The Simplest Math Problem No One Can Solve - Collatz Conjecture

429 000 Weergaven 12 mln.

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

Reacties

  1. Rutmer Hoitema
    Rutmer Hoitema
    16 minuten geleden

    But why is it a problem?

  2. Expulsion Science
    Expulsion Science
    Uur geleden

    So interesting!

  3. GHOST5663
    GHOST5663
    Uur geleden

    15:09 - Why do minus figures get three loops? Could it be that these numbers, which exist on the -y axis, mean/suggest, that this information is not of this dimension and does not follow our normal way of analysis?

  4. ScienceXplorer
    ScienceXplorer
    2 uur geleden

    Just my doubt here is , everything normal with the number system design ,Is it sufficient to explain everything mathematically. A lot of things seems to get stuck around within just this "1,2,3.... ∞ " circle. We cannot prove or be sure about one thing without having something else to verify it with . 1 = 1 makes sense , but its contradictory when we go through the proofs . Is there a way in which we can represent 1 , 2 and 3 all at the same , physics needs some mathematics models like this to be considered .

  5. Ee J
    Ee J
    4 uur geleden

    I have no idea what any of this means but was really cool to watch. And infinity means endless right? Like if you start counting you can never stop, there is no end number, it just goes and goes up and up. I heard something about you can't even fit all the numbers in the universe if it was filled with paper or whatever, everything ends I guess at 1 but there is nothing you can't not add 1 to. I don't know, I just like to try and feel smart and then get a headache and go to sleep. It's fun to think though, math, riddles, physics, I love it all.

  6. D R
    D R
    5 uur geleden

    This isn't a "math problem". Its just trying to analyze a trend.

  7. Jake Kim
    Jake Kim
    8 uur geleden

    No ads plz

  8. Sid M
    Sid M
    9 uur geleden

    Cut it in half ½ 0.5

  9. Pepsi Max
    Pepsi Max
    10 uur geleden

    My first question is why would you waste your time doing this?

  10. X-style
    X-style
    10 uur geleden

    for me, the only problem with these numbers are in my bank account, every month ends in the same loop :(

  11. neonpeacocks
    neonpeacocks
    11 uur geleden

    Surely I’m not the only one listening to this video with a blank stare…too stupid to understand maths club!

  12. Anti -
    Anti -
    11 uur geleden

    The answer is Taco 🌮 chow.

  13. Aquea Ventus
    Aquea Ventus
    12 uur geleden

    2 is required to complete the loop 1 being singular and is the starting point for all things therefore 1 must dived to become 2

  14. Aquea Ventus
    Aquea Ventus
    12 uur geleden

    42 the meaning of life !

  15. -.-
    -.-
    13 uur geleden

    - 1/3X

  16. A D
    A D
    13 uur geleden

    Why is it a problem??? What do they want instead ???

  17. Thomas Hoens
    Thomas Hoens
    13 uur geleden

    The progression ends when 3x+1 equals a power of 2, at which point the progression stops increasing and collapses down to 1. Shouldn't we be looking at it from that perspective?

  18. Fahim Montasir
    Fahim Montasir
    14 uur geleden

    12:34

  19. Adu Balu
    Adu Balu
    15 uur geleden

    This video increased my anxiety

  20. Sean Chandler
    Sean Chandler
    16 uur geleden

    seems once you hit a number to the power of 2 it drops all the way down to 1.

    1. Релёкс84
      Релёкс84
      16 uur geleden

      It is also the only possible way to drop to 1, if you think about it.

  21. Cosmo Thompson
    Cosmo Thompson
    17 uur geleden

    Have you tried 2^68 + 1 though? I have a feeling about that one

  22. ジ
    18 uur geleden

    Keep it up

  23. Kalyan Boro
    Kalyan Boro
    19 uur geleden

    just another time pass till the next season of "Money Heist" releases!!

  24. ariel krische
    ariel krische
    19 uur geleden

    The blue jewel namely extend because soldier covalently miss but a tranquil postbox. gifted, ritzy step-aunt

  25. Hazbin Hotel
    Hazbin Hotel
    20 uur geleden

    What 3x =1 shows you(proves?) is that every natural number plugged into x eventually gives you a sequence that devolves into a 4-2-1 loop. This loop is what gives us quadratics, differential equations our understanding of algebra and geometric proofs. another way to think of this is any higher dimensional universe eventually collapses down into a 4 dimensional universe. 3x=1 is the soviet hammer/grim-reaper death-sickle to string theory....muah hahahahah

  26. Robert M
    Robert M
    21 uur geleden

    i realized that only the numbers are infinite, everything else has an end...even the universe, the planets, all the sand on a beach, etc, you can count everything, but you cant get to the last number.

  27. itszian
    itszian
    21 uur geleden

    Wow now try to prove all the fractional numbers following the conjecture

  28. Jimbob Robob
    Jimbob Robob
    21 uur geleden

    I was able to keep up somewhat to about 7 mins... 😢

  29. LeeWAM
    LeeWAM
    22 uur geleden

    i think i got proof there is no other loop than 1-2-4

    1. LeeWAM
      LeeWAM
      19 uur geleden

      @Релёкс84 im not fooling, i even wrote it here but i edited, after checking i tell you if it was correct or not

    2. Релёкс84
      Релёкс84
      19 uur geleden

      @LeeWAM you're not fooling anyone.

    3. LeeWAM
      LeeWAM
      19 uur geleden

      @Релёкс84 it still needs to be checked, but i do have

    4. Релёкс84
      Релёкс84
      19 uur geleden

      @LeeWAM I still think you don't have a proof

    5. LeeWAM
      LeeWAM
      20 uur geleden

      @Релёкс84 i got (un checked) proof that there's no other loop, and idea for proof it can't go infinitely without reaching 1-2-4 loop

  30. Bob Zim
    Bob Zim
    22 uur geleden

    That was good.

  31. Justin TimberFlake
    Justin TimberFlake
    Dag geleden

    Does it have something to do with the possibility that all numbers have some connection to a power of two? Whenever a sequence runs into a power of 2, it automatically goes down to 1

  32. Dwight Gutierrez
    Dwight Gutierrez
    Dag geleden

    The waiting kilometer revealingly mend because butcher reportedly scrape beyond a amusing girdle. upset, addicted sweets

  33. Joseph Martillo Palacios
    Joseph Martillo Palacios
    Dag geleden

    To prove that conjecture is to show what the value of infinity is, that is, it does not make sense if it does not have boundaries.

  34. vqynszn
    vqynszn
    Dag geleden

    what if you just find a number that divides into 6 so it goes 6, 3, 1.5, 5.5 lmao don’t make fun of me

  35. Brian Colbert
    Brian Colbert
    Dag geleden

    To me it looks like something simple then mathematicians make it hard. On the other hand I don't know much about math. On the other hand I guess it doesn't really matter.

  36. Milky1L
    Milky1L
    Dag geleden

    Dude imagine if we are just living in one computer complex that had been trying to figure out the answer to this problem for so long and so fast that it created an entire organic galaxy within itself. In the video, the 3D module looks like some sort of plant, so think about what it could create if it had been running for thousands of years on a machine infinitely times as powerful as powerful as our computers.🧠

    1. Noé de Cominges Arce
      Noé de Cominges Arce
      12 uur geleden

      i'm too high for this

  37. Laramie On Location
    Laramie On Location
    Dag geleden

    Why is this something that people want to “crack”? Nobody cracks 2+2=4. There are tons of patterns in nature. I don’t see the big deal. But I’m not a mathematician. Or a Russian.

  38. Andre
    Andre
    Dag geleden

    The sequence of kaos

  39. Brandon Brouillette
    Brandon Brouillette
    Dag geleden

    You're multiplying a random number by 3, then adding 1. But also applying different rules depending on the outcome after that. So, it's just a simple eventuality that I'm sure a smarter person than myself could 'solve'. It sounds interesting on paper, "nobody can solve this". But really, there's nothing to solve. It's simple mathematics.

    1. J Modified
      J Modified
      Dag geleden

      If someone could solve it they would. There is a (slightly over) $1,000,000 prize.

  40. Saoud Alzoabi
    Saoud Alzoabi
    Dag geleden

    Actually, there was no problem in the first place. This equation is very ordinary, but people decided to put a rule to make it hard to solve. Why on the earth would I divide by 2 if even, and use 3x+1 if odd. There is no need to apply such rule, unless you are out of mind and want to play a stupid game.

  41. TGC
    TGC
    Dag geleden

    Try 963

  42. Abylssent
    Abylssent
    Dag geleden

    I know the answer its MATH

  43. Sticks
    Sticks
    Dag geleden

    I don't understand anything about this at all, but when he said Fibonacci sequence....😓😓😓 that brings back memories

  44. Dale
    Dale
    Dag geleden

    "As yet, no loop has been found" Ummm...4?

  45. Ruhaan Burger
    Ruhaan Burger
    Dag geleden

    I am a bit confused. Numbers are never ending. Even 2^1000 is nothing, and still a finite searchable area (although not by current computers). Going by this the conjecture can never be proven. Only disproved (if possible). At what point do you simply assume that it is true for infinity?

    1. J Modified
      J Modified
      18 uur geleden

      @Ruhaan Burger See the Wikipedia page on "mathematical induction" for example. Most likely if Collatz is true, any proof would involve induction of some sort, though nothing as simple as the examples on that page. Another possibility is to show through a series of transformations that the problem is equivalent to one for which the solution is already known. Proof by contradiction is another possibility. For example you could show that if there is a non-trivial loop, that implies that something else is true, where that thing is known to be false.

    2. Ruhaan Burger
      Ruhaan Burger
      Dag geleden

      @J Modified Pls elaborate on the many possible methods.

    3. J Modified
      J Modified
      Dag geleden

      You can never assume it is true. A discrete proof is required. There are many possible methods for achieving that.

  46. James Targin
    James Targin
    Dag geleden

    What does “solve” mean in this context? What exactly is the goal here?

    1. J Modified
      J Modified
      Dag geleden

      To prove the conjecture true or false.

  47. Karlee TDM
    Karlee TDM
    Dag geleden

    You forgot about the decimals. 🙃

  48. Whatisthisthing
    Whatisthisthing
    Dag geleden

    How is this a problem rather than a pattern? Also how is it random if you're following 2 set rules? I don't get it.

  49. Koon Troll
    Koon Troll
    Dag geleden

    in leftist ideology math ls racist

  50. Karl Davis
    Karl Davis
    Dag geleden

    I'm an engineer who uses a lot of math, but not a mathematician. 2^32 is 4 billion, and it's also the size of an unsigned integer on a 32 bit OS. In my world, if something is true up to 4 billion, it's true. My world has heuristics, not proofs. I wrote a Woodoku optimizer for fun. I do it on multi-million dollar equipment at work.

  51. Anton Novikov
    Anton Novikov
    Dag geleden

    @9:56 Laniakea?

  52. Bad News Broadcast
    Bad News Broadcast
    Dag geleden

    This is impossible to solve so dont even bother trying

    1. Релёкс84
      Релёкс84
      Dag geleden

      How would you know?

  53. shredx81
    shredx81
    Dag geleden

    Hold my beer

  54. Bálint Éliás
    Bálint Éliás
    Dag geleden

    I wrote a code for my Arduino to brute force this thing. I had a memory overflow at 32k proven numbers and I fixed it by changing integers to "long integers". After 36 minutes of running, it reached 338k, but it is slowly slowing down, because it has to do more and more calculations to prove that a number will end up in the 4-2-1 loop. In fact, when the result of a calculation is less than the number it's trying to prove, it jumps to the next number to prove, because it reached a number that was already proven. The program skips even numbers, because the result would be instantly less than the number it started with. Now it is at 421k proven numbers. Looks like something took a lot of time before 338k. And I don't print the calculations, only the progress, because it would slow down the process.

    1. J Modified
      J Modified
      Dag geleden

      Oops, I missed that you are already doing (1) and (4). Anyway, even on a super slow processor your program should not be anywhere close to that slow. Maybe it is purely limited by printing speed.

    2. J Modified
      J Modified
      Dag geleden

      That's very slow. You might want to take advantage of these: 1) You only need to test odd numbers. 2) Test for even/odd using bitwise "and", which is much faster than mod 2. 3) Divide by two by right shifting, which is much faster than a divide operation. 4) If testing in order, you can stop when the number goes below the seed. 5) Since you are only testing odd numbers, you can immediately do a 3x + 1 then divide by two before testing in a loop. 6) After a 3x + 1 you can always immediately divide by two without testing for odd again or checking the result against the seed, since the result will be even and higher than the seed if x was higher than the seed. 7) If you must print progress, use a bitwise test to print every hundred billion numbers or so, or however many it gets through about every ten seconds (I have no idea how slow the processor you are using is).

  55. Dani_Stars230
    Dani_Stars230
    Dag geleden

    Mathematicians: "I fear no man, but that thing (3n+1) it scares me..."

  56. Vasu Gupta
    Vasu Gupta
    Dag geleden

    Have you tried negativesss....

    1. Hi Hi
      Hi Hi
      Dag geleden

      Yes. They said that in the video

    2. Релёкс84
      Релёкс84
      Dag geleden

      Have you watched the entire video?

  57. mwilliams6464
    mwilliams6464
    Dag geleden

    I'll bet the guy who thought up this problem solved it, he just couldn't fit the solution in the margin.

  58. Damien Butts
    Damien Butts
    Dag geleden

    What is the objective in this video?

  59. Tri Dave
    Tri Dave
    Dag geleden

    I saw a special Andrew Wiles* about who solved Fermat's Last Theorem. People had warned him that working on it wasn't real math, the solution did so much to advance math it was far from a waste time. *Thanks for the correction magicmulder

    1. magicmulder
      magicmulder
      Dag geleden

      @Tri Dave Fermat's proof was very very likely wrong. It's highly unlikely an "elegant" proof has evaded people for 300 years (although I know of one modern case where a proof took 30 years and it was a few lines and super easy to understand).

    2. Tri Dave
      Tri Dave
      Dag geleden

      @magicmulder thanks for the name fix, yes that was my point. It used so much modern math (all way beyond my comprehension) we still don't know how or if Fermat had an actual proof but it wasn't a waste of time or not 'real' math as Wiles had been told early on his career. Who knows what will be unraveled when someone finally figures this one out.

    3. magicmulder
      magicmulder
      Dag geleden

      *Wiles Also Wiles and Taylor effectively proved a lot more than just a curious riddle from 300 years ago. Proving the Taniyama-Shimura conjecture was a lot more important to mathematics than that.

  60. TOP GAMER SITES
    TOP GAMER SITES
    Dag geleden

    3x+1=10

  61. Data
    Data
    Dag geleden

    It always confuses me when someone calls something a problem but does not describe what you achieve by solving it.

    1. magicmulder
      magicmulder
      Dag geleden

      We do not yet know, but solving it may yield lots of knowledge on the way, just like Fermat’s Last Theorem.

  62. _
    _
    Dag geleden

    My question is, why are we picking a random number and applying 3x + 1 to it? Then adding different rules based of even or odd? That is why it doesn't work.?

    1. Релёкс84
      Релёкс84
      Dag geleden

      @_ It's more than random numbers: this is actually the simplest variation of the problem (i.e. with the smallest numbers) where the solution is not known. For things like 2x+1, 1x+1 etc the behavior is fully predictable for any number.

    2. _
      _
      Dag geleden

      @Релёкс84 so its just random numbers somebody has picked that dont have a solution.

    3. Релёкс84
      Релёкс84
      Dag geleden

      it's just how the rules are defined. You can absolutely choose a different set of rules if you want, but that would make it a different problem.

  63. MrVipitis
    MrVipitis
    Dag geleden

    I think there are beautiful growing trees that start at 1 instead of any number and go down.

  64. Chris Hansler
    Chris Hansler
    Dag geleden

    Put a decimal in the mix because nothing is a whole and problem solved.

  65. Nate AAiel
    Nate AAiel
    Dag geleden

    So this is why Charles Xavier went bald.

  66. Xolo
    Xolo
    Dag geleden

    how is this a question tho? so assuming an answer was discovered what could it look like?

    1. Релёкс84
      Релёкс84
      Dag geleden

      The question is "Do all numbers eventually fall back to one?" and the answer is either "Yes" or "No". But to give a definite answer you'd need a proof behind it, and that's where it becomes hard. The problem itself is super easy to understand, but practically impossible to solve with current knowledge.

  67. Gold MSP
    Gold MSP
    Dag geleden

    It´s not a problem though, it´s a simple fact. There is no solution. It´s a dumb question. Some questions don´t have answers. You´re always going to reach 1 if you use division of even, positive integers, because it´s the first positive integer, and even numbers are unavoidable using this sequence. No? What am I missing, I´m 17 and no mathematician so I have to be missing something big lmao pls someone tell me

  68. Goto M
    Goto M
    Dag geleden

    Meh; it's like one of those tricks about how to find your age. The simple fact is that the equation has gravity. Two rules that lead any number to move in one direction. Down.

  69. LGE
    LGE
    Dag geleden

    thx brillant

  70. la6beats
    la6beats
    Dag geleden

    Does it work with irrational numbers going by if the last digit is even or odd?

    1. la6beats
      la6beats
      Dag geleden

      @Релёкс84 my brain was afk that moment my bad

    2. Релёкс84
      Релёкс84
      Dag geleden

      There is no "last digit" for an irrational number.

  71. Hover Daily
    Hover Daily
    Dag geleden

    I theorize that the answer or more practically the way to "avoid" this problem lies with people or more specifically, psychology. Though sounding ironic try thinking of it with births and deaths. Theoretically it can be used more in 'living' applications.

  72. adrian th
    adrian th
    2 dagen geleden

    12:35I thought it was real😂

  73. Ag64
    Ag64
    2 dagen geleden

    have they tried decimals

  74. Lazy Turtle
    Lazy Turtle
    2 dagen geleden

    Please read this. Hello NLrock comments I'm from Bosnia and Herzegovina so my writing in English will be bad. I know that this is not a place to ask for help but I feel like I don't have other choice. Let me explain, I'm born here in Bosnia in 1992 in a middle of war. In that war my family lost alot and I was 60 days old when I lost my father. So growing without a man to explain you alot of thing's which mother can't was harsh especially in this country where everyone is corrupt. But I did it. I think that I have grown in a solid man. After scool I got a solid job got a wife and we got 2 beautiful boys. So I had to take a loan to buy a home for us to live in and it was fine until October 2018 when I was diagnosed with diabetes then alot of changes I had to make in my life so I could be healthy and support my family. With diabetes came another sicnes I don't how to call it in English (I have to much fat in blood) and thanks God insuline is free here in Bosnia so it was not a big deal I had to spend only about 17 dollars on some pills every 15 days. Now in 2021 I got 3 heart attacks no one does not know how I made it alive but I did. The reason for heart failure is diabetis it stuck some veins and heart could not pump blood. Now the reason why I'm writing all of this is with all of this and alot of things happening to me in my journey tru life I'm in depression I have no idea what to do and how to help my family. I don't see an exit and I don't want to beg on the streets and my Country does not give a damn about me and 95% of other people here. The reason I'm searching for help is because wih heart like mine and diabetes I can't work and bring money home. We stil have 9 years of loan left. Since I'm not working now and I have to give 380 km to bank and my wife makes 500 km evry month then the medications are 120 km for me. We cannot afford nothing more. And we need to pay bills and bring food home. The reason I'm gona ask you guys to somehow help me if possible are the kids i can't explain how hard I'm feeling because I can't afford nothing to them and one of them will need to go in school next year. And I can't afford him a damn pen. I don't know what to do so I came here to ask for help. Thanks. Wish you all the best ❤️

  75. GOBSTOPPA
    GOBSTOPPA
    2 dagen geleden

    titactoe for grownups.

  76. EUREKA! I have found it
    EUREKA! I have found it
    2 dagen geleden

    If u wanna have a career lol Stop watching such problems

  77. DJZofPCB
    DJZofPCB
    2 dagen geleden

    4x+2, two rules if it's odd multiply by 8, if even divide by 3.... yay I made a problem

  78. KARL Shipley
    KARL Shipley
    2 dagen geleden

    3 6 9

  79. Renee Tin
    Renee Tin
    2 dagen geleden

    Is there anyone know why the geometric mean at 8'37'' is calculated as in the video >.

  80. Ronnie
    Ronnie
    2 dagen geleden

    This is the math problem that made the Unabomber go crazy lol.

  81. Johnson DMG
    Johnson DMG
    2 dagen geleden

    Maybe with modern supercomputers we could solve those mistery problems.

  82. Blue
    Blue
    2 dagen geleden

    Just like history if u know what i mean

  83. Turki Kaboha
    Turki Kaboha
    2 dagen geleden

    Easy. 28

  84. Alex De Silva
    Alex De Silva
    2 dagen geleden

    I hate maths

  85. Enru
    Enru
    2 dagen geleden

    No degree here, high-school dropout. But I have a question/theory If you could somehow simulate this with a form of energy, like say a more commonly known one, electricity, couldn't you come up with a formula for infinite energy?

  86. Kiralea Swan
    Kiralea Swan
    2 dagen geleden

    you don't have to brut force all numbers to one you only have to get them down or up to a number that leads to one. but the time it takes to show that one doesn't lead to one. AAAAAAAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHH I hate this thanks

  87. Jacob Wansleeben
    Jacob Wansleeben
    2 dagen geleden

    An idea that was not brought up in this video would be to instead of proving that any positive integer, when these two rules are applied to it, eventually ends at one, instead try to prove that you can start at one and apply the two rules in reverse to reach any positive integer. Start at one and keep applying the x2 rule, you can also apply the (-1)/3 rule whenever you want, but only if this results in a positive integer. Show that by doing this, you can reach any positive integer.

    1. J Modified
      J Modified
      2 dagen geleden

      While that is somewhat faster at first, it requires a lot of memory since you need to track all the numbers encountered. Testing in order requires almost no memory. To forward-test 2^68 numbers, you'd need a memory chip the size of our solar system.

  88. David Rice
    David Rice
    2 dagen geleden

    Vain foolishness.

    1. Luis
      Luis
      Dag geleden

      Says the guy commenting on a computer that was once considered vain foolishness. Grow up.

  89. Wowwwwwwzer
    Wowwwwwwzer
    2 dagen geleden

    18:22 "It's very hard to prove a theorem that's false."

    1. Релёкс84
      Релёкс84
      Dag geleden

      @J Modified The intended meaning of the citation is that you'll have a really hard time proving a statement if that stamement is actually incorrect.

    2. J Modified
      J Modified
      2 dagen geleden

      Which makes no sense. You could always state the Collatz conjecture as its negation. I don't see any reason to prefer it stated one way or the other.

  90. Mordecai Gutierrez
    Mordecai Gutierrez
    2 dagen geleden

    Why can’t we just write a computer program to check these numbers?

  91. vera2laura
    vera2laura
    2 dagen geleden

    I gnow whay and the answer 🤔maybe.. You are wrong on the way you put the problem that whay 🤔??? The bigest mistake Is that zero Is missing e without that you try to do mathematic when zero Is a part of It way????without zero you can Not talk about this

    1. vera2laura
      vera2laura
      2 dagen geleden

      If you whant continuity the use It the (zero)if Not It ends like this

    2. vera2laura
      vera2laura
      2 dagen geleden

      With zero everthing change

  92. Seth Tye
    Seth Tye
    2 dagen geleden

    i have one question.......... Why do we care if its false or not?

  93. Myname MyLastname
    Myname MyLastname
    2 dagen geleden

    3x+1 is the stock market prices. That is where all the stock prices end up because that is how much they are worth.

  94. Dhiraj babu
    Dhiraj babu
    2 dagen geleden

    Solution to this I think is to wait for a bit and use a quantum computer to its highest computing powers in order to simulate lot more numbers and see if there really is a solution

    1. magicmulder
      magicmulder
      Dag geleden

      If the solution is somewhere beyond TREE(3), no quantum computer in the next billion years will help us.

  95. Grit
    Grit
    2 dagen geleden

    SCOTUS refused to acknowledge Benford's Law.

  96. Monkey8492
    Monkey8492
    2 dagen geleden

    i dont get it

  97. BAragon94534
    BAragon94534
    2 dagen geleden

    I would have thought that with the advent of super computers which can do calculations so fast, that we would have been able to see the pattern, despite the seeming chaos, and prove one way or the other.

  98. AnimeWeirdoUwU
    AnimeWeirdoUwU
    2 dagen geleden

    Haven't watched, 8 th grade. I say 4x