The Simplest Math Problem No One Can Solve - Collatz Conjecture

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    VeritasiumVeritasium

    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

Woody
Woody

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

Vor 2 Minuten
Mike van Gaans
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
mozziezapper

Seems pretty easy to me 😐

Vor 9 Minuten
a human
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
Not Noob1234

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

Vor 32 Minuten
look it up
look it up

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

Vor 44 Minuten
look it up
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
Jesse James

X=1/3

Vor 46 Minuten
E. M. C.
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
Abbas Rayyan

3x+1 is 4

Vor Stunde
Mario Bircea
Mario Bircea

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

Vor Stunde
Carly
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
gamer corns

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

Vor Stunde
Ace2R
Ace2R

x=0.3

Vor Stunde
Sung Woo
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
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
SerpentLord666

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

Vor 2 Stunden
Harryboi
Harryboi

This problem is already simplified enough it’s practically solved

Vor 2 Stunden
Kalson Chua
Kalson Chua

Wouldn’t a quantum computer work?

Vor 2 Stunden
Alien Chefs
Alien Chefs

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

Vor 2 Stunden
James Kelvin
James Kelvin

NERDS!!! GET 'EM!!!

Vor 2 Stunden
Garrison Guillory
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
Aashish Khadka

wait, what's the problem again?

Vor 2 Stunden
Aloysius Janofski
Aloysius Janofski

Isn’t Pi a number?

Vor 2 Stunden
Marcos GV
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
Wildcatbeer

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

Vor 2 Stunden
Josiah Traeger
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
Shirtless halo_ Leader

But I said 1

Vor 3 Stunden
Shintaro Iwata
Shintaro Iwata

Clickety click

Vor 3 Stunden
todd
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
Kendall Scrimshaw

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

Vor 3 Stunden
Abigail
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
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 ✔︎
Pokémon Kid I guess ✔︎

4

Vor 3 Stunden
Raidell Almelor
Raidell Almelor

yea i cant even

Vor 3 Stunden
Jenny The Potato
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
Vinh C

X= -1/3

Vor 3 Stunden
Hamezz
Hamezz

I leaned this as the hurricane problem or somthing

Vor 3 Stunden
Aiden Callaway
Aiden Callaway

X=1/3

Vor 3 Stunden
Vinh C
Vinh C

It’s x= -1/3

Vor 3 Stunden
CreativeTime
CreativeTime

Answer is 4

Vor 3 Stunden
Tryston Anderson
Tryston Anderson

4

Vor 3 Stunden
DoctorBean
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
Ruben Palma

That Terry Tao introduction was hilarious haha great work

Vor 4 Stunden
Blob // smiley256
Blob // smiley256

i tried it and i got 1.0

Vor 4 Stunden
vincent barnes
vincent barnes

calculator do you think im a joke

Vor 4 Stunden
Gone fission
Gone fission

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

Vor 4 Stunden
Sheperdz
Sheperdz

uhhh 0.3 ?

Vor 4 Stunden
Dominick Spaziani
Dominick Spaziani

it 3x+1 is 4

Vor 4 Stunden
touristguy87
touristguy87

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

Vor 4 Stunden
Nabeel S
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
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
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
chloe m

this is so helpful lol

Vor 5 Stunden
Adalia_Editz
Adalia_Editz

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

Vor 5 Stunden
Amy Smith
Amy Smith

It's 4x

Vor 5 Stunden
Will See
Will See

7.2 and it goes ever upward.

Vor 5 Stunden
Henry DA pro
Henry DA pro

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

Vor 5 Stunden
mcinnisdale
mcinnisdale

its simply 3

Vor 5 Stunden
Adrian Haroon
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
Cup 12

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

Vor 5 Stunden
Bonnie Crowther
Bonnie Crowther

3+1 is 4 4X3 is 12.

Vor 5 Stunden
christopher ramirez
christopher ramirez

4

Vor 5 Stunden
Bonnie Crowther
Bonnie Crowther

The awnser is 12

Vor 5 Stunden
Raja kesavan
Raja kesavan

I couldn't understand the equation

Vor 5 Stunden
mike GG
mike GG

it =4

Vor 5 Stunden
blurr
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
Bösein

Is there any conceivably useful application of this?

Vor 6 Stunden
screaming cat
screaming cat

It’s 10 3+3+3=9+1=10

Vor 6 Stunden
Mr. Bopper
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
Fresh

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

Vor 6 Stunden
Wings Fly Far
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
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
Systenize

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

Vor 6 Stunden
Blaze BS
Blaze BS

X= -1/3

Vor 6 Stunden
Monkey man
Monkey man

4x

Vor 6 Stunden
Letsgoleo
Letsgoleo

EASY (joke) =3X

Vor 6 Stunden
Jaydek Kozloski
Jaydek Kozloski

I know how to solve it

Vor 6 Stunden
Jaydek Kozloski
Jaydek Kozloski

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

Vor 6 Stunden
Ricky Smalls
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
J

4x lol

Vor 6 Stunden
Zane Woodling
Zane Woodling

A counter example is 0

Vor 6 Stunden
GalaxC
GalaxC

The problem on the thumbnail is x=1/3

Vor 6 Stunden
_ub4
_ub4

I mean who even made this? And why?

Vor 7 Stunden
CAS Poetry
CAS Poetry

I swear 3x+1=10

Vor 7 Stunden
Ortega O
Ortega O

I guess 1

Vor 7 Stunden
Kassim houssein
Kassim houssein

what about 0

Vor 7 Stunden
Broster41
Broster41

7

Vor 7 Stunden
Dragon Boss 37
Dragon Boss 37

What about decimals?

Vor 7 Stunden
oof
oof

WOAHHHHHHHHHHH

Vor 7 Stunden
Godtear 10
Godtear 10

Algebra

Vor 7 Stunden
abcswitch_
abcswitch_

Technically x=0

Vor 7 Stunden
Josh Marriott
Josh Marriott

What if u put pi in the loop?

Vor 7 Stunden
asing red
asing red

Bruh this is the easiest problem

Vor 8 Stunden
D1doscar
D1doscar

But what is there to solve?

Vor 8 Stunden
Toastey2020
Toastey2020

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

Vor 8 Stunden
Xx_SneakyFox_xX
Xx_SneakyFox_xX

I am guessing 4

Vor 8 Stunden
LoFi Boy
LoFi Boy

3x+1=3x

Vor 8 Stunden
Francesco Scudeletti
Francesco Scudeletti

How in tf 1x3 its 3 lol

Vor 9 Stunden
Neel Dhingra Dhingra
Neel Dhingra Dhingra

the awnser is 3x+1

Vor 9 Stunden
AserXD
AserXD

3x1+1=4

Vor 9 Stunden

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