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 • 5 904

  • TheBlack Vixen
    TheBlack Vixen Day ago

    It cant be exactly +infinity tho because infinity is not a number

  • titaniumsandwedge

    There are many parents in this world who hope their children go into a STEM field. But maths of the type discussed in this video are not used in the real world. The first bridge an engineer designs using a Zeta function will be his last. If not practical and useful, what then is the value of 1+2+3...= -1/12 in our society? I think its useful function is for very smart mathematicians to devine the anomolies of our numbering system. They chuckle and say: "you don't have to feel good about this result but its found in string theory." Is it string cheeze they are referring to or string bikinis? Back to the parents: If you see your child wandering into the morass of maths as described in this video, you have a smart kid. But he is also disconnected with reality and you must snap his mind back into place if you want him in STEM. STEM is all about making things that enhance the living standards of mankind. It is not about creating unbelievable maths conundrums that have no connection with reality and then the creators chortle about it because they are the only ones that understand it. STEM students should view Maths as a toolbox: you don't have to use all the tools available; choose the ones that make sense and help you in your goal of making something that works.

  • Nico
    Nico 2 days ago

    90% likes 10% dislikes

  • A sea lion
    A sea lion 2 days ago +1

    srsly there's no drama between mathologer and numberphile, but comments.

  • counting floats
    counting floats 3 days ago

    Actually the sum = n(n+1)/2, which is not a constant and will increase forever.
    It cannot be -1/12 nor can it be infinity as infinity is not a positive/negative integer or rational or floating point number. It is simply an admission of surrender.
    Moreover there is no such a thing as a sum of infinite series, as the sum is being computed as we speak (i.e. it can never be reached ).
    There is a limit to converging sums, which is never equal to the sum, no matter how big n is.

  • counting floats
    counting floats 3 days ago

    The fatal fault is the use of +… in equations, as the construct +… is not a valid
    mathematical term. End of story.

  • Bharath danappa bilagi

    Indian ramanuja

  • PallaPonteng
    PallaPonteng 4 days ago

    sum of the terms in an in finite geometric progression: a/(1-r)
    The first sum(S1):
    1-1+.......
    A=1
    R=-1

  • Carlos Mejia
    Carlos Mejia 4 days ago

    I guess numberphile made that video on purpose to create polemic around the subject...and based on the comments their CALCULATIONS were precise....😎

  • Nole Cuber
    Nole Cuber 4 days ago

    Ok, is it equal to -1/12?????!!!

  • Amit Jha
    Amit Jha 4 days ago

    They have shown that this sum is used in string theory which is widely accepted by smart physicist.Then why did the whole community is accepting this.

  • DAVINDER SINGH
    DAVINDER SINGH 5 days ago

    What?

  • Robloxian Gamer YT
    Robloxian Gamer YT 6 days ago

    at time 5:29 he changed his shirt that means no serious stuff forward I agree before that there was some serious stuff. But anyways LOL!!!

  • François Miville
    François Miville 6 days ago

    I have a more intuitive way not to get dazzled by those three formulae : let us extend the notion of convergence to the more general case of orbit so to speak. Certain sequences converge in the same way motionless or motion-poor masses too near a planet fall, certain sequences make a rather circular trajectory like a satellite, but that orbit has a more and more definite centre as time elapses, and other ones have enough kinetic energy to go into the wide space, but as they get freer and freer the point they get further and further from is more and more definite. In the vector space of geometrical transformations of the plane or space onto itself (that can be described by 2 by 2 matrices for the plane) you have got the dilatations and the rotations, the former comprising the contractions and the expansions. There should be defined far more rigorously than I am hinting at, for the profane's intuition's sake, a homological relationship between geometrical transformations and number sequences : 1 + 2 + 3 +3 + ... as rank elapses escapes more and more definitely - 1/12. It is equal to that value, within the playfield of a very special algebra, quite in the same way some people are more determined by the other people they hate or flee rather than by those they love and join. The equal sign after sequences should be augmented with an arrow showing two heads for convergent series, showing head and tail for orbiting series, and two tails only for pure divergent.

  • Plextoy
    Plextoy 7 days ago

    В русских комментариях ошибка 36:26 - z=0 правильно z=1

  • Chunkkrink
    Chunkkrink 9 days ago

    On the first equation if u land on odd u get 0, and if land on even u get 1.... Since we dont know if the last number in infinite is even or odd its actually either 1 or 0

  • Hafeez Raza
    Hafeez Raza 9 days ago

    If u don't mind how about looking at the 1-1+1-1+1-1+1... thing as a Geometric Progression with the first term(a)=1 and the common ratio(r)= -1. Having said that we can use the formula for sum of the infinite geometric progression with r(-1). So its basically a limit not a value......

  • Ajmal Ghan
    Ajmal Ghan 9 days ago

    What about Ramanujan notebook results

  • éric tréfeu
    éric tréfeu 10 days ago

    Z= 1^x + 2^x + 3^x + 4^x + 5^x -.....
    Z*(1 - 2^(x+1)= 1^x - 2^x + 3^x - 4^x + 5^x -..... = S
    S = (1^x)/2^2 - (2^x -2.1^x)/2^3 + (3^x -3.2^x +3.1^x)/2^4 - (4^x -4.3^x +6.2^x - 4.1^x)/2^5 +..........
    1 - 2 + 3 - 4 + 5 -..... = 1/4
    Z= S/(1 - 2^(x+1))
    1 + 2 + 3 + 4 + 5 -..... = -1/12

  • Lady D
    Lady D 10 days ago

    "...Otherwise you'll burn in mathematical hell..." LMFAO!!!!!!!!!!!!

  • Mad Child
    Mad Child 10 days ago +5

    Has numberphile replied to this?

  • MaulDervish
    MaulDervish 11 days ago

    Isn't the number -1/12 from the sum of each natural number used in a proof in string theory? Perhaps they should take another look at this theory as well

    • Not Broihon
      Not Broihon 6 days ago

      No, the link between the sum of all natural numbers (→ infinity) and -1/12 is used in string theory. Look at the string theory book in the numberphile video. There's no equal sign but an arrow → indicating a link and NOT that those are equal.

  • mick mccrory
    mick mccrory 12 days ago

    The convergent series does not =1..... It = the next number just this side of 1. Dot Dot Dot means infinity, which means there is no "answer". They say nature is expressed with mathematics. Nature switches to "Quantum reality" somewhere around the Plank length, due to the "Uncertainty principle". If math is to reflect reality, it will also need to switch to "Quantum" numbers, somewhere around the Plank length. Plank discovered "Quantum" because the black body radiation problem exploded into the wrong answer unless the concept of Quantum was introduced. If Dot Dot Dot ... is on the left side of the equation, then you can never get done adding the series up, therefore you can never get to the right side of the equation.

  • Icestrike Cubing
    Icestrike Cubing 13 days ago

    It makes no sense to me that a whole lot of positive numbers add up to a negative numbers

  • trut hurts
    trut hurts 13 days ago

    I want to understand what his second shirt means, with the human figure equation. Anybody?

    • Niko Yochum
      Niko Yochum 4 days ago

      trut hurts zombie + human = 2 zombies

  • Ibrahim Farooqui
    Ibrahim Farooqui 13 days ago

    I understood everything till 16:00

  • PAUNOMOLUSCO
    PAUNOMOLUSCO 13 days ago

    I knew there was something fish on the sum of 1 -1 + 1 -1 + 1 -1 + ... being 1/2

  • Pirate's Piggy
    Pirate's Piggy 13 days ago

    20:16 talking about mistakes why is there a minus there

  • Pirate's Piggy
    Pirate's Piggy 13 days ago

    OMG guys a human made a mistake that doesn’t EVER happen

  • HereComes ThePain
    HereComes ThePain 14 days ago

    Der is doch deutsch

  • Akshaya Shanbhogue
    Akshaya Shanbhogue 14 days ago

    Are there random Ganeshas popping up in this video? Scared to watch.. Lol

  • Brian Dayton
    Brian Dayton 14 days ago

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
    en.wikipedia.org/wiki/Grandi%27s_series
    en.wikipedia.org/wiki/Summation_of_Grandi%27s_series
    en.wikipedia.org/wiki/Zeta_function_regularization
    en.wikipedia.org/wiki/Ramanujan_summation

  • Remy Pinto
    Remy Pinto 15 days ago +2

    I think people are forgetting that -1/12 has actual applications in physics and has been proven to work. The numberphile video wasn't to get you marks on your maths exam, it was to show that this method can be taken to get -1/12 even though there are actually many other ways to reach this answer that have been proven to be true for the cases they state in other videos.

    • Not Broihon
      Not Broihon 6 days ago +1

      +Edgar Nackenson That and it's not even true. As Mathologer said the "link" between -1/12 and infinity is used. Not even in quantum physics people think that the sum of all natural numbers is equal to -1/12. Can't wait for Remy to prove his thesis by naming some literature in which it's equal.

    • Edgar Nackenson
      Edgar Nackenson 8 days ago +1

      +Remy Pinto It being used in quantum physics is blatantly an argument to the exact same extent as it being used in string theory is. In other words, it's still not an argument.

    • Remy Pinto
      Remy Pinto 10 days ago

      +deez nuts it's used in quantum physics

    • Remy Pinto
      Remy Pinto 10 days ago

      +deez nuts Again I didn't state “It is used in string theory” you completely made that up again.

    • deez nuts
      deez nuts 12 days ago +3

      That’s idiotic. “It is used in string theory” is not an argument that proves anything, ever. Mathematical arguments need to be rigorous and correct. Albert Einstein himself could’ve claimed 1 and 2 add up to 5, but authority or anything for that matter do not change math. “Proving” a statement even with rigorous methods whose assumption is false is meaningless.

  • Marlos Campos
    Marlos Campos 15 days ago

    Very good! Here at the University of Brasilia, physics teachers, undergraduate students in physics, students of the master's degree in physics, etc., believe that 1 + 2 + 3 + .. = - 1/12. When I argued that there is a theory in calculus that shows that the series is divergent, everyone ignored, one of them said that it was thing of was an outdated mathematics. I realized that when we merely reproduce knowledge and do not stop to think, it is very easy to believe in anything.

  • Nonconcensusical
    Nonconcensusical 15 days ago

    Convergence and Divergence, sounded like the Mandelbrot set.
    1/2 & -1/2 = coaxial of the inertial plane.

  • Sergey Dubrov
    Sergey Dubrov 16 days ago

    The most boring math video I've seen. You are too stupid.

  • leila Oger
    leila Oger 16 days ago

    1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ... = -1/12
    0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + ... = 5/12
    0 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + ... = 23/12
    0 + 0 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + ... = 53/12
    0 + 0 + 0 + 0 + 1 + 2 + 3 + 4 + 5 + ... = 95/12
    0 + 0 + 0 + 0 + 0 + 1 + 2 + 3 + 4 + ... = 149/12

    0 + 0 + ... (k times) ... + 0 + 1 + 2 + 3 + 4 + 5 + 6 + ... = (k^2)/2 - 1/12
    where k is the number of right-shifts (i.e. number of zeros added to the left of the divergent sum)

  • Kunal Dhage
    Kunal Dhage 16 days ago

    Watch his t shirt

  • leila Oger
    leila Oger 16 days ago

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

  • Chris Blananas2
    Chris Blananas2 16 days ago

    "This is not mathematics. Don't use it. Otherwise, you will burn in mathematical hell."
    xD

  • Hallowizer
    Hallowizer 17 days ago +1

    Give the Numberphile people -1/12. They will be proud that they got a score of 1+2+3+4+5+...

  • Daniel Wilkowski
    Daniel Wilkowski 17 days ago

    Infinity is not a number, come how then that adding all numbers equal in something that's not a number?

  • zee Gh
    zee Gh 18 days ago

    Thank you for explaining. I have always doubt that video and the explanation way

  • Gurdeep Singh
    Gurdeep Singh 18 days ago

    sir i think you'r get tired, you need to refresh your mind after that you will relies, you are not Good enough to Ameliorate that formula which is made by person who is youngest member of royal society of London ever had till now. for getting views on your video your should do something on which you are good at,for sure that is not mathematics.

  • favio h.
    favio h. 19 days ago

    5:25 jajaja

  • drew laredo
    drew laredo 19 days ago

    Thank you... N-phile even says something to the effect that he's manipulating some of the mechanisms....

  • FUN VIDS
    FUN VIDS 21 day ago

    which means Great mathematician SN Ramanujan was wrong and this bald potato looking guy is right?

  • quicktastic
    quicktastic 21 day ago

    In summary: If you believe that Santa Claus really exists, the sudden appearance of presents on Christmas morning makes perfect sense. Once you get that out of your head, the more logical conclusion that mom and dad put the presents there becomes clear. You already kind of knew that, but it was a fun little fantasy for a while.

  • khizar khan
    khizar khan 22 days ago

    They literally linked the video on how you get 1/2. Watch the videos please

    • Not Broihon
      Not Broihon 14 days ago

      Yeah, only problem is that that's crap because it doesn't work with infinite sums which are nondivergent.
      Here:
      S = 1 - 1 + 1 - 1 + 1 etc.
      So S is either 1 or 0.
      This is their arithmetic "proof":
      1 - S = S
      ⇔ 1 = 2S
      ⇔ 1/2 = S
      You can't do this with a non well defined S.

  • Thok
    Thok 22 days ago

    I love the T-Shirts

  • Fragile X kivekset
    Fragile X kivekset 23 days ago

    I wish that person in the background was quiet instead of yelling out tired jokes every 2 minutes

  • Baka Ero
    Baka Ero 23 days ago

    I wanna that T-shirt!

  • Jesse W
    Jesse W 24 days ago

    This a great explanation of the flaws in the numberphile video. I think it was meant to be a bit of a math joke, not to be taken so seriously.
    Pro tip: if you have two people talking, give them each a mic, that way we can all enjoy the conversation.

  • erikmaurits
    erikmaurits 25 days ago

    M =s= 1+0-1+0+1+0-1+ ...
    M =s= 0+0+1+0-1+0+1+...
    2M =s= 1
    M =s= 1/2
    Also I've evaluated this numerically to about 1000 terms: result 1/2.
    Why should it be 0?

    • erikmaurits
      erikmaurits 14 days ago

      with the notation =s= I meant to indicate "supersum".
      instead of writing the s above the =

    • Not Broihon
      Not Broihon 14 days ago

      You can't do
      1 - s = s
      ⇔ s = 1/2
      with s being a non divergent sum.

  • Neil Rosenbaum
    Neil Rosenbaum 26 days ago

    Exploiting S= -1/12 in Theoretical Physics seems like a nice way to "get something out of nothing" or a "whole lot out of very little." Hey, The Big Bang Theory!!

  • DarkFalcon Productions

    Video is pretty good, if long, but I was not a fan of Grumpy Background Voice, who didn't seem to be making any actual contribution to the content, just kind of dissing half-heartedly.

  • migga86
    migga86 26 days ago

    I wonder why you didn't split the -1 +1... equation to two equal halfs (1+1+1+1+1... and -1-1-1-1-1...) each diverging to their respective inifity (postive and negative). So for the sum it could be said that +infinity and -infinity cancel out to zero. Which is wrong as well and could give the same sum another wrong finite value. To put it in a meme: One does not simply add infinities. There are a lot of things around with simple math making wrong proofs. My favourites are www.education.com/activity/article/Algebra_Sleuth_Proof_that_1_2/ which clearly states that 1 = 2 (using dividing by zero in the equation) and math.stackexchange.com/questions/12906/the-staircase-paradox-or-why-pi-ne4 which proves that pi = 4 (assuming something like this videos series that the infinite operation of cutting corners from a square results in a circle). Calculating with zero and infinity is dangerous if not handled properly.

  • Shane Garstig
    Shane Garstig 26 days ago

    I always knew there was something fishy about that video

  • nothing. 2
    nothing. 2 27 days ago

    1+2+3+4+5+6+7+8+10+11+12=69

  • Carl Fels
    Carl Fels 27 days ago

    In the p-adic Norm they are right

  • Easy Mathematics
    Easy Mathematics 27 days ago +1

    Hello,
    it's very sad, that you - as a professor - take another video too serious.
    Numperphile made a joke about this topic.
    And the sad thing: u know that.
    Do u really expect that they don't know what's going on? Never.
    U could wrote them an email, like:
    "Hey guys, please notice..."
    But your way is very disrespectful.
    That is not way how feedback works. U should know that.
    Greetings.

  • Richard S.
    Richard S. 28 days ago

    25:53 let's just slide *neatly*

  • Louis Cyphre
    Louis Cyphre 29 days ago

    Numberphile is much more entertaining

  • dhruv gaur
    dhruv gaur 29 days ago

    Maybe our understanding of infinity is primitive.

  • Adam D
    Adam D Month ago

    Is it just me or did his shirt change? EDIT: he changed his shirt 4 times

  • Donald Trump
    Donald Trump Month ago

    Isnt it just a thought project thing? I never thought for a second that they actually think the answer to that hypotheticall problem is-1/12. He begins by talking about string theory...

  • William Simon
    William Simon Month ago

    Can someone explain the t-shirt with two people being added together?

  • Matthew Hondrakis
    Matthew Hondrakis Month ago

    Well for the function at 27:20 you can continue it another way. Namely |x| + C. This would make it go the other direction.

    • Mathologer
      Mathologer  18 days ago

      Yes of course but that's not the point. Have another close look :)

  • swat sas
    swat sas Month ago

    The 1+2+3+....=-1/12 is a bug of nature. When God was creating Math he checked that if he assigns this series to be equal to logical infinity, Math crashes, so he said "Ahhh... Fuck,let it be to equal i dont know -1,04848483...", again math gives a crash, and God said "Fuck", and he assigned new value again and again until Math worked, and so when he came to -1/12, everything is worked.

  • SETH WHITE
    SETH WHITE Month ago +1

    A long-winded explanation, but as short-and-sweet as I can make it.
    (**SUMMARY AT THE END)

    (-1/12) isn't "equal" to the zeta function evaluated for (-1), because the zeta function is undefined at (-1). HOWEVER, plugging in (-1) to the analytical continuation of the zeta function produces an output of (-1/12). This is only possible because the zeta function, which is only defined for SOME numbers (in the complex plane), has one specific analytical continuation into the rest of the complex plane (--into the part where the original function is undefined). Since it has one specific analytical continuation -- there is only one possible output for any and every input -- the analytical continuation can be represented as another function. This new function isn't exactly "defined" at (-1) either, but within it there is ANOTHER layer of "continuation", in this case a continuation of an infinite sum beyond its normal defined inputs (specifically, a Cesàro summation).

    So, the analytical continuation of the zeta function can be represented as another function, and if you plug (-1) into this new function, using the Cesàro summation for the infinite sum within said function, it turns out you get an output of (-1/12).

    SO...

    (-1/12) is the output of the extension of a function within the extension of another function which represents a series, a series which depends on a variable for which an input of (-1) produces the sum of all natural numbers; HOWEVER, the actual function ITSELF (not its extension) is UNDEFINED at (-1), because the series it represents (the sum of an infinite set of numbers) DIVERGES when the variable within it is set to (-1) (i.e., when it becomes the sum of all natural numbers)
    .

    **ERGO, the sum of all natural numbers does not “equal” (-1/12), but rather corresponds to (-1/12), according to a function which extends beyond the realms of the very numbers we’re adding together.

  • Amp Pear
    Amp Pear Month ago

    Great video! Your explanation made a lot more sense than Numberphile's did though I don't have a Ph.D. in mathematics...

  • SUPERindian CHESS
    SUPERindian CHESS Month ago

    plz reply that is ramanujan wrong

  • Fand
    Fand Month ago

    Popcorn and hot chocolate?!

  • Andrey Stegno
    Andrey Stegno Month ago

    zeta(-1) == -1/12

  • AfternoonBaboon
    AfternoonBaboon Month ago +1

    That was the mildest and yet most smug diss video I have ever seen.

    • AfternoonBaboon
      AfternoonBaboon 27 days ago

      +Adomaster123 I'm not even going to disagree with you there...

    • Adomaster123
      Adomaster123 27 days ago

      AfternoonBaboon if you don't want nitpickery why are you even watching math videos. ”Nitpickery” is the entire field.

    • AfternoonBaboon
      AfternoonBaboon Month ago +3

      +Brian talks about Nah, I don't even think he's jealous but the felt nitpickery is just...up to eleven.

    • Brian talks about
      Brian talks about Month ago

      Super smug.... he is just jelly over the views

  • Piyush kumar
    Piyush kumar Month ago

    It's not numberphile it's S.Ramanujan who proved it 100 years ago and it is used in string theory

    • Not Broihon
      Not Broihon Month ago +1

      +Brian talks about you sound like someone trying to bring esoterism into maths. No thanks.

    • Brian talks about
      Brian talks about Month ago

      +Mathologer I can goto my local hardware store and buy a spring. And then I can hang a mass on it and watch it bounce up and down. The way I model this is by using the differential equation f=ma and I can find equations of motion for this mass on a spring. The only way I can do this is imaginary numbers.
      So yes imaginary numbers are real. They are part of our universe and are not some magic loophole used by math trolls like me. That's the first part of my argument.
      The second part is that that since we have imaginary numbers... we now have the whole complex plane to "walk" on.
      And the results of this fact is the cauchys integral formula. And this is what I did in my first video (differintegral and zeta function using bernoulli numbers) and my 4th video (the functional equation).
      I did not break any rules... even at the point where I used the geometric series... all terms were less then one.
      It seems that the complex planes gives us the wiggle room we need to walk around those dangerous poles that real analysis could not handle (because they couldn't walk around the pole at the harmonic series because they were stuck on the 1 dimensional real line!)
      I took a different approach then other people and used fractional calculus to do "analytic continuation "... because it makes more sense to me. Seems more fundamental. But I can also do a video on the gamma/beta relationship if u so wish and get the result.
      And I get the same results as riemann did a hundred years ago.
      Ya I don't know what I am talking about. But you dont either. No one does.
      But my intuition is that this sum 1+2+3+... does equal -1/12. And it has something to do with numbers being pieces of Information..... not things.
      There is some deep stuff going on here. And for anyone reading this... that is what my channel will focus on: the personality of the numbers. So stay tuned and I will be thinking of a better response to you Mr mathologer .... this video has been on the back of my mind for a year now. I think it needs a response.
      Talk to u soon friend ;)

    • Mathologer
      Mathologer  Month ago +1

      +Brian talks about "But if u accept that imaginary numbers are real... then the sum equals -1/12." clearly demonstrates that you have no clue :)

    • Brian talks about
      Brian talks about Month ago

      +Mathologer I do know what I am talking about... as I have done videos on it myself (see channel).
      Ya numberphile broke some rules. But if u accept that imaginary numbers are real... then the sum equals -1/12.
      I also believe that there is no single human who knows why this is..
      But I do know that the future of math hinges on this mystery and I think u are doing a disservice for the kids out there by taking away the magic and mystery of this sum.
      I think u are wrong.

    • Mathologer
      Mathologer  Month ago +2

      Sign, if someone gave me a dollar every time some fool makes this comment I'd be rich :) NO, 1+2+3+... = -1/12 is NOT used in string theory and NO, Ramanujan did not "prove" this 100 years ago. What's used in string theory and what Ramanujan proved is the complicated relationship between 1+2+3+... and -1/12 that I talk about in this video. You must know that you don't know anything about this stuff. So why comment ?

  • Aditya sharma
    Aditya sharma Month ago +1

    I have one question
    How to calculate 0.03 raised to the power 0.03

    • _-*Trap House*-_
      _-*Trap House*-_ Month ago +2

      Aditya sharma 3/100 raised to the 3/100 is the 100th root of 27/1,000,000

  • pokeperson zach
    pokeperson zach Month ago

    This didn’t prove that 1+2+3... couldn’t equal -1/12 it just proved it wasn’t necessarily true. It’s up for debate because both have mathematical evidence behind them.

  • aasy jepale
    aasy jepale Month ago

    I refused to believe it and so to even watch the video, but my schoolmates fell for it and now I am proud :D

    • Mathologer
      Mathologer  18 days ago

      Sigh, maybe watch the video :)

  • 284mbp
    284mbp Month ago

    Can we talk about the drag queen off camera who's throwing so much shade? Girls, math shade is the best shade.

  • jm76464
    jm76464 Month ago

    Good job.

  • Khutso Makobe
    Khutso Makobe Month ago

    Give this Man a million dollars. The sum 1+2+3+... is always infinite!!

  • Z's Life
    Z's Life Month ago

    The beautiful thing about this video is that even though it's right and very well explained... it's perfect for arguing for a conpletely different reason, any of my friends try and throw that numberphile bs at me I just send them this video. *friend looks at the time length of the video, closes it* you know what bro, you were right from the start.

  • Worra Mait Kosit
    Worra Mait Kosit Month ago

    Thank you, now I can talk to people whomst'd've watch Richard and Mortympany

  • Viktor Åsbrink
    Viktor Åsbrink Month ago

    850 000 people have watched a 40 minute video about how some math is wrong.

  • CalvinistOnACouch
    CalvinistOnACouch Month ago

    Even though I don’t understand any of your videos I still love them

  • waverly2468
    waverly2468 Month ago

    There's a 1977 movie on you-tube "Too Hot to Handle" with Cheri Caffaro. The climax features a guy trying to untangle a complicated knot before a bomb goes off. Check it out if knots have anything to do with mathematics.

    • waverly2468
      waverly2468 17 days ago

      On the you-tube search box enter "Too hot to handle 1977 en ingles + 18 manuel alejandro 2016 copy". Or on amazon look for "too hot to handle, cheri caffaro", and it looks like it's a part of a roger corman "lethal ladies" 3-picture set. The scene in question happens at 1:19:00 on the you-tube video.

    • Mathologer
      Mathologer  18 days ago

      That sounds interesting. Do you happen to have a link to a clip?

  • Scott Dow
    Scott Dow Month ago

    When can we expect a video on the Euler-Maclauren formula? I'm very much looking forward to it!

    • Mathologer
      Mathologer  18 days ago +1

      Will still be a while, I keep getting sidetracked by other neat math :)

  • austin oehring
    austin oehring Month ago

    If I eat 1 m'n'm, then 2, then three. And so on. Will I eventually eat -1/12 of an M'n'M? When will math ever realize that even its continuous theory has a limit?

    • Mathologer
      Mathologer  Month ago

      +austin oehring Cool, all under control then :)

    • austin oehring
      austin oehring Month ago

      ​+Mathologer I took a reflection from the time you wrote me to ask, what is math really about? I only had the concept that math was used for applicable purposes, such as sciences and engineering. My mindset was "why take such an abstract idea any further then what it could be applied to." After reflecting and talking with some of my classmates, I came to realize that math can just be for math. Even if there is no point in expanding math for what is needed in a physical world. It still can be fun to prod at math for a further explanation of why this or why that. I'm not dumb, I won't be taking my money back. Why would I when I still have lots to learn? I'll have to admit, I question my interests of being a mathematician. Why do I do what I do? What does this prove? I understood that 0/0 has uses that could be applied for other majors, but since I never was interested in those fields, I never saw how to use it outside of a volume or water pump problem. I knew it was being used, but I didn't know for what. Therefore, I lack the knowledge of what a problem like this could accomplish. But what I have concluded today is that it doesn't matter. It's math. That's all it had to accomplish, just 'to be'. Of course, I'm furthering my education everyday, so I adapt, I think, I reach. It's the part of me that wants to find new things in math. (P.S. I'll need all the luck I can get for trying to understand modern theoretical physics, as it's way past my head even thinking about the name).

    • Mathologer
      Mathologer  Month ago

      +austin oehring So you are taking classes about infinity and 0/0 and nobody has bothered telling you what this is good for? If I were you, I'd ask for my money back! No infinity, no calculus. No calculus, no lots and lots of engineering and physics. None of the stuff I talk about in this video, good luck getting to grips with modern theoretical physics. No higher dimension , no ... Where to start ... :)

    • austin oehring
      austin oehring Month ago

      I'll never understand what a theory is meant to represent if it can't be applied to the real world. Why talk about something that has no point? How does this benefit the world? Can we apply this to something greater? Or is this just interesting to say, as a hobby? The classes I take have shown that arbitrary, 0/0, and infinity provide insanely cool things to bring up. We can break all sorts of concepts and axioms. But when you put logic into the formula, you have nothing more then incoherent babbling; even if something intelligent could be brought up. Counting is all you need in this question. Counting! This IS primary school mathematics. To take it further is just illogical. I get the math behind it because it's elementary. Although, putting so much effort into an easy problem does not change that the problem is easy. If you could find me a real use for how we could use this to the world's advantage,that'd be awesome. That's what I want to see in math, potential for contribution in other fields.

    • Mathologer
      Mathologer  Month ago

      When will people ever realise that primary school math only gets you that far :)

  • Brian Will
    Brian Will Month ago

    Here we see a nerd pissing contest...




    I love it.

  • Jonathan Ramirez
    Jonathan Ramirez Month ago

    Thanks for the information, just one thing, the cameraman's jokes were totally out of place.

  • BaBoon_OW
    BaBoon_OW Month ago

    at 27:30 you state that the only way to continue that line as a linear function is the one you show. actually i think there is at least another one by putting the absolute value to the x (eg. f(|x|))

    • Mathologer
      Mathologer  18 days ago

      You can extend in infinitely many ways but the point is that there is only in one analytic way :)

  • Electro wizards
    Electro wizards Month ago

    No.

  • federico saviano
    federico saviano Month ago

    Pi=22/7

  • E1LGaming
    E1LGaming Month ago

    Actually countable infinities can be subtracted....

  • Prince Francisco
    Prince Francisco Month ago

    But they have a similar video saying 1+2+3... Is -1/12

  • vLinh dh
    vLinh dh Month ago

    n=(-sqrt(3)plus or minus 1)/2*sqrt(3)

    • vLinh dh
      vLinh dh Month ago

      n=-1/2 plus or minus 1/2*sqrt(3)

  • Filipe Pereira
    Filipe Pereira Month ago

    You have a video from 2016 explaining this very same concept of 1+2+3+...= -1/12
    In 2018 you basically ridicule Numberphile for talking about it.
    What gives?

    • Mathologer
      Mathologer  Month ago +1

      "What gives?" Hmm, I'd say your understanding of what exactly I am saying in BOTH videos ? :)

  • Gagarin Rout
    Gagarin Rout Month ago

    This is an exception proof without which 26 dimension s of string theory would collapse....huh !

  • Nabeel Khan
    Nabeel Khan Month ago +1

    This is how disses happen in math !