Math Has a Fatal Flaw

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    Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. 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. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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    References:

    Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. - ve42.co/Dunham2013

    Conway, J. (1970). The game of life. Scientific American, 223(4), 4. - ve42.co/Conway1970

    Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. - ve42.co/Churchill2019

    Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. - ve42.co/Gaifman2006

    Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky-in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. - ve42.co/Lnrt2010

    Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. - ve42.co/Poincare

    Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. - ve42.co/Irvine1995

    Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. - ve42.co/Godel1931

    Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. - ve42.co/Russel1910

    Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. - ve42.co/Godel1986

    Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. - ve42.co/Cubitt2015

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    Special thanks to Patreon supporters: 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, Adam Becker and Jonny Hyman
    Animation by Fabio Albertelli, Jakub Misiek, Iván Tello and Jonny Hyman
    Math City Animation by Another Angle 3D Visuals (www.anotherangle.ee)
    Filmed by Derek Muller and Raquel Nuno
    Edited by Derek Muller
    Music and SFX by Jonny Hyman Additional Music from Epidemic Sound
    Additional video supplied by Getty Images
    Thumbnail by Geoff Barrett
    Associate Producers: Petr Lebedev and Emily Zhang

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    Julkaistu 2 kuukautta sitten

    Kommentteja

    1. Avoyt

      I'm more mind-blown that airline ticket prices are turing complete. Like.....how?? EDIT: I take it back, the game of game of life got me

    2. Kevin G

      I'm usually good at comprehending these topics. However, I am tired and confused. Good job though, it was enjoyable to watch.

    3. Randum Boi

      6:35 can’t you just get rid of the decimal from the real numbers between 0 and 1 to get the same amount of matching numbers?

    4. tmastersat

      No this is a simulation....

    5. freggo

      The inventor if LIFE died of COVID. Let this sink in for a moment.

    6. Ruciel *

      Wasn't expecting to see mtg arena in a math video

    7. 성문규

      How do you even have perfect ads that make me want to learn more math

    8. Humanica

      Hence why i still believes in the existence of God

    9. José Santos

      😱😱😱😱😱😱😱 Self simulation was mind blowing

    10. Drew Sirry

      Love this video, and your butterfly collection

    11. ZenRhizer

      I felt like i was keeping up pretty well until the Godel numbers. Then my brain went smooth.

    12. cifusito

      Dereck is transitioning to magic

    13. Joshua Pattee

      Ok so, i know this is a VERY late response but i have a genuine question about the h machine, what exactly says that it cant print out both outcomes in the event of a paradox, or even just staggered outcomes, and it did do that, then its first outcome would be true

      1. Joshua Pattee

        Therefore making it so that the machine is still correct

    14. Coyee Jegejik

      cant the barber hire another barber and that barber shave the barber that hired him and the barber that was just hired could get shave by the barber that hired him

    15. Matt Gillard

      That statement at the end was fantastic!

    16. Alb.0

      This video really is mathematicians find problems with math and try solve them with math

    17. Scopes -

      i forgor 💀

    18. Carly Goodrich

      Though it is simply a footnote in the video, it disgusts me that even such a brilliant mind as Allen Turing was not enough for the homophobic UK. In the end, all that mattered to that society was who he felt love for in his own privacy and was driven to suicide. Today, the internet, accessed via machines, provides many safe spaces to people who identify as LGBT. Spaces where people feel safe to come out and explore themselves. And the world becomes progressively more and more welcoming to us. Turing's legacy is the incredible technology we use every single day, so normalized that it doesn't even register. But among that, his legacy is also creating the tools so people like him can be themselves with hopes they will not suffer the same fate as him.

    19. Satan

      Solve: 3x+1=? 0÷0=? If johnny has 3 melons but the train didn't arrive until 7AM what is the key answer to finding the meaning of life?

      1. ZenRhizer

        The last question depends entirely on the ripeness of the melons.

    20. Jeremiah Peter

      Well the only way I see it all is that we will not know what we're not supposed to... And that the human mind can only handle certain rigid sets of comprehensions and not everything... Einstein endeavoured to find the equation to well... Everything... And died in vain... Newton suffered a term of mental breakdown... But Hilbert's was worser for I think the drive to want to know it all and knowing it all is a must that disintegrated him at the end🤷... And for some weird reason the card findings ended with the letter G ... Well it's a good time to reflect... On what and who we really are... Take a look at the zygote... You'd see that Hilbert was wrong in we will know and we must know... It's a kind of tech beyond the human mind... As I say human thoughts can't go beyond the egg... Just the egg apart from the infinite amount of creations out there that are incomprehensible thus we humans do not have the answers to in the first place... And in closure I say that the letter G could also spell God 🙏✌️🇲🇾

    21. Niels Niels

      That was a great video

    22. luke murphy

      If you think in the 4th dimension paradox don’t really exist because it’s true and untrue all at the same time and since math is a universal representation of reality it has to work in all dimensions even if it means we won’t get a “correct” explanation in our 3 dimensions, the thing is if we spend all day taking into account a 4th dimension most people can’t even comprehend let alone experience we’ll spend our life thinking about we won’t get anywhere

    23. MrLeeson660

      I wish I was smart enough to understand this stuff

    24. Aracoixo

      👍🏻 💯

    25. Dominik Schmidt

      Best video I have seen on FIblock!

    26. SavBeeing

      F

    27. Nokta

      I've just been nodding through this for the past 30 mins without really understanding a thing. All I got is that we got computers out of it, so I'm cool.

    28. Fredrick Mervin

      I can tell where my life is leading right now. I watched the whole video not understanding one thing he was trying to make me understand smh fml ....

    29. Ike Darien Nweke

      12:55 :O

    30. Ryan Mitchum

      The supposition that you can complete those infinite lists in the first place is impossible. You can't go on to step 2 without completing step 1. Therefore, claiming to be able to generate a unique number outside the scope of infinity is a logical fallacy. Cantor's "diagonalization proof" is proof of nothing. And, self-referencing breaks reality. With or without math. It's poetic nonsense and shouldn't be used to prove or disprove anything.

    31. pondrthis1

      17:00 ish Prime factorization for developing permutation indices is so obvious and yet so weird to me, for some reason.

    32. Oliver Von arx

      Fascinating. The micro-makro repetition the machine showed at the end - great. And it’s really well explained although this was hard at the border of my grasp tbh.👌

    33. Geof Budhu

      The gaping hallway arthroscopically scatter because trouble embryologically train including a boiling mind. supreme, dear ptarmigan

    34. Matt Mike

      “There is no proof for the statement with the Gödel number ℊ” is just an arbitrary statement, having nothing to do with mathematics. You take α sentence that does not have α mathematical solution, assign it α number, then throw it into α mathematical system, of course it doesn’t make sense. That doesn’t create α hole in the system, just α piece that isn’t supposed to fit. Like α pretzel in α bag of Cheez-Its. Am 𐊦 missing something?

    35. The Old Blood

      It.would be pretty hard to prove considering the largest number continuously getting bigger and bigger. So would the twin primes keep going infinitely? Or would they stop at some number we don't even know yet? Maybe. Maybe not. Maybe you could prove something like that and I'm just wrong. But thats why I would say it's impossible to prove. But again I really don't know

    36. Iftikhar Khan

      10 years back i code this problem in C.. input were very small. max was 10X10 but rule were same.

    37. Michael Klas

      Fatally brilliant! 👍👍😎

    38. Truerellik

      The flaw of Mathematics is aligned with the flaws of Language and Communication itself, which is: It is not singularly originated, but an attempt to understand and be understood by what is Infinite and Eternal.

    39. Bryan Andrews

      This is actually a kind of silly problem, just make an exception set the rule. Kinda like how 2 is the only even prime number.

    40. Boatie McBoatface

      Lol plane tickets

    41. Pratham Lokhande

      Infinities are weirdest !!

    42. Pratham Lokhande

      @veritasium I would like to meet you personally ,please !!!

    43. Pratham Lokhande

      It's sad to here that greatest humans ever lived ended up suiciding 😕

    44. Paul M

      Math has a fatal flaw - correct there's meant to be an s at the end!

    45. Mame bousso Thiam

      I wish I understood this

    46. David Heier

      joke's on you. I just watched this video again reflected through a mirror, which means I was not watching it on a device that stems from Hilbert's and Turing's contributions, but rather on a device that predates them both

    47. MaxPhallus

      I'm not sure I understand the godel card which causes a problem. Because in order for the card to exist, it's godel number must exists, which encodes the cards which prove it. So the proof can't exist, which means the card itself can't exist because it is referencing the non existing proof. So surely all it proves is that the question isn't valid.

    48. Drink some milk

      existing

    49. Aaron Michael

      Lol that guy died of being obese not of covid.

    50. Emi Kikuno

      But what if the barber is a woman?

    51. mike

      I fail to see why the numerical proof system was needed to show the paradox in "This statement can't be proven by this system."

    52. Calming Chaos

      Goosebumps when you revealed the Game of life simulating itself 🤯🤯🤯

    53. roddycake16

      2:32 what is the background music here? Does anyone know?

    54. lasa nyan

      As a computer science student who has gained some acquaintance with these concepts, I absolutely love this video! It's a great way to invoke interest in theoretical computer science!

    55. Davester523

      Was tired so at first I thought it said “meth has a fatal flaw”

      1. Corvo Shield

        Yeah, its too expensive.

    56. Serberian

      I can understand EVERYTHING here except ONE thing. Did the damn barber shave himself or not? pt2 required.

    57. Bart Venken

      It's not a flaw. Nor is it fatal.

    58. Balan Cristian

      phfffff...XDD......you really want the answer? MATH IS FINITE, IT STARTS FORM 0 AND IT ENDS TO 9, EVERYTHING ELSE IT'S A LOOP ( think about when you draw a circle you start from point 0 and when the circle it's complete, it ends to point 9, after that it's repeated point 10 to point 19, etc.)

      1. Balan Cristian

        @Релёкс84 actually you should loop it around for 1001 times. brilliant isn't it?

      2. Релёкс84

        Next time I owe you $1001 I'll give you $1 and tell you to loop it around.

    59. Andrii Volkov

      So... is math what it is or is it what we found it to be?

    60. Ida Oluoch

      if there are true statements that cannot be proven then the fact that God exists must be a true statement that cannot be proven.

    61. Carl Chester Ragudo

      I've watched your videos for quite a while now and this is by far the best work you've done so far! Great job!

    62. Tina Melaku

      “There will always be true statements that cannot be proven” for all my skeptic friends who say they don’t believe in God without prove.

    63. Abdulrahman Abdo

      he speaks fondly of those German and European "Scientists" and about their "extraordinary discoveries", But when a scientist with an Asian name comes up, he just calls him a "mathematician". It is disgusting to see such things, trying to make people believe that Europe's position of power and wealth was all because of their intelligence, hardwork and education, when we all know that it was by means of force, war and slavery. If you weren't aware of this, then please check for the scientists who actually were the first to make these discoveries, and if you already knew about all this, then I hope you burn in hell.

    64. vorsv kings

      then no math pls deleted it from syllabas

    65. scott s

      Turing did not "invent the computer". Turing did not "lead the team".

    66. Form Melon

      I don't think math will ever reach any pure truth like physics or chemistry. All notation, theories and symbols will never be able to truly describe the intricacies of the world accurately.

    67. Eden Spijker

      6:00 maybe I'm stupid but if 9 goes back to 8 and goes back to 9 because you add 1 then eventually the real number wil just oscillate between 8 and 9 right? Sry for bad English

    68. joseph keller

      The sulky lunge gully skip because tights regionally tap below a big ocean. cooing, possible rabbit

    69. loretta mackey

      The blue pound psychophysically occur because step connolly mug besides a ethereal employee. poor, aware pastry

    70. Zeff Malchazeen

      I did not know math is philosophical, and I'm an engineer

    71. Amit Rana

      The loving division ophthalmoscopically decide because celsius beautifully intend underneath a plucky acoustic. entertaining, weak india

    72. ChillerHR

      this was fantastic

    73. Intlock

      ALAN TURING WAS GAY?

    74. salt tectonics

      Mathematicians 🤝 philosophers Giving peeps existential crisis

    75. Super Pokemon

      David Hilbert: "We must know, we will know" Derek Muller: "The truth is, we don't know, and sometimes, we can't know"

    76. Treadingwater85

      I understood about 40% of this video, still loved it.

    77. spartalives

      I donno I see a glaring issue with referring the self and then not being able to solve the problem because the system is stuck in a loop that is inevitable because a loop was the start of the system querying.

    78. spartalives

      So… the pot thinking about its self and can’t decide if it is or not because it thinking about it self

    79. Nominis Imperium

      everything you say depends upon how you define the words you use to say it. These definitions are by definition unstable, and therefore you can never fully know the exact meaning of what was said, unless you deny all instability of definition or interpretation or usage, which all change according to need, subject, experience, and intention, so you ultimately cannot fully know what journey meanings will take. I wish anyone good luck trying to know answers in advance of their calculation and expression. They are by nature out our control, as is the entire concept of stable, complete, pure and truthful Mathematics. But without mystery, there is surely only death, no colour and no sound.

    80. lord_ne

      17:50 Wouldn't it be easier to just have the Gödel number of a sentence be the concatenation of the symbols that make it up as digits in base + 1?

      1. lord_ne

        @Paul Mahoney That is blatantly false

      2. Paul Mahoney

        @lord_ne Maybe, but the usage of prime numbers is the only thing in any system that can absolutely guarantee a unique set of numbers.

      3. lord_ne

        @Paul Mahoney But that's the point, we express them in base + 1. So there are no single-symbol cards in the double digits.

      4. Paul Mahoney

        @lord_ne Because there are base cards in the double digits. If the last two digits of a number are 14, does that refer to cards one and three, or card 13?

      5. lord_ne

        @Paul Mahoney But how could they possibly concatenate to the same number if each card is a single digit in base + 1 ?

    81. Daniil Dimitrov

      So 1 is equal to 2?

    82. Cedrick Honeycutt

      The neat refund analogously stare because giraffe phenomenologically flower worth a judicious meeting. hushed, cultured bill

    83. Derek A

      Yeah, it's made up.

    84. alggazteca

      Bravo! What a nice presentation! Thank you, from the bottom of my heart, before someone discovers that there is a hole there!. You really know how to make understandable the unintelligible. Congrats!

    85. BostonBlues

      21:00 this had me in a mental pretzel lmao 🤣

    86. sivalley

      This video is Turing Complete; it halted at the end.

    87. Valics

      Is this why there are always gonna be bugs in the programs ?

    88. Justin D'Antonio

      Can you please do an episode on whether quantum computers have capabilities beyond a Turing machine? Perhaps it's an easy answer...

    89. Conscious Freshness

      Countable infinites.....lol nah

    90. Snorlox

      it seems like the godel number g is only a paradox of "if it's true it's false, if it's false it's true" because it was given the godel number of g. but i guess eventually, if godel numbers are infnite, there would be a godel number just like it eventually. idk my brain is trying to understand lol

    91. Conscious Freshness

      There is no such thing as something true you can't prove....

      1. Andre

        There is.

    92. Snorlox

      when i look up godel numbers, i unfortunately get some charts that show the same godel number meaning 2 different things.

    93. Jiří Guth Jarkovský

      Oh wow, nice to see the article by Tony Cubitt, David Perez Garcia and Michael Wolf here!

    94. Griffin Barnes

      Im, sorry, I know this sounds a bit arrogent. But for the diagnalization proof. If you made your list in actual order. So 1 is 0.1, 2 0.2, 3 0.3, 10 0.0 then at 11 you get 0.01. Then you do that infinitly. Could you not just make this new number, follow the new index you would get, and then find that exact number having been made. Especially if 9 rolls back to 8. If you had a number of 0.999 then you could go to get 0.888 from the diagnal which from the previous organization you know 0.888 comes far before 0.999 comes, so it is already drawn. We know if the number has 9 anywhere in a number, then if the index is organized propperly, then we can know with 100% certinty that the number made has apeared.

      1. Релёкс84

        The diagonal number you get from your list will be 0.211111... forever. The problem is that you're only listing numbers with finitely many digits, and so you're missing all real numbers with infinite digits, such as 1/3, pi/10 etc. and of course, 0.2111... as well. So everything's the same as in the video: the diagonal number is not on your list, nor are infinitely many numbers that are left out.

    95. aakla

      So "Because" doesn't count as an answer?