Numberphile v. Math: the truth about 1+2+3+...=-1/12

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  • Published on Jan 13, 2018
  • Confused 1+2+3+…=-1/12 comments originating from that infamous Numberphile video keep flooding the comment sections of my and other math TheXvidrs videos. And so I think it’s time to have another serious go at setting the record straight by having a really close look at the bizarre calculation at the center of the Numberphile video, to state clearly what is wrong with it, how to fix it, and how to reconnect it to the genuine math that the Numberphile professors had in mind originally.
    This is my second attempt at doing this topic justice. This video is partly in response to feedback that I got on my first video. What a lot of you were interested in were more details about the analytic continuation business and the strange Numberphile/Ramanujan calculations. Responding to these requests, in this video I am taking a very different approach from the first video and really go all out and don't hold back in any respect. The result is a video that is a crazy 41.44 (almost 42 :) minutes long.
    Lots of amazing maths to look forward to: non-standard summation methods for divergent series, the eta function a very well-behaved sister of the zeta function, the gist of analytic continuation in simple words, etc.
    The original Numberphile video is here
    thexvid.com/video/w-I6XTVZXww/video.html . Also check out the links to further related Numberphile videos and write-ups in the description of that video.
    Here is a link to Ramanujan’s notebook that contains his Numberphile-like 1+2+3+… = -1/12 calculation. www.imsc.res.in/~rao/ramanujan/NoteBooks/NoteBook1/chapterVIII/page3.htm
    This notebook entry was also one of the starting points of my last video on this topic: thexvid.com/video/jcKRGpMiVTw/video.html
    Other good videos that deal with this strange “identity” include the following:
    thexvid.com/video/0Oazb7IWzbA/video.html (a Numberphile video featuring the mathematician Edward Frenkel who is also talking about the connection between the Riemann Zeta function and Ramanujan's crazy identity.)
    thexvid.com/video/sD0NjbwqlYw/video.html (a nice 3Blue1Brown video about visualizing the analytic continuation of the Riemann Zeta function).
    If you know some calculus and want to read up on all this, beyond what is readily available via the relevant Wiki pages and other internet resources, I recommend you read the last chapter of the book by Konrad Knopp, Theory and applications of infinite series, Dover books, 1990 (actually if you know German, read the extended version of this chapter in the 1924 (2nd) edition of the book "Theorie und Anwendung der unendlichen Reihen". The Dover book is a translation of the 4th German edition. The 5th German edition from 1964 can be found here: gdz.sub.uni-goettingen.de/id/PPN378970429).
    People usually recommend Hardy's book, Divergent series, but I'd say only look at this after you've looked at Knopp's book which I find a lot more accessible. Having said that, Hardy's book does have quite a bit of detail on how Ramanujan summation applies to the Zeta function; see chapters 13.10. and 13.17.
    The article by Terry Tao that I mentioned at the end of the video lives here: terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/
    Thank you very much to my mathematician friend Marty Ross for all his feedback on the script of this video and for being the grumpy voice in the background and Danil Dmitriev the official Mathologer translator for Russian for his subtitles.
    Enjoy :)
    Burkard
    P.S.: Here is a scan of the page from that String theory book that is shown in the Numberphile video. Note, in particular, the use of equal signs and arrows on this page. www.qedcat.com/misc/String_theory_book.jpg
    For today's maths t-shirts google: "zombie addition math t-shirt", "label your axes math t-shirt".

Comments • 5 599

  • Андрей Смирнов

    Сумма 2-х или более расходящихся рядов может к чему-нибудь и сойтись... Например к -1/12... ))))

  • Joshua Reed
    Joshua Reed 3 hours ago

    WOAH! Either your shirt can change, or you filmed this on multiple days! But filming on multiple days is preposterous! I must have your shirt that can change its graphic.

  • Joshua Reed
    Joshua Reed 3 hours ago

    15 minutes in thinking "this sure is a long video, hope it ends soon." Looks down at time, sees theres still 25 minutes left.
    This is a lecture, not a video! You tricked me into relearning my math that I worked so hard to forget!

  • Anant Kumar
    Anant Kumar 6 hours ago

    So, if this video was infinitely long, the number of annoying giggles in the background would diverge to positive infinity?

  • David Beaumont
    David Beaumont 10 hours ago

    Best visualisation of the Riemann Zeta function and analytic continuation you'll ever see: thexvid.com/video/sD0NjbwqlYw/video.html

  • Abdullah AboMuhammad
    Abdullah AboMuhammad 11 hours ago

    I only unDerstooD first half of the viDeo. anDthen my brain mal functionD

  • Rui Dias
    Rui Dias 13 hours ago

    I had just watched the numberphile video and posted a few replies along the same lines, that you cannot invert an analytical continuation (generally, at least). Ignoring all the personal rants and rudeness one sees so often, I think that these discussions are enlightening for those who have a genuine interest in maths, which includes revising previous assumptions and admitting that one can be wrong sometimes, as is built in the heart of science. It's easy to make a misstep. Thanks to Mathologer for an elegant and straight to the point explanation. And to the hard work put in it.

  • Archangel Raphael
    Archangel Raphael 15 hours ago

    now explain the meaning of your T-shirt? ...

  • wassermeister
    wassermeister 22 hours ago

    math vs physics *eats popcorn*

  • JAGADEEP J L
    JAGADEEP J L Day ago

    Ramanujan :-- The man who knew infinity.
    😍😘😘😘😘😘😘

  • domino2515
    domino2515 Day ago

    So, anyone tried their hand at calculating that super sum from ca. 23:10? Cause I can't average it out like I think it's something over 1/2 but below 3/4... Maybe like 2/3. 2/3 jumps out at me the most.. I don't know. Anyone who has a good explanation? I'm not a great mathematician but I am very interested in math.

  • Rony Khati
    Rony Khati Day ago

    So I owe my brother 1+2+3+4+5+.. dollars...should I just ask him to collect -1/12 dollars ? This is trick Math, not present in real life. Thanks!

  • Engineering Bear
    Engineering Bear 2 days ago

    23:16
    In the transition from rational to real we loose 'countability' or as Dr. Grimes from Numberphile puts it (which I also like better) 'listability'

  • Engineering Bear
    Engineering Bear 2 days ago

    I found that the 'supersum' of this 1+0-1+0-1... thing eventually converges to 1/2 after jumping between to 2/3 and 1/2, whereas the jumping up gets decreases in magnitude.
    Did I get that wrong?

  • 1234Daan4321
    1234Daan4321 2 days ago

    Infinity + 1/12 = 0

  • Roman Fedyashov
    Roman Fedyashov 2 days ago

    34:50 mixed sum order for not converging sum. if you put zeroes in the result brackets and find a difference with dzeta you won't get zero. In not coverging sums you MUST align Nth part with Nth part not Nth part with 2*Nth part as its made in the video. So the function in square bracket is not dzeta. And the next assumption of the guy is its dzeta. So the video is not correct.

  • Вячеслав Иванов

    I find I should add another idea in defence of -1/12, about counterintuitivity. Well, isn't the idea of equating of convergent infinite sums like 1/x^2 to a finite number a counterintuitive thing? What about relativity theory? Taking square roots of negatives? Come on, -1/12 is not so much worse then these. The rules to work with such series haven't been developed yet, but it is very likely the whole -1/12 thing is not wrong. So again, I don't see a firm debunk here.

  • Rashik Kalita
    Rashik Kalita 3 days ago

    Then why the summation of 1+2+3+4+5...= -1/12 is used in string theory in physics ??? Answer me

    • Mathologer
      Mathologer  3 days ago

      It's not even used in physics. That's the other thing that really needs debunking. What is true is that an incarnation of the complicated connection between 1+2+3+... and -1/12 that I talk about in this video is used in physics. It is definitely NOT true that 1+2+3+...=-1/12 is used.

  • Константин Меляйкин

    Огромнейшее спасибо за перевод.

  • Razor 1
    Razor 1 4 days ago

    Hey he didn't use 1+1-1+1-1+1-1....as g.p he has explained it in another video....

  • Cobb Butterscorn
    Cobb Butterscorn 5 days ago

    1-1+1-1+1-1... = 1/2 = 0 marks

  • Kapitan Candy
    Kapitan Candy 5 days ago

    2x=1
    x=1/2
    2x=1
    x=1-x
    x=1-1+x
    x=1-1+1-x
    x+1-1+1-1+x
    x=1-1+1-1+1-x
    x=1-1+1-1+1-1+1-1+...
    Explain how 1-1+1-1+1-... doesn't have a sum

  • Nomen Nominandum
    Nomen Nominandum 5 days ago

    Why use the zeta-function in the first place ? Couldn't there be another complex function that (when analytically continued if necessary) gives me, say 1+2+3+4+...= 42 ?

  • Ricardo Ochoa
    Ricardo Ochoa 6 days ago

    Mate, i love every t-shirt that you use in your videos, they're something hilarious.

  • edouard Bail
    edouard Bail 6 days ago +1

    except you're the one who is wrong on that case.

  • Dirk-Ulrich Heise
    Dirk-Ulrich Heise 6 days ago

    I heard about that numberphiles -1/12 thing and wondered what they did. Thanks for the explanation. They're physicists? That explains it.

  • Manuel Odabashian
    Manuel Odabashian 6 days ago

    Has the zeta function been proven?

  • Jeremy Nathan
    Jeremy Nathan 6 days ago

    I love Numberphile. But I definitely learnt more from this explanation than their 7 minute video. I mean: I appreciated the spirit of "creating the doubt". But youtube teaching is not just to provide "doubts". It is also to teach what it is rigorous in mathematics and what is not. The explanation proposed in Mathologer is really complete and clear. And if you consider the concepts behind, 40 minutes are ridiculously short! Even that, they provide a deep discussion on what is wrong in the Numberphile approach (and I am pretty sure the Numberphile professors know what it is not allowed in some of their steps). Moreover, they provide some useful insights in Z Riemann function. I think it is a good job in clarification.

  • picampicam
    picampicam 6 days ago

    In the STRICT math sense, youre right, its not -1/12.
    Also +1-1+1-1... is not 1/2, in the STRICT math sense.
    BUT, take the physical interpretations of +1-1+1-1+1-1..., it diverges from 0 to 1, than 0 than 1...
    Imagine a light bulb being switched on and off at infinite speed, what would that look like?
    It would not shine, nor be off at the same time, it would shine but weaker, dimmer, lets say at a half of its maximum luminosity.
    So, in real world it makes sense to say that +1-1+1-1+1-1...equals 1/2.
    So...,why not say that for the 1+2+3+4...=-1/12?
    It could also have its physical interpretation, its just that we cant comprehend that.
    Take the Mandela effect for example, how can you explain that with regular maths and physics?
    You cant.

    • Mathologer
      Mathologer  4 days ago +1

      Maybe consider actually watching the video? :)

  • Nishan de silva
    Nishan de silva 6 days ago

    you should cut out the sarcasm. Takes away from what you say. But I want to say your videos are very interesting.

  • Darth Drake
    Darth Drake 7 days ago

    We live in a society

  • Jabrane Amami
    Jabrane Amami 7 days ago

    numberphile is not a certified mathematical institute. you didn't need to do all this, mathematicians will know the difference.

    • Mathologer
      Mathologer  4 days ago

      This video is not aimed at mathematicians but at the millions of people won't know the difference unless someone tells them.

  • Josh Wilkinson
    Josh Wilkinson 7 days ago

    I'm really glad that I found this immediately after watching the numberphile video. Otherwise I probably would have ran my mouth about it to anyone who would listen. I learned a lot about sums, too, thanks for clearing everything up! One small suggestion though: the guy talking in the background is obnoxious and distracting. This video would much better without his input.

  • Michael Scrocca
    Michael Scrocca 8 days ago

    reminds mi of the eclipse we where taught to draw in drafting with a string two foci radius 1/2circumference circle or eclipse distance of foci mathematics language encryption coding z-ero geometry mathematics

  • Waffles With Syrup
    Waffles With Syrup 8 days ago +1

    I'm just gonna say that 1+2+3+...=-1/12 is right purely based off of the fact that questioning Ramanujan is pretty much pointless

  • Jakub Jankovec
    Jakub Jankovec 8 days ago

    For the puzzle, I got 2/3... how bad is it?

  • Green Sombrero
    Green Sombrero 9 days ago

    R+a+m+a+n+n+u+j+a+n = -1/12

  • Ondřej Karbaš
    Ondřej Karbaš 9 days ago

    Maths.. the only subject in the world you can pay attention to for forty minutes and still be entertained

  • Johnson Barnaby
    Johnson Barnaby 9 days ago

    i have a better proof
    1 + 2 + 3 + 4 +5 ....
    = 1 + (1+1) + (1+1+1) + (1+1+1+1) + (1+1+1+1+1)........
    = 1 + 1 + 1 + 1 + 1 + 1+ 1 +1 +1 +1 +1 +1 +1 +1 +1.......
    = Infinity

  • Ruben J
    Ruben J 10 days ago +1

    That yellow infinity looks like a giant bow

  • Shiny Cupcake
    Shiny Cupcake 10 days ago

    Wrong. 1/2 plus 1/4 plus 1/8 ....... does not equal one. It would never reach 1 because each denominator is greater than the last but the numerator is still one less than the denominator. This would go on to equal 0.999999999999 ..... repeating.

    • Herald of Sorath
      Herald of Sorath 8 days ago

      @Shiny Cupcake: Don't overthink it. You cannot ever finish a mile that way, that is true, but neither can you go infinitely many steps. We simply >define< an infinite sum to be equal to the limit of all its finite partial terms, that's all there really is to it.

    • Shiny Cupcake
      Shiny Cupcake 8 days ago

      Oh ok, its ok I just didn't know that if it repeats it would be equal to one. Because for example, let's say I'm walking 1 mile. First, I walk half that distance than half the remaining and then half of that. technically I would never reach that one mile. Its the same as saying 1/2 plus 2/4 plus 1/8. It would never reach that one. Can someone explain this to me?

    • Herald of Sorath
      Herald of Sorath 8 days ago

      @Shiny Cupcake:
      First of all: An infinite Sum (aka Series) is DEFINED as the limit, that its partial sums approach.
      Second: 0.999...(repeating) is exactly equal to 1. (You can easily see this, if you write 0.999... as a fraction, which is 9/9.)
      Your comment seemed to contain a lot of statements, that often spark heated 'debates', because alot of people (who usually do not know alot about maths) are very up in arms against the things I just stated, (especially the second), hence I thought you might just be a troll, trying to cause unrest (sorry for that, if you're not).

    • Shiny Cupcake
      Shiny Cupcake 9 days ago

      Why?

    • Herald of Sorath
      Herald of Sorath 9 days ago

      Please be a troll.
      Please be a troll.
      Please be a troll.
      Please be a troll.
      Please be a troll.
      Please be a troll.
      Please be a troll.

  • inox1ck
    inox1ck 10 days ago

    So the 1+2+3... clearly tends to ∞, and this shows why 1-1+1... can't be 1/2 otherwise you get s=-1/12 which is nonsense. A sum of positive numbers cannot be a negative number.
    Whatever number of terms you have (for the s1) the result will always jump between 1 and 0. ∞ is not something where you stop, so this alternates forever between 0 and 1.

  • ice spirit
    ice spirit 10 days ago

    5:32 black shirt

  • Frimchin
    Frimchin 10 days ago

    Just dont watch numberphile when james grime isnt on the thumbnail...dummies

  • mEmE sTeAlEr
    mEmE sTeAlEr 10 days ago

    This is the math professor version of a TheXvid callout.

  • Fahad bin Islam
    Fahad bin Islam 10 days ago +1

    Dear Mathologer, I tried to find the super sum of 1+0-1+0+1+0-... and I got -1/2! The first series of partial sum averages is 1, 1, 2/3, 1/2, 3/5, 2/3, 4/7, 1/2, 5/9, 3/5... The even terms form this series: 1, 2/3, 3/5, 4/7, 5/9... and the odd terms form: 1, 1/2, 2/3, 1/2, 3/5... The series of even terms converges to 1/2 and the series of odd terms also converges to 1/2. So, the super sum is 1/2 (Well, according to my calculations, which might be wrong!). I also calculated the second series of partial sum averages: 1, 1, 8/9, 19/24, 113/150, 133/180, 1051/1470, 289/420, 1909/6835... This also seems to converge to 1/2! Please point out my flaw. Thanks.

    • moo3heril
      moo3heril 7 days ago

      Check the second term of your partial sum averages. It should be (1+0)/2 = 1/2. That should get you started

  • The Dancing Vegan Atheist

    How does 1/2 plus 1/4 plus ETC. converge to 1? Thanks for any help!

    • The Dancing Vegan Atheist
      The Dancing Vegan Atheist 5 days ago

      Eliza K Yes, they say that, but I still don't know why.

    • Eliza K
      Eliza K 5 days ago

      If you keep going for a time 'infinity', they say you will get to the end some time. I think. Or the pieces will get so small, they become irrelevant compared to the whole (physics mindset)

    • The Dancing Vegan Atheist
      The Dancing Vegan Atheist 6 days ago

      I'm missing something. How does it get to the whole piece? If you add a half to a fourth to an eighth, etc., isn't there always a little bit left over?

    • Eliza K
      Eliza K 6 days ago

      Take a piece of paper. Tell yourself the length is 1. If you cut it in half, you have 1/2 on the left side. If you cut the right side in half and add it to the one on the right, you have 1/2+1/4. And so on. Eventually, if you keep going to infinity, you will have used your entire piece of paper, with length 1. I hope this simplification helps.

  • carado
    carado 11 days ago

    funny you say that while wearing a t-shirt that confuses ⇒ for =

  • Paul v
    Paul v 11 days ago

    I’ll believe whoever wins a fist fight!

  • Shrimat Kapoor
    Shrimat Kapoor 11 days ago

    After doing some real analysis, I realised Numberphile fooled me when I was naive

  • Александр Каренин

    В видео Numberphile было чисто и ясно сказано - мы считаем сумму сходящейся если сходитася среднее арифметическое i-й частичной суммы. Если обычный ряд сходится к k, то и новый сходится к k. Но некоторые расходящиеся ряды становятся сходящимися.
    Есть такая наука - топология, как говорит мой препод - наука о пределах. Так вот, типичный пример выбора других окрестностей точки -1/12 таких, что аналоги i-х частичных сумм, начиная с каког-то номера за исключением быть может конечного их числа попадают в наперёд заданную окрестность.
    Не говорю уже о том, что это используется в дзета функции римана.

  • Daniel Schuster
    Daniel Schuster 11 days ago

    I love his laugh...

  • jlh530i1
    jlh530i1 11 days ago

    the guy commenting in the background detracts from the quality of the video.

  • Some Guy
    Some Guy 11 days ago

    wouldn't the 1-1+1-1+1-1... be 0? since they're in the same term we can rearrange them to be an infintely repeat +1 and -1. so then it turns into x=[8!]-[8!]=0
    note: if I write '[8!]' It is meant to be an infinity symbol, but my phone cannot type that.

    • Eliza K
      Eliza K 6 days ago

      From what I understand, it is alternating between 0 and 1. So it depends where you 'stop' your series.

  • Abdelmoutaleb Kandil
    Abdelmoutaleb Kandil 12 days ago

    if u have 1 dollar bill + 2 +3 ....in your bank account , there is a big risk that your banker can turn your bank account into -1/12 or 0 hilarious u will get the rieman serie in the reverse page of ur bank statement
    Math is so simple so dont turn it into ridiculously complex

    • Abdelmoutaleb Kandil
      Abdelmoutaleb Kandil 11 days ago

      +Mathologer of course i did to say 1-1+1-1+1+.....+=1/2 is rubbish because the equation is either 0 or 1 cant be average

    • Mathologer
      Mathologer  12 days ago

      Math is simple? Most people would disagree with that statement. Did you actually watch the video before you wrote this?

  • Sebastian Kranzinger
    Sebastian Kranzinger 12 days ago +1

    friend: *makes a racist comment in class*
    me: 5:25

  • Azure Flash
    Azure Flash 12 days ago

    That Numberphile video made me unsubscribe from them and all other Brady channels. I don't know how anyone can propagate such insanity. It's not just an unintuitive result, it's a plainly and obviously wrong result. "Astounding result" my ass.

  • Christopher Ellis
    Christopher Ellis 13 days ago

    And onward, towards the distribution of primes

  • Russeljrjs OwlyLife
    Russeljrjs OwlyLife 13 days ago

    Not to offense anyone but this video never fail to make me sleep every night

  • Daniel Gomes Machado Junior

    FINALLY, DAMMIT FINALLY someone made sense into this BULLSHIT of -1/12. I felt outraged when I saw that video and, being Numberphile the makers of it, it made me believe that the Mathematical community actually took that for truth when obviously the statement 1+2+3...=-1/12 is its own debunk by absurdity.Thanks for the video!

  • Wilfredo Martinez
    Wilfredo Martinez 13 days ago +1

    Who cares/

  • Aaron Stone
    Aaron Stone 13 days ago +1

    it's a divergent series for the sum of first n natural numbers is n(n+1)/2 put *lim n tends to infinity* .. although it's a well known fact that sum of positive numbers yields a positive sum.

  • cngbuddah
    cngbuddah 14 days ago

    +Mathologer mannnn, way to bury the lead, last ten seconds of the video "oh btw, -1/12 is the integral between -1 and 0 of the polynomial..." So my takeaway was really numberphile was just glued up and doing algebra on higher math functions. "hey this string theory shit is really just about whiting out a few terms and who stole my can of rubber cement so i can go post this in the quad?"

  • Keisyuu O
    Keisyuu O 14 days ago

    This is really brilliant! and I love the timings that you changes your T-shirt!

  • Princeofcups Poc
    Princeofcups Poc 14 days ago +1

    The math isn't the problem. It's that people want to think that they are smarter than "truly" smart people. Also known as Dunning Kruger. In other words, "I want to feel that I am smart, so I will think about it for 5 minutes, say that known smart people are not as smart as me, and smugly walk off." US in particular has a war against intelligence. Kids are taught that no-one is less smart than anyone else, that everyone's view is valid, the average grade should be an A. effort is as important as being correct, and that everyone is a winner. No. Some people ARE "smarter" than others. There are correct answers. Words mean things. Sorry if that hurts your self esteem.

  • David Bennack
    David Bennack 14 days ago

    The camera man should keep his comments to himself.

  • Timothy T
    Timothy T 15 days ago

    Why if we put 0 in the z gunction we get a -1/2?

  • 1 subs with no videos
    1 subs with no videos 15 days ago +1

    It is valid in physics. It is completely different type of math. It is comparing apples with oranges. Yes they are both food but they are different. Normally you would be right but when talking physics you are not.

    • Mathologer
      Mathologer  15 days ago +5

      It's not even valid in physics. That's the other thing that really needs debunking. What is true is that an incarnation of the complicated connection between 1+2+3+... and -1/12 that I talk about in this video is used in physics. It is definitely NOT true that 1+2+3+...=-1/12 is used.

  • JamesJoyce12
    JamesJoyce12 15 days ago

    if we double infinity then we still get infinity - let infinity = a then 2a = a and subtract a from each side then a=0 and since a = infinity then infinity = zero - owwwwwhhhhh - how mysterious is that?

  • John Coppola
    John Coppola 15 days ago

    isn't that the same answer the analytic extension of the riemann zeta function yields?

  • Aurongroove
    Aurongroove 15 days ago

    This was exactly what my instinct told me when I watched the Numberphile video!

  • Vincent Lextrait
    Vincent Lextrait 15 days ago

    G. H. Hardy has indeed turned in his grave with that Numberphile video. They slipped into pre-Hardy-lack-of-rigor...

  • John Brownridge
    John Brownridge 16 days ago

    Infinity isn't a number. It's a size. You can't say a sum is equal to it. You can't use it in equations, unless, of course, you are doing equations in the system of hyperreals instead of real numbers. He uses infinity and negative infinity like they are just any old real numbers. You can't do that. I'm twelve, so don't quote me on this, and don't go too hard on me trying to prove me wrong.

  • Mr Kitrid
    Mr Kitrid 16 days ago

    So, to sum it up, if I got it all right:
    1+2+3+4+5+... = +inf
    ζ(-1) = 1+2+3+4+... = -1/12

    • Herald of Sorath
      Herald of Sorath 11 days ago

      Not quite:
      a) 1+2+3+4+5+... = +inf
      b) 1+2+3+4+5+... = -1/12
      c) 1+2+3+4+5+... = -1/12 (R)
      a) and c) are correct, b) is wrong.
      Mathologer wrote the relation "a = b (R)" as "a =S b" (with the S above the "="-symbol).
      Note, that the "="-symbol in c) does NOT represent the equality relation, as denoted by the (R) slapped behind the result. (or again, in this video's case, the S slapped above the "=").

  • Bibula Fluency Joy J
    Bibula Fluency Joy J 16 days ago

    The physicists were right...the camera guy uploaded what he understood from the video he edited stuff and highly misrepresented it. It's a way of making sense of the sum

  • ManuJulianShulian
    ManuJulianShulian 16 days ago

    You say that the properties of finite sums are applicable to all infinite convergent sums but that's not really true, is it? You should distinguish between conditional and unconditional convergence.

    • Mathologer
      Mathologer  16 days ago

      Listen to what exactly I say :)

  • Danish Kamaal
    Danish Kamaal 16 days ago

    That last part. You really left me sleepless there.

  • alex tworkowski
    alex tworkowski 16 days ago

    They're all going nuts on MindYourDecisions with What Is 60÷5(7-5) = ? The Viral Problem Everyone Is Arguing About. Can you settle some of this?

  • Wai Shing Tseung
    Wai Shing Tseung 16 days ago

    all, i am know why numberphile is wrong

  • Wai Shing Tseung
    Wai Shing Tseung 16 days ago

    0.5+0.25+0.125+0.0625+0.03125+…=1,*1+2+3+4+5+6+…=○○

  • angenogu
    angenogu 16 days ago

    ''What if it was possible to define a super sum'' -> *T-Shirt evolves to a Super T-Shirt*

  • Pilletta Doinswartsh
    Pilletta Doinswartsh 17 days ago

    I have only one question. why are you staring at my chin?

  • Jens Philip Höhmann
    Jens Philip Höhmann 17 days ago

    18:50ff The 2nd series? I think it's rather a sequence.

  • Alexis Ramis
    Alexis Ramis 17 days ago +1

    Dr. Zola sounds pissed in the background

  • Alf Lacis
    Alf Lacis 18 days ago

    I noticed at 11:37 he give the "proper" European thumb+two fingers sign for three, which given wrongly in the Western way, started the shootout in "Inglourious Basterds".

  • Vojtěch Sedlický
    Vojtěch Sedlický 18 days ago

    What is it good for in real life? Like the everyday life? Just for fun? I get the proof, but i cant see any reason to bother with this - except long winter evenings and nothing else to do with your life...

    • Vojtěch Sedlický
      Vojtěch Sedlický 17 days ago

      +Mathologer Well, that sums it up, thanks.
      And to be honest, I was just curious, what could it be used for. Theories are fine example.
      I am happy that it does not have anything to do with common logic/sense (not the Math logic, btw...) :)

    • Mathologer
      Mathologer  18 days ago +1

      Doesn't have any direct applications to flipping burgers I think :) Having said that this particular piece of high level math the complicated meaningful connection between 1+2+3+... and -1/12 is used in physics to explain the so-called Casimir force, maybe google this. Also quite a few of the summation methods that I an talking about in this video, e.g. Cesaro summation are very important when it comes to making sense of weird physical phenomena that engineers deal with (Fourier analyisis).

  • yash bhinwal
    yash bhinwal 18 days ago

    Then why this result is used in string theory?.??????????????

    • Mathologer
      Mathologer  18 days ago

      Sigh, please check through the comments. That nonsense is worth another debunking video :)

  • n5sdm
    n5sdm 19 days ago

    Fail.

  • bonnome2
    bonnome2 19 days ago

    Well, can you explain the Casimir effect that uses the zeta(-3) does lead to the correct answer?

    • Mathologer
      Mathologer  18 days ago

      Sure I can explain how the connection between -1/12 and 1+2+3+... that this video is about shows up in the Casimir effect. However, since that also involves a crash course in a pretty esoteric branch of theoretical physics, the result would be a video that is even more challenging than this one. Are you ready for a 60 minute video? :)

  • LordFvckingHorst
    LordFvckingHorst 19 days ago

    To be frank, I never understood advanced mathematics. I got good grades on my university examns simply by memorizing how to use certain formulas, which - as we all know - is a great way to understand exactly nothing of what you are doing. And yes, I didn't know what Numberphiles tried to pull off. "Okay, we proof that 1+2+3+4+5+... = -(1/12) by substracting some random other infinite series". I don't get it, like AT ALL. How does substracting 1-1+1-1+1-1+... from 1+2+3+4+5+.... proof anything at all? It's like trying to proof that 2+2 = 5 by adding +1 to the equation. It doesn't make any sense. Or maybe it does and they just did a shitty job at explaining it (which is true either way, because they didn't explain it AT ALL).

  • tubehepa
    tubehepa 19 days ago

    Not necessarily over 6 million people, rather *views*?

  • nick hadloc
    nick hadloc 20 days ago

    "why are you the way you are?" -Michael Scott

  • Endrit Shabani
    Endrit Shabani 20 days ago

    well I am going to subscribe you make sense unless like that -1/12 shit I knew all answers were wrong but yet if the first was correct the second would be clearly wrong as if you have a series of 1,2,3,4,5,6 and if you shift for one on the right you get 1-1+1-1+1-1 but in the end is left that 6 just like 1 was alone and so on but I cant believe actually they fooled so many people with a nonsense bullshit

  • Jay
    Jay 20 days ago

    The real question is: when are you gonna release a *diss track* ? 😁

  • leonard TheReal
    leonard TheReal 20 days ago

    8:23 the answer has to be 0.999.... so neverending because it never gets to 1 it always stays below

  • Curtis Rahman
    Curtis Rahman 21 day ago

    shouldn't s - s2 = 0.25

  • ajsdoa
    ajsdoa 21 day ago

    20:00 should be + there after 7.

  • abu abdulah
    abu abdulah 21 day ago

    Your experience make maths easy to understand thanks sir

  • Desiree Disco
    Desiree Disco 22 days ago +1

    🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽 thank you. Math grad and that video bugged me