Math Has a Fatal Flaw

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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Komentari

  1. Croldfish

    CroldfishPrije 45 minuta

    1:25 i forgor :skull:

  2. Heaven&Hell

    Heaven&HellPrije 54 minuta

    none of this can be proven to be true.. concurrent quantum states prevent this.

  3. KLEIS

    KLEISPrije sat

    Math can prove a lot of things but it can't prove life, it is coz of math is itself incomplete by knowledge of human has created, completeness or creation of all things that has life is fundamental things that it is not related by math. So math is not absolute and it is just one of many knowledge to prove something by what creation has created

  4. TheBeast

    TheBeastPrije sat

    just learned set theory for my computer science degree really interesting stuff

  5. Bijou Smith

    Bijou SmithPrije sat

    @28:20 so, the undecidability of the spectral gap property amounts to the first proof quantum physics, as we conceive it presently, does not admit reductionism? Have I got that right? That's pretty signifcant for philosophy of science, which has previously generally operated under the paradigm that science (whatever it is) is reducible _in principle_ to base physics, through obviously not always in practice. So either that's a false paradigm or quantum physics is not base.

  6. ayy lmao

    ayy lmaoPrije 4 sati

    Russell's paradox is a violation of the law of excluded middle. Ergo the law of excluded middle is wrong. Ergo superposition.

  7. Kim Tae Hwan

    Kim Tae HwanPrije 4 sati

    The voice is good though I'd never understand the contents...

  8. Afqwa

    AfqwaPrije 4 sati

    This really murders the idea that math is some kind of divine tongue bestowed upon us by the gods. Murders it in its crib by smothering it with a pillow. Why does math work . . . _uhhhh sometimes it has empirically useful results._

  9. Giap Chin

    Giap ChinPrije 6 sati

    "This is the game of life, running on the game of life." Then proceeds to slow zoom out. Wow my mind literally was blown.

  10. Andrew C. Mumm

    Andrew C. MummPrije 7 sati

    Enter quantum entanglement... a proof can be true and false at the same time until observed. And when observed, the universe splits into different realities... :D

  11. Ascot

    AscotPrije 7 sati

    Mind Blown

  12. Andrew C. Mumm

    Andrew C. MummPrije 8 sati

    The game of life animations at the start are awesome - does anyone know how they were made?

  13. Gerard Ligonde

    Gerard LigondePrije 10 sati

    The erratic canada methodologically dare because oboe endosonographically sin aboard a tall afghanistan. curious, meek broccoli

  14. enthusiasticGeek

    enthusiasticGeekPrije 10 sati

    25:57 and it vanishes in a puff of logic

  15. hieu dang

    hieu dangPrije 11 sati

    somehow i heard "godel" as "good old" for almost the entire video

  16. Babe Root

    Babe RootPrije 13 sati

    The language of God...the Creator/Designer, and mind of ALL information. The language of God...Mathematics. Amazing...isn't it? ☀️

  17. Andre

    AndrePrije 2 sati

    _"The language of God...the Creator/Designer,"_ There is no god and no creator.

  18. ayy lmao

    ayy lmaoPrije 4 sati

    More like word salad

  19. flobbie

    flobbiePrije 14 sati

    Yeah, but it is neither a flaw, nor is it fatal.

  20. flobbie

    flobbiePrije 4 minuta

    @Andre, i don't understand. There are no flaws in math. What is that even supposed to mean. Your axiomatic system may be flawed, as it is contradictory. Or your proof may be flawed as it contains errors. But there is no flaw in the general way of how somone is supposed to process language. Do some math and you will see there is no flaw.

  21. Andre

    AndrePrije 2 sati

    Not being able to prove consistency is something I would call a "flaw".

  22. Robin Collins

    Robin CollinsPrije 14 sati

    The actually ice cytologically add because brother noteworthily note an a tacit volleyball. fanatical, subdued pine

  23. darth biernot

    darth biernotPrije 15 sati

    My brain nearly exploded while watching this! People always say: "Math is logic" I personally am more comfortable with language. I speak German natively, English and French fluently but when it comes to a simple mathematic equation with a variable in it my brain goes: "system just crashed due to missing math.dll" 😆

  24. MrBizaaro

    MrBizaaroPrije 15 sati

    Excellent Video ! Feels like one of your best

  25. Jeffrey Wiegley

    Jeffrey WiegleyPrije 16 sati

    Holy crud!!!! I *finally* understand the diagonal proof after 30 years... Prof. Leonard Adelman (The 'A' in RSA) used in Gödel's Incompleteness theorem in Second Order Logic class and I blew that on the final exam. Oh... I can die happy now.

  26. Matthew Means

    Matthew MeansPrije 17 sati

    Alan Turing a story is my favorite depiction of humanity. A single human was enough to determine the difference between a world with and without Nazi Germany thru his contributions which would have otherwise plummeted us into a darker world with less insigh, yet in response to his glorious contribution to humanity, he was treated as a plague for being gay and made the other on premise of his differences that hurt no one. Humanity will respond to it's very saving with its own doom.

  27. why bread

    why breadPrije 18 sati

    This video and his “how a infinite hotel ran out of rooms” video match up I just thought about it

  28. Peter Shmain

    Peter ShmainPrije 18 sati

    Cantor's diagnolization proof is incorrect because when you use that method to think of a new number, it must then also be assigned to a new index which is just 1 more than the previous number therefore disproving infinite inequality. However, that's not to say that his ideas are incorrect. It's just that this proof doesn't completely work in this way

  29. Andre

    AndrePrije 2 sati

    _"Cantor's diagnolization proof is incorrect"_ No. _"when you use that method to think of a new number, it must then also be assigned to a new index"_ No. _"t 1 more than the previous number "_ What "previous number"? _"However, that's not to say that his ideas are incorrect."_ The idea and the proof is correct. _" It's just that this proof doesn't completely work in this way"_ It does.

  30. Michael Borisow

    Michael BorisowPrije 19 sati

    I don't know how many of all 8 million of yall are understanding this, but I'm gonna have to pause and look up stuff from this vid another ∞times before I understand anything

  31. Aymane Sghiar

    Aymane SghiarPrije 19 sati

    Best video I've watched in a looooooooong time.

  32. Anaya Barata

    Anaya BarataPrije 19 sati

    So is the fact that not all true things can be proven also unprovable?

  33. Andre

    AndrePrije 2 sati

    It is the opposite.

  34. Robin Hodson

    Robin HodsonPrije 20 sati

    But this depends upon the assumption that recursion and logic contradictions disprove systems. That's not necessarily universal, otherwise we wouldn't be capable of comprehending them. Saying "This is incomprehensible," an apparent paradox, is actually comprehensible, and thus not not invalid.

  35. costaran

    costaranPrije 20 sati

    MEGALIKE 👍

  36. James Corey

    James CoreyPrije 21 sat

    Thank you for this waste of time.

  37. Michael MAnville

    Michael MAnvillePrije 21 sat

    More like insufficient computational ability to prove true, but can never be prove false.

  38. Релёкс84

    Релёкс84Prije 21 sat

    Absolutely nothing to do with "computational ability"

  39. Boysfifa010

    Boysfifa010Prije 22 sati

    What does it say about me that i read the title as "Meth has a fatal flaw" ??

  40. Furqan Siddiqui

    Furqan SiddiquiPrije 22 sati

    That's the reason I love watching this channel. It forces me to "THINK"

  41. James White

    James WhitePrije 22 sati

    I don't know if there is truth to be found studying mathematics, but there is much beauty to behold.

  42. Jacob Alexander

    Jacob AlexanderPrije 22 sati

    Godel hurts my damn head. How would you come up with that.

  43. Prototype 81

    Prototype 81Prije 23 sati

    To say things like "always" or "we will never know" is a fallacy. This is similar to clickbait. Nobody can day for certain what can be or cant be possible in the future. That is a simple fundamental of life. So... why is this guy using terms that are incorrect?... What else is he invorrect about. Why trust this guy on anything when hes obviuosly romancing the structure.. Lame.

  44. Mr Blue

    Mr BluePrije dan

    1 + 2 = 4

  45. János TÓTH

    János TÓTHPrije dan

    Lobachevsky and Bolyai, Gauss is at most the third.

  46. kamahll goodarz

    kamahll goodarzPrije dan

    Perhaps maths really is the language of reality in so much as they are both paradoxical

  47. Solar Plexus

    Solar PlexusPrije dan

    I knew it.. Remember "Computer Code Discovered In Superstring Equations" ?

  48. Galina Zwerlein

    Galina ZwerleinPrije dan

    We don't know what we don't know.

  49. Reilly 25

    Reilly 25Prije dan

    Can you not? Math is hard already stop giving them ideas on making it harder I'm still studying just do it after I graduate ty

  50. infinite define

    infinite definePrije dan

    I don't have to know any of this. I'm richer than yall could ever be. But I only know arithmetic. Chile imma count my money now. Also I don't actually have physical money anymore

  51. Adam Keeley

    Adam KeeleyPrije dan

    There is no preferable side of the equal sign.

  52. Gleichtritt

    GleichtrittPrije dan

    Well now you have it, I am suddenly interested in math....

  53. Fat Al

    Fat AlPrije dan

    Hrhr he said "googleplex" like in google... SMART!

  54. Pieter

    PieterPrije dan

    At 17:17, where do the prime numbers come from? 2, 3 and 5. Is it just because those are the first three prime numbers, and the equation holds three elements, or is it something else?

  55. Spider-Jonah- Man

    Spider-Jonah- ManPrije dan

    It’s boring

  56. Noriaki Kakyoin

    Noriaki KakyoinPrije dan

    Somehow I understood what was going on and it facinated me even though I could never explain it myself

  57. Jesse Thomas

    Jesse ThomasPrije dan

    Trying to use math to prove math is like trying to use light to prove light. As you would say, this is a self reference. The light needs the dark to be proven. Math is part ‘logos,’ the logical foundation of all that exists. It’s part of the source of all things.

  58. Sam Re

    Sam RePrije dan

    Godel, Escher, Bach

  59. Frank Harcourt

    Frank HarcourtPrije dan

    This guy is a total moron and he has no idea why. Everything he says is crap. The universe does not work the way he says it does.

  60. James Sonke

    James SonkePrije dan

    The Barber Paradox is not a paradox. Just because something is illegal doesn't mean it's impossible to do. Just because it's illegal for the Barber to shave someone who shaves themselves doesn't change the fact that he is probably going to shave himself It's just an imperfect law. And just because each set supposedly cannot contain itself doesn't change the fact that R (itself) was made up. It exists as an idea. And ideas are infinite

  61. Zora Marslink

    Zora MarslinkPrije dan

    Infinites sort of have different sizes though, so it's not exactly obvious.

  62. Grilled Flatbread

    Grilled FlatbreadPrije dan

    This is really similar to not knowing whether you are dreaming, alive, or a simulacrum

  63. John Woodall

    John WoodallPrije dan

    Math is God. -True, yet unprovable -Consistent as far as we know -Unable to be fully understood

  64. Hedgehog3342

    Hedgehog3342Prije dan

    Math is honestly quite confusing at times. Definitely not my strong area.

  65. Adobe Reviews

    Adobe ReviewsPrije dan

    The sad salmon ipsilaterally untidy because yugoslavian genotypically switch underneath a untidy edward. boring, versed milkshake

  66. Philip Berthiaume

    Philip BerthiaumePrije dan

    I'll stick with 2 + 2 for now, thx....

  67. Jesus Shuttlesworth

    Jesus ShuttlesworthPrije dan

    Godel grief

  68. Teflon  musk

    Teflon musk Prije dan

    What a good ole number

  69. KZisNBKosplay

    KZisNBKosplayPrije dan

    Math is just a Riddle.

  70. Seth Solomon [Student]

    Seth Solomon [Student]Prije dan

    My life is a lie

  71. Tea Drinker

    Tea DrinkerPrije dan

    The set that contains everything can't contain nothing

  72. Alaa Ashraf

    Alaa AshrafPrije dan

    Wow

  73. Colby Black

    Colby BlackPrije dan

    Little “g”. Gods mathematical devil in the equation of life.

  74. San Ien Jao

    San Ien JaoPrije dan

    Very interesting yet I understood less then 50%... 🤣

  75. Daniel Methner

    Daniel MethnerPrije dan

    Georg Cantor... That was the name of my high school :D

  76. Michael Fitzgerald

    Michael FitzgeraldPrije dan

    Sounds like you need a second barber lol.

  77. Fractalator _

    Fractalator _Prije dan

    Yes, but the machine h is flawed in this situation as there is no paradox output. Even if we add the rules to h+: > if h outputs paradox then halt, > if h outputs halt then go into a loop, > if h outputs loop then create a paradox, and pass h+ into h+ as both instructions and input, h+ will just halt. If it halts, h is correct, because, to get to the point of halting, h has to detect there is a paradox. The fact that h+ has stopped does not mean that h is wrong as a paradox occurred before halting. Reasons for this: > h would be wrong to output halt as a paradox occurred before halting. > h+ will not go into an infinite loop as I have already pointed out that h would be wrong to output halt. > h+ will not create a *second* paradox because, as stated above, there is no chance of h+ entering a loop. If you then pass that h+ into h, then the output will still be paradox. Now, there is complete decidability. Btw, I'm not entirely sure if this is correct and I would be highly interested in arguments against it: "If you think that something is true, you should try as hard as you can to disprove it." - Derek Muller.

  78. Llama Vicky

    Llama VickyPrije dan

    3:20 me: you forgot about the youtube algorithm, why was this recommended to me and why am i watching it

  79. an 17121981

    an 17121981Prije dan

    Stopped watching after narrator started bs claims touring was the brains behind cracking enigma when in reality he just improved the already working system designed by rejewski, rozycki and zygalski

  80. Rakshath G. Poojary

    Rakshath G. PoojaryPrije dan

    30:05 goosebumps 🤯

  81. BOB A

    BOB APrije dan

    Since the "rules" are made up, you can't use these examples as proof of anything other than math needs rules to work (i.e. its all made up and not a naturally occurring truth).

  82. Abderrahim Benmoussa

    Abderrahim BenmoussaPrije dan

    There is something inherently limiting in the universe by itself and even more in our brains. We are not infinite, our body and brains have limits and that is probably our Turing limit. The universe limits and wether it is infinite or not (and if yes, can someone tell me how it is growing ?) Is the universe limit. I think the universe is finite but infinitely divisible like the distance between 0 and 1. But I am bad at doing maths so I can't prove it xD

  83. Nigel Siya-d

    Nigel Siya-dPrije dan

    Bravo

  84. Azizur Rahman siyam

    Azizur Rahman siyamPrije 2 dana

    the cards literally went above my head.

  85. Kenichi Sasaki

    Kenichi SasakiPrije 2 dana

    ma head HELP

  86. Андрей Иванов

    Андрей ИвановPrije 2 dana

    The set of all sets is empty. This axiom resolves all contradictions of the set theory . Because the empty set containes themself. :-)

  87. Дмитрий Косолобов

    Дмитрий КосолобовPrije sat

    @Андрей Иванов You didn't understand, it seems. What you say is wrong: the empty set is not an element of every set; what is true is that the empty set is a _subset_ of every set. This is what confuses you. If the empty set is denoted by {} and a set of elemens a,b,c is denoted by {a,b,c}, then {{}} denotes a set that contains the empty set, but the empty set {} does not contain {}.

  88. Андрей Иванов

    Андрей ИвановPrije 18 sati

    ​@Дмитрий Косолобов According to definition empty set is an element of every set without exception. So empty net contains itself by definition. I don't see reason to argue about definition. :-)

  89. Дмитрий Косолобов

    Дмитрий КосолобовPrije dan

    @Андрей Иванов The empty set cannot be the set of all sets because the empty set does not contain at least one existing set, the empty set. This means that the axiom "the set of all sets is empty" leads to a contradiction and, thus, cannot be accepted. What might confuse you is that the notion "a set A contains B" is not equivalent to "A is a superset of B": in the former case A contains an object B (be it a set or anything else), and the latter case means that all elements of B are elements of A. The set of all sets _contains_ all sets, it is not a superset of all sets.

  90. Андрей Иванов

    Андрей ИвановPrije dan

    @Дмитрий Косолобов >> The set of all sets should then contain itself. Accept that "set of all sets is empty" like axiom and all contradictions will be eliminated. Empty set is the only ordinary set. Turn on imagination. Do you remember "Сказка о рыбаке и рыбке"? :-)

  91. Дмитрий Косолобов

    Дмитрий КосолобовPrije dan

    The set of all sets should then contain itself. So, it can't be empty. A resolution could be that there are no sets at all. But we always assume that at least one set, the empty set, exists. Thus, the problem remains here.

  92. Guillaume Ohz

    Guillaume OhzPrije 2 dana

    I dont understand why you allow self reference as an axiom, in the first place. Why the barber is not a woman? Or a special citizen that has other laws.

  93. TheDeadPoet

    TheDeadPoetPrije 2 dana

    Most of us hit "Like" just for the title.

  94. John Cantu

    John CantuPrije 2 dana

    “We will never know everything with certainty”…… There you go, a true statement we can’t prove. But even that is without certainty.

  95. can_of_woopwoop

    can_of_woopwoopPrije 2 dana

    Rephrase... 'science has a fatal flaw'

  96. Asma Angel

    Asma AngelPrije 2 dana

    The lean discovery dfly spell because cauliflower reassembly measure mid a grubby gruesome target. silent, festive turkey

  97. Sure, Indubitably!

    Sure, Indubitably!Prije 2 dana

    Can't believe I see "math" and "fatal flaw" together except if the sentence is "your answer in this math equation has a fatal flaw" lol

  98. zmunk

    zmunkPrije 2 dana

    Love the MTG shoutout!

  99. El Mino

    El MinoPrije 2 dana

    Who are we? Where are we? Why are we still here?

  100. Felipe El Guapo

    Felipe El GuapoPrije 2 dana

    2nd time thru... So has it been decided? Can set theory be on an infinite loop?

  101. Araceli Perez

    Araceli PerezPrije 2 dana

    Bitches be like "bitches be like~" like they ain't like the bitch that be like, like ... bitch?

  102. Peace22

    Peace22Prije 2 dana

    It seems like common sense to me, I haven't even finished a minute of the video. I however understand that just in the most basic view, if math is to have an infinity (as it does) than there can never be an end answer to many questions. If you have box, and in that box you have 3 problems and 3 solutions that can all intertwine, you will always have 9 possibilities of a problem/solution scenario. With math, and life, there are infinite numbers and infinite possibilities. You can't put infinity into a box. That's just one example, and I'm sure as I watch more I'll understand in greater detail and more about this topic.

  103. dodiswatchbobobo

    dodiswatchboboboPrije 2 dana

    There’s a popular saying that math is the universal language. It is false. Math is the language we are attempting to translate the universe into. It is man made. We do not have words for many many things.

  104. Megananium

    MegananiumPrije 2 dana

    Surprisingly i actually understood most of this

  105. Daniel DaSilva

    Daniel DaSilvaPrije 2 dana

    Using math and theoretical equations to prove scientific law 🙄 no one is even seeing what’s really going on?

  106. Mordechai Vanunu

    Mordechai VanunuPrije 2 dana

    Maybe everything has its time and cant be solved before we get there.The questions from 500 years ago are in some ways solved now and maybe 100 years from now questions we have now will be solved by the generation at that time.And i do believe there's a limit to the human capability.Just the fact we cant even tell by 100% what happens after we decease.

  107. LiT TV

    LiT TVPrije 2 dana

    My brain hurts

  108. Iuri MC

    Iuri MCPrije 2 dana

    5:53 You said "by the end of this process" but it is clearly an infinite process...

  109. Diggensagg

    DiggensaggPrije 2 dana

    Why must the set of sets with more than 5 elements contain itself? Iam confused.

  110. Moyprod

    MoyprodPrije 2 dana

    I doesn't have to, but you can define one.