor Stunde## Carly

Solving this is beyond me, but in trying to understand, it confuses me why we use 3x+1. Perhaps I'm confused about what is trying to be proved. Thinking about the problem in terms of only odd and even numbers, it seems quite logical that repeated division by a common factor other than 0 should inevitably result in 1, or at least trend towards 1. 1) How do we determine the common factor? Well, we know that any even number can be divided by 2. 2) What should we do about odd numbers then? Well, adding two odd numbers should always result in an even number, so the easiest thing would be to add or subtract 1. Now we have an even number that can be divided by two. 3) Why does the result always end up back at 1? It might have something to do with the chain created by 2^1=2 ,2^2=4, 2^3=8, etc. The answer will always be even, except for 2^0=1. Hence the loop. 1+1=2/2=1 3+1=4/2=2/2=1 3-1=2/2=1

Vor Stunde## gamer corns

"pick a number" me: fiv- "seven me: seven

Vor Stunde## Ace2R

x=0.3

Vor Stunde## Sung Woo

Its and every lasting cycle bruh I been watching this for like a 1 min and my head Hurst already 😒

Vor Stunde## New Western Front

lol he said 7 was a good one to pick starting out because all of the other preceding numbers fall to 1 really quickly

Vor 2 Stunden## SerpentLord666

Why are you considering it a problem? It's a result; a solution to a formula. That's all.

Vor 2 Stunden## Harryboi

This problem is already simplified enough it’s practically solved

Vor 2 Stunden## Kalson Chua

Wouldn’t a quantum computer work?

Vor 2 Stunden## Alien Chefs

The possible raven postsurgically unpack because gauge neuropathologically tour throughout a strange song. warm, real branch

Vor 2 Stunden## James Kelvin

NERDS!!! GET 'EM!!!

Vor 2 Stunden## Garrison Guillory

Technically speaking, wouldn’t a repeating number or an infinite number be unable to break it down to the core function of 1 since they technically go in an infinite number cycle

Vor 2 Stunden## Aashish Khadka

wait, what's the problem again?

Vor 2 Stunden## Aloysius Janofski

Isn’t Pi a number?

Vor 2 Stunden## Marcos GV

wouldn't it be 0 since you can divide by 2 and give u 0 and it goes on to the infinity :)

Vor 2 Stunden## Wildcatbeer

Why do we think we're ready for an answer? Huh...

Vor 2 Stunden## Josiah Traeger

This is really interesting. I'm just curious though, if the conjecture is proven true, what does that mean really?

Vor 3 Stunden## Shirtless halo_ Leader

But I said 1

Vor 3 Stunden## Shintaro Iwata

Clickety click

Vor 3 Stunden## todd

Earth is a circle. I not sure why you out this up. It's a simple math trick. Boring. Get out of my circle.

Vor 3 Stunden## Kendall Scrimshaw

Has anyone tried 3x+1 with the imaginary number 'i'?

Vor 3 Stunden## Abigail

Here is another way to put it. So 3x+1: the + represents positive numbers, even tho numbers have a invisible +, they maybe put that to trick people. So it is 3 times positive 1, so to put that in a equation it is 3x1, again the 1 is positive so it has an invisible + sign so that’s what the +1 is. Boom the answer to the equation 3x+1 is 3

Vor 3 Stunden## Kartik Dubey

BRO. I THINK THAT SCIENTIST CAN CREATE A TIME LOOP MACHINE BY THE HELP OF COLLATZ CONJECTURE. MAY BE

Vor 3 Stunden## Pokémon Kid I guess ✔︎

4

Vor 3 Stunden## Raidell Almelor

yea i cant even

Vor 3 Stunden## Jenny The Potato

Could you do this with pie? I know it’s never ending but I was just wondering.

Vor 3 Stunden## Vinh C

X= -1/3

Vor 3 Stunden## Hamezz

I leaned this as the hurricane problem or somthing

Vor 3 Stunden## Aiden Callaway

X=1/3

Vor 3 Stunden## Vinh C

It’s x= -1/3

Vor 3 Stunden## CreativeTime

Answer is 4

Vor 3 Stunden## Tryston Anderson

4

Vor 3 Stunden## DoctorBean

I just the thumbnail and thought the ans was x=1/3 but knew I was wrong looking at the video time😂

Vor 4 Stunden## Ruben Palma

That Terry Tao introduction was hilarious haha great work

Vor 4 Stunden## Blob // smiley256

i tried it and i got 1.0

Vor 4 Stunden## vincent barnes

calculator do you think im a joke

Vor 4 Stunden## Gone fission

I want that Mathematica file used to show the “bits” part toward the end.

Vor 4 Stunden## Sheperdz

uhhh 0.3 ?

Vor 4 Stunden## Dominick Spaziani

it 3x+1 is 4

Vor 4 Stunden## touristguy87

so, again, you're not a real mathematician.

Vor 4 Stunden## Nabeel S

I don't get what the problem is and why are we multiplying by 3 and adding 1. Who cares?

Vor 4 Stunden## Allison Shuttz

I’m really good at math a real pro but this is really hard and I would like for people to not do this I have tried for 2 years and not found anything don’t try this

Vor 4 Stunden## Natalie Jimenez

I saw the thumbnail and it looks like 3 times positive 1. I have not watched the video but I’m assuming that’s what it is. I better be right. Edit: well I’m kinda dumb

Vor 5 Stunden## chloe m

this is so helpful lol

Vor 5 Stunden## Adalia_Editz

The answer is 3x + 1 because they’re not like terms so you can’t combine them

Vor 5 Stunden## Amy Smith

It's 4x

Vor 5 Stunden## Will See

7.2 and it goes ever upward.

Vor 5 Stunden## Henry DA pro

What happens if the start number is something like 3.5 instead of 3 or 4

Vor 5 Stunden## mcinnisdale

its simply 3

Vor 5 Stunden## Adrian Haroon

I think its 4 bc 3x1 is 3 bc its 3 rows of 1 plus one so 3x plus 1 is 4

Vor 5 Stunden## Cup 12

3x1=1 1+1=2 It's 2

Vor 5 Stunden## Bonnie Crowther

3+1 is 4 4X3 is 12.

Vor 5 Stunden## christopher ramirez

4

Vor 5 Stunden## Bonnie Crowther

The awnser is 12

Vor 5 Stunden## Raja kesavan

I couldn't understand the equation

Vor 5 Stunden## mike GG

it =4

Vor 5 Stunden## blurr

i saw it an was like oh easy 3 + 1 then got 4, read the title and said "YO IM A GODDAMN PRODEGY ALIEN IM SMARTER THEN EVERYONE" then saw the x after 3 and was like oh, tried again and my brain started hrted

Vor 6 Stunden## Bösein

Is there any conceivably useful application of this?

Vor 6 Stunden## screaming cat

It’s 10 3+3+3=9+1=10

Vor 6 Stunden## Mr. Bopper

The answer to the thumbnail question is the thumbnail because you can add coefficients with constants 😎 (presses send even tho I’m prob wrong 💀)

Vor 6 Stunden## Fresh

My first thought was that the problem was 1+1 cause no one can answer that

Vor 6 Stunden## Wings Fly Far

I think this is stupid from a layperson's perspective and actually reminds me of other buskers I worked with who were magicians, on anything numerical. 50% of numbers between 1-100 will divide twice to another even as a minimum and even many more times at time. Evens times with evens = evens. Odds X odds = odds. Adding 1 means every number is artificially reverted to an even so you tip the chances against odd. The only significance in x3 is that it's the lowest odd you can times with which means it's going to multiply by the lowest amount possible to create the lowest number before. Try this with x5+1. Then maybe the odds have a chance of increasing themselves through multiplication by outweighing or equalling the same chance as an even number is given in this equation to divide itself down to one. Thus it's not interesting to see what a tipped rigged game is because the equation is doing everything to increase the chances of division so of course it will divide more than it will multiply. The interesting question is not even a really a true mathematical one, but at least less predictable in outcome (so not 4-2-1, which is inevitable if you give more chances to divide), but is there a number where an odd is equal to an even in terms of a stalemate. At what point can we flip it the other way so that it always increases infinitum. We might find that oddx3+1÷2 always leads to 4-2-1. Oddx5+1÷2 always leads to a stalemate (though it might involve decimals to find ultimate stalemate). Oddx7+1÷2 leads to ever increasing numbers. It might tell us something about how we can use numbers, but it might explain how we work psychologically. If this is all a trick to make us believe there is a pattern and a coral reef like tree when it simply weighed odds towards a controlled outcome by the creator of the equation, then it might just prove that even our most intelligent human beings are still idiots and sheep like everyone else.

Vor 6 Stunden## Wings Fly Far

Not saying I haven't missed something, but I am agnostic enough to know, our smartest known human beings made some serious assumptions that led them everywhere the next set of smartest human beings descredited, that did the same thing with their ideas. To find anything resembling an answer, it might help to start from the assumption that even trying to work towards an assumption creates assumptions, and a whole package of equations, theories and mutual pat on the backs. For all we know, staring at our products of thoughts wipe out all the other maths going in the background we can't yet imagine because it's impossible to exist without well known equations taking your focus. And if you have it in your head, then like the 4 humours, you will always try to tie in anything new into a mistake

Vor 6 Stunden## Systenize

My teacher: "How is it possible that you forget your homework each time?" Me: 20:33

Vor 6 Stunden## Blaze BS

X= -1/3

Vor 6 Stunden## Monkey man

4x

Vor 6 Stunden## Letsgoleo

EASY (joke) =3X

Vor 6 Stunden## Jaydek Kozloski

I know how to solve it

Vor 6 Stunden## Jaydek Kozloski

Just don't multiply then add 1 or devide by 2

Vor 6 Stunden## Ricky Smalls

I’m saying it’s negative 2 before the video and if I’m wrong I’ll reply to this message

Vor 6 Stunden## J

4x lol

Vor 6 Stunden## Zane Woodling

A counter example is 0

Vor 6 Stunden## GalaxC

The problem on the thumbnail is x=1/3

Vor 6 Stunden## _ub4

I mean who even made this? And why?

Vor 7 Stunden## CAS Poetry

I swear 3x+1=10

Vor 7 Stunden## Ortega O

I guess 1

Vor 7 Stunden## Kassim houssein

what about 0

Vor 7 Stunden## Broster41

7

Vor 7 Stunden## Dragon Boss 37

What about decimals?

Vor 7 Stunden## oof

WOAHHHHHHHHHHH

Vor 7 Stunden## Godtear 10

Algebra

Vor 7 Stunden## abcswitch_

Technically x=0

Vor 7 Stunden## Josh Marriott

What if u put pi in the loop?

Vor 7 Stunden## asing red

Bruh this is the easiest problem

Vor 8 Stunden## D1doscar

But what is there to solve?

Vor 8 Stunden## Toastey2020

Who new 3x+1 could be answered in 22:00

Vor 8 Stunden## Xx_SneakyFox_xX

I am guessing 4

Vor 8 Stunden## LoFi Boy

3x+1=3x

Vor 8 Stunden## Francesco Scudeletti

How in tf 1x3 its 3 lol

Vor 9 Stunden## Neel Dhingra Dhingra

the awnser is 3x+1

Vor 9 Stunden## AserXD

3x1+1=4

Vor 9 Stunden