Math Has a Fatal Flaw

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  1. Patrick Gueriguian
    Patrick Gueriguian
    19 seconds ago

    the diagonal proof doesnt apply to an infinite list imo. to me thats not a proof at all but trying to apply a concept that might work in the finite realm to the infinite realm

  2. KÏd BÚddŸ
    KÏd BÚddŸ
    2 hours ago

    This was the best add for game of life I’ve ever seen

  3. Marcin
    3 hours ago

    Absolutely best science show! Thank you for inspiring us!

  4. Andrea Croci
    Andrea Croci
    4 hours ago

    One of the most interesting videos I have watched in a long time, although I have to admit I got lost in a couple of passages.

  5. Johanna Richardson
    Johanna Richardson
    6 hours ago

    The past waiter unexplainably fool because bracket immediately twist before a decorous luttuce. noiseless, holistic ghana

  6. wavingdragon
    7 hours ago

    This video shows me why there are only a few Turings in this world while the plentiful of mostly hairless apes on Earth have ignorance and violence instead.

  7. MotorsportsX
    8 hours ago

    0 doesnt exist in the real world. only in math. there is never nothing. only equilibrium.

  8. Anthony Gonzalez
    Anthony Gonzalez
    10 hours ago

    This video is really going to make me switch my major

  9. vinit sharma
    vinit sharma
    11 hours ago

    Pls explain tht how godel proved true statements can't be proven

  10. Super Pokemon
    Super Pokemon
    11 hours ago

    I'm fan of conways game of life

  11. Luka Chanadiri
    Luka Chanadiri
    11 hours ago

    I think that's where god enters the chat.

  12. Michael Lazarus
    Michael Lazarus
    12 hours ago

    Pretty sure Alonzo Church published his proof prior to Turing.

  13. Graham Fisher
    Graham Fisher
    13 hours ago

    Pre pubic Gents Barber Required. must be prepared to take early retirement. 🤔😌👍😁 🤣

  14. tachion
    15 hours ago

    Then why Odifreddi is still trying to convince us that God does not exist?

  15. Dusky Racer
    Dusky Racer
    16 hours ago

    There are infinite integers. However, if you pick any integer and its neighboring integer, there are infinite real parts between them. So between every integer there are infinite real numbers. Jesus.

    1. Moyprod
      Hour ago

      Actually also between real numbers. Pick two that are really close but not the same: x=0.00...01 and y=0.00...012. There are also infinite real numbers inbetween these, kind of freaky.

    2. Релёкс84
      16 hours ago

      Yes that's true, but that fact alone is not enough to conclude they have different cardinalities (i.e. they are infinities of different sizes).

  16. Leo
    16 hours ago

    Why didn’t you choose coloration that more people can see?

  17. Nikhil Thakur
    Nikhil Thakur
    17 hours ago

    took me 5 minutes to understand the R set line😂😂

  18. Mick Logan
    Mick Logan
    18 hours ago

    What is the pink blob below Australia on your globe, when you are holding up the Godel cards?

  19. Floki
    20 hours ago

    If are some trues that can't be proven, how we know these truths??If can't be proven we can't know it's true. We can only have a guess??like faith?? Edit: truth exists, but we don't have access to it

  20. HyperSpify
    21 hour ago

    Ah homophobia, ruining math, science, and engineering..

  21. Kevin Luo
    Kevin Luo
    22 hours ago

    10:45 Wang Hao is a chess player

  22. Jasper Rosa
    Jasper Rosa
    Day ago

    You realized math doesn't make sense. A realization we've all made

  23. Lord Trollalot
    Lord Trollalot
    Day ago

    Godel: "ill finish quick this h+ code, then i eat something... "

  24. ubaldo de badajoz
    ubaldo de badajoz
    Day ago

    Self-referent statement: "X is not X". What wisdom, so appropriate for the year 2020 (which equals the year 1984 of Orwell).

  25. Black Bird
    Black Bird
    Day ago

    6:30 im not convinced we couldn't find the same number anywhere on the list, can someone explain me please?

    1. Black Bird
      Black Bird
      Day ago

      @Релёкс84 ah thanks if it's simply defined as such then yeah sure

    2. Релёкс84
      Day ago

      It is defined as being different from every number on the list. So if it ever were on the list, it would be different from itself, which is quite impossible.

  26. M V
    M V
    Day ago

    6:36 Why does the proof concludes this as you will also get an index for this new number?

  27. talenttrading
    Day ago

    Hilbert is wrong.

  28. David
    Day ago

    my brain hurts

  29. adkr grc
    adkr grc
    Day ago

    no jocking the fatal flaw is that humans invented math, so stupid to believe that the universe all of the sudden after billions of years will just follow those rules.

  30. Anton Hanzelik
    Anton Hanzelik
    Day ago

    thank you well, much obliged

  31. Прохор Шляхтун
    Прохор Шляхтун
    Day ago

    8:00 "informal leader of the formalists" - sounds funny

  32. Necrotic Uterus
    Necrotic Uterus
    Day ago

    who wants to be a next gen parasite ?

    Day ago

    But if an axiom is unprovable, then how can we know that it is true???

  34. JCGoogle
    Day ago

    The fatal flaw of this "Math Has Fatal Flaw" video is math only has a fatal flaw when you put fatally flawed restrictions on it. For example - the barber at 9:35. The paradox comes from the set of fatally flawed rules. Why must the law say the barber can't shave himself? Most of the range in which these kinds of questions are being asked is beyond where it provides practical usage. For example Newtonian physics works within a certain range and then at some point General Relativity has to be used. Or you can make up a problem that is not answerable,.. such as,.. "Which came first the chicken or the egg?" or more specifically "which came first, the chicken or the chicken egg?" The question has a fatal flaw that restricts the answer to only two possible outcomes,... when neither is true. On an evolutionary scale, the egg obviously came before the chicken. But regarding the chicken and the chicken egg question,... the answer is they both came at the same time. The chicken evolved with the chicken egg simultaneously. This kind of metaphorically proves that if something proves to be unprovable, we just may be using the wrong tools to prove it or asking a fatally flawed question.

  35. Amine Amine
    Amine Amine
    Day ago

    Maybe contradictions are true 🤔

  36. László Tungli
    László Tungli
    Day ago

    Next possibility: Does not exists such a g. Proove: g contains g, it means, that g must be more complicatued than g. It is'nt true. Indirect proove.

  37. Beldan4
    Day ago

    and this is why people take such comfort in systems of faith. Even within the video itself, if people couldn't have faith (faith is the assurance of things hoped for, the evidence of things not seen) that one day the hole would be filled, they would go crazy thinking existence shouldn't be possible.

  38. Tamás Hercz
    Tamás Hercz
    Day ago

    So Math itself is infinite. And Math's infinity could be only proven by Math itself. So Math's biggest flaw is itself being a Self Reference Paradox.

  39. Eleanor Lim
    Eleanor Lim
    Day ago

    i come here when i'd like to get a migraine

  40. Yankosh Badal
    Yankosh Badal
    Day ago

    The statement below 👇 is false The statement above ☝️ is true

  41. Golden Eagle Arbor
    Golden Eagle Arbor
    Day ago

    Sounds like a lot of these guys could of had better lives if they hadn't of taken "show your work" a little to seriously

  42. Hamoudi
    Day ago

    "Not all infinities are the same size" 😂😂 Size means that something is finite and has dimensions to it. This statement is so wrong in itself!

  43. Hamoudi
    Day ago

    In an infinite row of numbers, you cannot know for certain that the new number you created will not appear, how in the world one could prove of disapprove this? Nobody could write down an infinite list to begin with.

  44. John Counts
    John Counts
    Day ago

    Or there’s a third alternative to the goodle number g It’s not a number, thus it doesn’t prove anything at all other than that this guy was a tad off his rocker

  45. John Counts
    John Counts
    Day ago

    But………….if the index were made with the real numbers instead then you could make the same statement in reverse…….

  46. Astig Astig
    Astig Astig
    Day ago

    Hello, veritasium. So if 'trueness' and 'provability' are seperate, then: (While A= a statement) A can be true but can be unprovable A can be true and provable A can be false but unprovable A can be false but provable So if the statement with godel code 'g' is false, could it be that it's not a contradiction? Since if that statement is false, then it means that proving is true. Proving it as false means it's guaranteed that it's false, and there's no contradiction. Proving is proven to be true. Can anyone share some insights pls

  47. Eli C
    Eli C
    Day ago

    wait what did you use to play the game of life like that? or is it all just animation?

  48. Crypt0tagz
    Day ago

    Cool but ........ what???

  49. HLQA
    Day ago

    Godel's parents were cousins?

  50. YordanYoshi
    Day ago

    Seeing the game of life run itself honestly amazed me

  51. 유리 큐브 제왕Lord of the Glass Cube
    유리 큐브 제왕Lord of the Glass Cube
    Day ago

    God: "hehe, I remember when I was in pre-school"

  52. maruftim
    Day ago

    Prinkipia or prinsipia..?

  53. Nathan5791
    Day ago

    Hilbert - I'm gonna probably win a nobel price for this... Godel - Hold my beer while I wreck this guy's whole career!

  54. Darren A
    Darren A
    Day ago

    How the hell are there over 6K dislikes of this video? What morons.

  55. Lelsewhere Lelsewhere
    Lelsewhere Lelsewhere
    2 days ago

    The whole Turing punishment is very misunderstood. Like, imagine if a person created a device that could do the 1940s equivalent of cracking nuclear launch codes. Now imagine that person keeps getting drunk, keeps picking up (very socially unacceptable) prostitutes, is continually arrested for causing disturbances with these prostitutes, and continually bailed out by his friends in government. Do you think this person can keep the device or its workings secret? Do you think that such a person could be blackmailed into giving his secret device up? Do you think this person's role in the device could be found out, and that could then be manipulated or kidnapped and forced to work with "the enemy"? That's almost literally the situation. I mean, if he just chose to live a quiet (though yes, somewhat secret and discrete) life with one gay lover, I'm 99% certain the government would have looked the other way, as they usually did with important men who were gay, even back then. Or do you think that there were no important, secretly gay (but known to the higher ups) men ever in Britain before the 1990s...

  56. Joao Caetano
    Joao Caetano
    2 days ago

    Very good video. Good work. When I was in basic school I wasn't very good. In secondary school I realised that some subject could actually help me understand, improve and do the tasks of the most ordinary routines of live. By "college" I notice that I was pretty much surrounded by knowledge and everything around me was almost cared for a different subject. Math's there too. But then a teacher had a sort of a public discussion about life and death and for a few days I had my brain wrap and immersed in all the knowledge I have learned so far. Unsurprisingly I came to the conclusion that every subject has its own development but as close that you get to the edge of it's circle the more that knowledge gets more and more mixed with the circule that is next to it. I think that this video is all about that as well. Is about the filosophy of maths. A sort of grey area between maths and filosophy. Or perhaps other subject. I always been convinced that is an area development by the best of maths but also by the ones more unsettled with the 1+1 is 2 who seek arguments in different subjects is order to support their ideas using their knowledge from another subject. It will certainly leave me unsettled for a few days.

  57. Brother Malachai
    Brother Malachai
    2 days ago

    The thing is, if our math is so incomplete and flawed, how do any of our modern equipment all? Since it's so dependent on accurate mathematics?

    1. Origami Master
      Origami Master
      Day ago

      It's more of that it was shown that there is no fundamental system of mathematics which can be complete or decidable and completeness is not provable. So, it's not that every computation in mathematics is wrong just that there are some statements that are unprovably true and that not every problem is actually solvable. It could be proven that it is not (such as the twin primes conjecture). Tbh this is what I understood from the video I could be misinterpreting.

  58. Matt C
    Matt C
    2 days ago

    Can someone please explain to me again the part when Derek says that proving the g card makes no proof? I understood everything else but i keep watching this statement and I can't seem to get it

  59. Ronnie Alacre
    Ronnie Alacre
    2 days ago

    9:55 is a meme.

  60. Jeremy Cheeseman
    Jeremy Cheeseman
    2 days ago

    Isn't the diagonalization proof wrong? It seems that in order for it to work you must get to the end of an infinitely long list, which can't happen since it is infinite in length, right?

  61. Mama Di
    Mama Di
    2 days ago

    I need to say: this video makes me cry. About math, but so touching and personal at the same time. Thanks for that.

  62. Reprint001
    2 days ago

    "This... is the game of life. Running... on the game of life." My response. "F..k". I don't know why that was my response.

  63. Truth Holder
    Truth Holder
    2 days ago

    @Veritasium, please consider doing an episode that goes through the proof of why computers use binary. In one of my college courses that was mathematics for computer science majors, we had to go through that proof. The number that came out was the natural logarithm e (2.71828). The following class when we went over the assignment those of use who came up with e (and were also confused as to how you can have a computer system that is BASE e) got our answer. He explained that e was correct, but would be impossible to physically do that. So he rounded both up and down. Hence, BASE 2 and 3 were both good number bases for computers. Few people know this because we also think of computers as using 1s and 0s, or electronically positive voltage or zero voltage (usually +5v and 0v). But there have also been tertiary chips using +1, 0 and -1. (negative voltage, 0v and a positive voltage) Thus, both are equally efficient but the industry rapidly settled on binary.

  64. Maynard Hahn
    Maynard Hahn
    2 days ago

    That does not make sense

  65. Truth Holder
    Truth Holder
    2 days ago

    When I was in a computer class back before PCs, we had to write a game of life program in FORTRAN. There's much truth out there that can't be proven by the means we know now. That's the beauty of truth. Someday we'll learn the proof, but for now, we're just not there. It's also the beauty of live (as in real life) itself. :) Also, my first degree was in mathematics. In one of my classes we had to show examples where x divided by 0 is undefined. So many people think it is infinity, but that's not always the case. I sure wish I would have saved that paper. But, after many decades, all that stuff is somewhere in a landfill.

  66. Nimish Shukla
    Nimish Shukla
    2 days ago

    Those who know how much wealth they have in bank should not stay here too long or else they might not have any brains left after trying to make sense of this maths-match here.

  67. Hiten Doshi
    Hiten Doshi
    2 days ago

    I didn't quite understand Bertrand Russell's argument about R - why if it does not contain itself then it must contain itself, and vice-versa. Can anyone explain the logic? Thanks.

  68. GriZz gamer
    GriZz gamer
    2 days ago

    I love this guy's videos.

  69. Yakubu Mshelia
    Yakubu Mshelia
    2 days ago

    I stopped understanding this video at 14:00 😂🤣

  70. Ol' Smokey
    Ol' Smokey
    2 days ago

    Math doesn't factor in chaos and consciousness probably because it can't and reality has shown time and time again to contain both.

  71. First Name Last Name
    First Name Last Name
    2 days ago

    How the hell did anyone come up with this and actually understand it. It’s so fascinating but I don’t understand it lol

  72. Blue Paint
    Blue Paint
    2 days ago

    press f for the barber

  73. LunDruid
    2 days ago

    Whenever I hear about this kind of thing, it really makes me wonder if part of the problem is that our current understanding and use of mathematics is fundamentally flawed even right down to arithmetic. But then I realize how impossible it would probably be to come up with some system of math that didn't work with arithmetic as a base, and my head ends up hurting.

  74. thefran901
    2 days ago

    Hilbert: "Math is complete." Gödel: "Well actually..." Hilbert: "Ok, fair enough, but math must be consistent." Gödel: "Ackchyually..." Hilbert: "Oh for fuck's sake, but it has to be at least decidable!" Turing: "LOL"

  75. Thefreakofthehill
    2 days ago

    As a object oriented programmer used to deal with composite objects that has references of itself, the R set blow my mind

  76. Kshitiz Gupta
    Kshitiz Gupta
    2 days ago

    Man I have seen this thrice now

  77. Priyanshu Goel
    Priyanshu Goel
    2 days ago

    This self referencing is the cause of me not understanding flipflops.

  78. Umang Ravaiya
    Umang Ravaiya
    2 days ago

    29:56 which music is this??

  79. kerry mackey
    kerry mackey
    2 days ago

    The secretive invoice optimally taste because milk lately carry unto a shocking dock. beneficial, soft retailer

  80. Andrew
    3 days ago

    Language is not a math! Car can be different pronounce and some people thinking about car call it a motor :-)

  81. 36nibs
    3 days ago

    How fortunate is it that you can apply these mathematical principles to other systems

  82. BonnetBee
    3 days ago

    A potentially stupid question: Why would you bother to create H+? Why wouldn’t you just create H and call it a day? And would the answer still be the same if you did? 🤔

  83. Nature
    3 days ago

    Why do people assume they need to count every vain of each leaf on a tree to know it's a tree? If red or green round things grow off twiggs attached to branches, it's a red or green "Apple" "tree". You do not have to count how many apples have worm holes to know it's an Apple tree, and worms like Apple too.

  84. Loruo Ditlhong
    Loruo Ditlhong
    3 days ago

    Lol just found the meaning of consciousness

  85. Gerardo Contreras
    Gerardo Contreras
    3 days ago

    I swear he makes this sound so simple but at the same time my brain cannot comprehend anything he is saying

    1. BBucky98
      3 days ago

      Me too the card part is too much

  86. Scots Diesel
    Scots Diesel
    3 days ago

    So sad about Alan Turing...❤️

  87. mohamed mada
    mohamed mada
    3 days ago

    Okay, that's the same explanation for the hotel with infinite numbers, My question is what if Cantor's"Diagonalization proof" is Wrong? What if in the set of infinite numbers there are infinite numbers with all the infinite possibilities of the diagonalization proof? I mean what if there are indeed numbers that are greater (and less) than the numbers in all indexes of all numbers with all different possibilities (antidiagonal)? Given the nature of infinity, this is a legit question. P.S I'm not trolling, I truly need an answer.

    1. Moyprod
      3 days ago

      @mohamed mada Not, it is not the same as Hilberts hotel. There you have only 1 infinity. The infinity of natural/rational/integer numbers. In Cantors diagonalization argument occur 2 infinities. One is bigger.

    2. Andre
      3 days ago

      @mohamed mada _"You didn't quite capture the essence of my question,"_ I did: Cantor was not wrong. _"I didn't say that there could be a number greater than another number in one set "_ You said: "I mean what if there are indeed numbers that are greater (and less) than the numbers in all indexes of all numbers"- There are the natural numbers. Those DEFINE the term "countable". It doesn't matter if there are other numbers. There are of course. The rational numbers for example. But those are not really more. And there are the real numbers. Those are "more". So we are already talking about this. _"My question simply is what if such a number already exists"_ There exists no such number. A number is not a set. And there is no natural number "greater than all natural numbers". _"and our list which contains infinite numbers having infinite possibilities?"_ All possibilities do not contain all real numbers in [0,1] as the proof has shown.

    3. mohamed mada
      mohamed mada
      3 days ago

      @Andre You didn't quite capture the essence of my question, I didn't say that there could be a number greater than another number in one set even though in an infinite set of numbers that could easily happen, I mean since the diagonalization proof says that in the list a different number would be created changing the index of each number increasing it by one ergo it won't belong to our list. My question simply is what if such a number already exists and our list which contains infinite numbers having infinite possibilities?

    4. Andre
      3 days ago

      _"My question is what if Cantor's"Diagonalization proof" is Wrong?"_ It is not. Next question. _"what if there are indeed numbers that are greater (and less) than the numbers in all indexes of all numbers with all different possibilities "_ A number cannot be greater than all numbers. This is trivial to prove. _"Given the nature of infinity, this is a legit question."_ No, it is not.

  88. johnnytheprick
    3 days ago

    I couldn't agree more, it's convoluted, isn't taught in ways most understand, and it doesn't olve man's greatest problem: stupidity.

  89. Alex Huggett
    Alex Huggett
    3 days ago

    This is so much better explained than everything else that it's the only one that actually says the problem how it is

  90. Justin Hamlin
    Justin Hamlin
    3 days ago


  91. Adhithyan Sreedharanarayanan
    Adhithyan Sreedharanarayanan
    3 days ago

    I have a Doubt Derek. If the Machine h has to produce some kind of output, It has to first run a code and an input for which the sequence of the output may or may not terminate. Then the machine h+ comes into play, Which implies that the sequence of the program and the input which was already coming is inverted completely which follows a loop around the machines h and h+ and I don't see why this creates a contradiction(like if the machine h gives out the output that the first inserted program and input produces a sequence that terminates. Then the not gate put inside h+ reverses the sequence and terminates it which in turn produces a inverted loop. In which the steps of procedure are inverted with respect to the steps mentioned before.)Which implies that the machine h when working in conjecture with the machine h+ never produces a stable output when it is fed with h+'s program code and the recurring input. Then I don't see why they simply assume that the machine h is impossible to make.

    1. Adhithyan Sreedharanarayanan
      Adhithyan Sreedharanarayanan
      3 days ago

      This can go in either one of two ways. 1) Either I am Stupid.2)Or You are a Genius to Understand this.

  92. 𝕲𝖆𝖇𝖗𝖎𝖊𝖑
    3 days ago

    We are immortal until the day we die

  93. Rex Dalit
    Rex Dalit
    3 days ago

    One issue here is that any "solution" for Russell's Paradox is probably translatable to a homologous "solution" for Godel's Incompleteness Theorem. My understanding is that there have been at least 3 PhDs generated in the last 100 years purporting to "solve" Russell's Paradox, in 3 different ways. Thus one (I) would expect that there are at least 3 corrective counter-theorems to Godel's Incompleteness Theorem. Hilbert might, and probably would, content himself with these, since if memory serves, these are more or less formal ways of encapsulating and manipulating Russell's Paradox. [Note that I would conjecture that homotopy theory implies there exits an (uncountable) infinity of such solutions to Russell, translatable to an infinity of solutions to Godel incompleteness. Cheer up, dead Hilbert, no need to twist in your mathematical grave; your glorious formal headstone still marks your intellectual location for would-be visitors.]

  94. One Issue Voter
    One Issue Voter
    3 days ago

    The problem with infinities is a problem of the human brain, not of mathematics. Consider : humans cannot truly understand what infinity is because our brains are finite. Stop considering infinity as a static object, and think about them more as multi-dimensional like space-time. The set of real numbers is infinite, as is the set of integers, but the real number set "grows" faster than integers. So they are both infinite but not the same size at the same point in some (newly defined) dimension.

  95. TravelBig
    3 days ago

    5:47. I think if we can get this new real number then we didn't actually write all the real numbers in the first step (we wrote all the real numbers minus one).

    1. Andre
      3 days ago

      _" then we didn't actually write all the real numbers in the first step (we wrote all the real numbers minus one)."_ And that is the reason why it is not possible and therefore there are more real numbers than natural numbers.

  96. flow_mang
    3 days ago

    Turing was essentially killed for being gay. Lot's of wonder and beauty presented in this video balanced with some dark stuff.

  97. Jayden Maree
    Jayden Maree
    3 days ago

    I love how much I hate this, but I also hate how much I love this.

  98. Grant Currin
    Grant Currin
    3 days ago

    4:06 I wonder how to search through all the comments and find out why a set of nothing is inside the set of everything?! >search:?

  99. TerrorHuhn
    3 days ago

    i'm new here.. why the heck are you explaining math in the middle of nowhere? :D

  100. Sasa Radetic
    Sasa Radetic
    3 days ago

    That is why man as a part of creation, will never be the creator god of everything.