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

  • 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 . 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.
    This notebook entry was also one of the starting points of my last video on this topic:
    Other good videos that deal with this strange “identity” include the following: (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.) (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:
    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:
    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 :)
    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.
    For today's maths t-shirts google: "zombie addition math t-shirt", "label your axes math t-shirt".

Comments • 6 262

  • Jeremy Snead
    Jeremy Snead 17 hours ago

    Abbot and Costello 7*13=28

  • kxtzEE
    kxtzEE 21 hour ago

    Yeah guys. 50+50=55

  • aryan bista
    aryan bista Day ago

    I don't know why do we always compare Maths to common sense?Currently we have reached such a stage where we need to imagine numbers that don't even exist and bring beautiful theories just like e^(i×pi) and in real life our common sense cannot define this equation!And if you really consider our common sense cannot be defied do know about time dilation and you will surely get blown after it defies your logic!!1+2+3+4=-1/12 is just beautiful though it seems a bit wrong as it lengthens to Infinity

  • BurnerProducts RocketStoves

    Right on the point!

  • Mr. Virtual
    Mr. Virtual 2 days ago

    29 k liked and 2.9 k disliked math kids!

  • Josh Paterson
    Josh Paterson 2 days ago

    His shirt changes thought the video

  • Saurabh Mishra
    Saurabh Mishra 3 days ago

    Divergent series whose partial sums don't explode to + or - infinity are "defined" to hav no sum.. why so ? Could one have defined it in some other way as well ? Say e.g. for 1-1+1-1+1... Where partial sums alternate between +1 and -1, why is it not "defined" as the average of the two ?
    Again, you seem to have simply "defined" the supersum in a specific way.. you could have defined it some other way too. I'm sure there must be some rigour to it, but it would help if u could explain a bit..

  • Metal Just Metal
    Metal Just Metal 3 days ago

    Both of them are right: In theory/Math this doesn’t fucking work at all but in practice/Physics it somehow works.

  • Mathematical Dofus
    Mathematical Dofus 4 days ago

    I think i found the real solution of this equation but i need some mathematicians to confirm my theory send me an email if you are interested.

  • Михаил Сибирев

    In the sum of S1 there was a substitution of the number for the probability of the sign + or - before a. The coin toss determines this sign randomly. When constructing a set of 2S1 rules of probability theory also work like a clock. 1+2+3+4 includes the sum of all even and odd numbers. The sum of all even numbers is an even number. The sum of all odd numbers with probability 1/2 is an even number (the number of odd numbers is even) and with probability 1/2 is an odd number (the number of odd numbers is odd). Number of even numbers for a series 1+2+3+4 equal to the number of odd numbers? Any even number is the sum of two odd numbers. The sum of even numbers can be represented as the sum of odd numbers. -1 /12? Each imaginary cat has 1 tail less than the real one :) I agree with this completely. I already wrote on the forum for the discussion of PI. The most exciting achievement of the last Millennium is the theory of probability. 2**(n+1)+2**n=3*2**n
    1, 1/2+1/2, 1/4+(1+1)/4+1/4, 1/8+(1+2)/8+(2+1)/8+1/8 ...

  • WeirdoAndy
    WeirdoAndy 4 days ago

    -1/12 is just the turning point of the triangle numbers

  • D HEAD
    D HEAD 4 days ago

    that laugh is gold

  • The Real Flenuan
    The Real Flenuan 5 days ago

    But they DID give disclaimers and further explanation in a follow-up video.

  • Jossi Afargan
    Jossi Afargan 5 days ago +2

    take a drink each time he says sum or will tend to infinite drunkenness

  • MarbleSwan666
    MarbleSwan666 5 days ago +1

    Yeah your kind of wrong though. The math checks out, but you can decide whether to converge or diverge. Your just wrong. Watch it again.

  • underestimated kid
    underestimated kid 5 days ago

    I disagree
    7 different people have a different prove of it which I was taught personally by them.

  • This guy
    This guy 5 days ago

    German Steve Jobs really knows his shit

  • LRH DarkLord
    LRH DarkLord 5 days ago

    Is this a math diss

  • 43labontepetty
    43labontepetty 5 days ago

    You're the kind of guy who couldn't be a theoretical physicist or a philosopher or anything. In quantum mechanics and things math as you explain it breaks down and does not work, as in black holes as well. New maths can be invented to explain new things. The fact that the sums they use are mathematically rigorous using the Riemann Zeta function and explains things in quantam mechanics makes it true in a sense. Just not a sense you care about.

  • TheDarknessIsWaiting

    Love your shirt.

  • Connor Schmidt
    Connor Schmidt 6 days ago

    So you said that using regular summation, the sum of 1+2+3... diverges to positive infinity, but with super summation it can be evaluated as -1/12.
    So which one is.. really correct? For a lack of better terminology. How does one reconcile the two different results provided by two different systems?
    Im thinking of how Newton's work doesnt make sense in Einstein's world and vice versa, so they're both correct in their respective categories, but I fail to really see that distinction here...?

  • the Epster
    the Epster 6 days ago

    In a former life in a parallel universe we lived infinite lives and I added up all the numbers - on croaking I muttered its minus one twelfth and I could hear laughter as my eyes closed that final time...

  • kartik abhinav Singh

    This math only write by quantum mechanics

  • K3AD
    K3AD 6 days ago

    THANK YOU! I‘ve lost my mind After seeing numberphiles Σ(-1)^x video. Great topic, but such badly explained.

  • Hilarius Ubaldias Arinarindra

    Numberphile takes a walk in Johto TheXvid Region
    *drum roll* Wild Mathologer appear *drum roll*
    Numberphile use math proves.
    Not effective! Mathologer thinks proves is argument!
    Mathologer use counter with argument!
    Argument meets argument! Infinite loop happens!
    Maggic happens!
    *drum roll* Resulting 1/2 *drum roll*
    No one wins,
    Spectator confused,
    This is not worth the effort,

  • DukeBox
    DukeBox 7 days ago


  • Professeur GigaWatt
    Professeur GigaWatt 7 days ago

    Well, Numberphile didn't compute this. It was done long before their video.

  • David Gordon
    David Gordon 8 days ago

    Great animations

  • Harsh singh
    Harsh singh 8 days ago +1

    String theory uses it in its calculation

  • Harsh singh
    Harsh singh 8 days ago +1

    So are you calling Ramanujan wrong!!

    • Not Broihon
      Not Broihon 7 days ago

      No, he doesn't. You should pay more attention. The Ramanujan Summation is -1/12. But saying this DIVERGENT series is equal to -1/12 is wrong. Especially if you do it like they did on Numberphile. Using these kinds of manipulations to a divergent series can basically give you any result. With similar methods you can prove that this sum is "equal" to -1/8 and -1/9.
      In addition to your 2nd comment: no, it's not used like that in string theory. What they did on Numberphile was showing a page (completely out of context) which stated that the sum is "related" to -1/12. There isn't even a = but an →. Watch their video again and read what it actually says on the page they show.
      What's used in physics is the relationship between the sum of all positive integers and -1/12 and not the fact that those two are equal.
      This sum diverges to positive infinity when doing normal algebra.

  • Abdilqadir Dalqamouni

    هذا تخريف وكلام فاضي.

  • Barry Island
    Barry Island 8 days ago

    All manipulations involving infinite series make the same mistake. Suppose we have a series of logical steps. Step 2, say, is S= 1 + 2 + 3 + 4 ....
    We cannot just write dot dot dot and move on to the next step. By moving on to the next step we are saying that the result of Step 2 is now available to us. This is not true. We cannot move on to Step 3 until we have finished evaluating Step 2. The fact that it would take us to eternity and beyond is just TOO BAD! Stay there and evaluate it! You cannot have Step 3 until you do!
    Dot dot dot doesn't give us something which we cannot have.

    P.S. Numberphile videos are a waste of electricity.

  • Cyberwizard Productions

    ugh. () make all the difference. you can get a whole bunch of different numbers for S1 depending on how you drop () into the sequence.

  • Dhamotharan R
    Dhamotharan R 9 days ago

    Loved this video !!

  • Bernardo Jordan
    Bernardo Jordan 9 days ago

    Oh man. I thought this was a short video but holy shit it's almost an hour long

  • George Hnatiuk
    George Hnatiuk 9 days ago

    Thank you for discussing this. I have been in endless discussions trying to point out to others exactly what you have stated. It is easy to get caught up in all sorts of paradoxes when applying rules for finite math to infinite series. One must be careful when applying algebraic rules and arithmetic in these cases.

  • Gigante Daileon
    Gigante Daileon 9 days ago

    Looks like a very obscure field of math that allows this result. Commonly is impossible to sum a lot of positive numbers and obtain a negative number.

  • Ohad Balash
    Ohad Balash 10 days ago

    i seem to recall that the properties you attribute to convergent series only apply to what we refered to as "absolute convergence" as in the series is convergent when all the terms are flipped to positive. if a series converges but not under absolute terms you could still fuck about by shifting things around.

    • Mathologer
      Mathologer  9 days ago

      Sigh, no, you were NOT :) The Riemann rearrangement theorem says that the sum of a series CAN change if you rearrange the terms of the series. However, this does not HAVE to be the case. In particular, just changing the order of a few terms or similar benign manipulations have absolutely no effect on the sum of any series. In turn the notion of absolute convergence and the Riemann rearrangement theorem have absolutely no bearing on anything we talk about in this video.

    • Ohad Balash
      Ohad Balash 9 days ago

      +Mathologer i did, i was right.

    • Mathologer
      Mathologer  9 days ago

      Please check your facts :)

  • Rémi Delloque
    Rémi Delloque 10 days ago

    This sum is to maths what the flat earth is to astronomy

    • Mathologer
      Mathologer  9 days ago +2

      Actually, no. The counterpart to flat Earth in maths is "0.999... is not equal to 1" :)

  • jimmy jones
    jimmy jones 11 days ago

    To whomever is really bored and watched this whole video:
    If you could let me know briefly what this is I would be grateful.
    I can't be asked to watch 41 minutes

    • Not Broihon
      Not Broihon 7 days ago

      Tl;dr: Numberphile did bad math. If you want more detail watch the video.

  • Philip Carollo
    Philip Carollo 11 days ago

    What about that formula on pg. 22 in the Numberphile's textbook: the sum of infinity (n=1) n -> -1/12...?

    • Mathologer
      Mathologer  9 days ago +1

      Well, I linked to a screenshot in the description of this video if you want to have a close look. The important thing to notice here is the use of the arrow -> instead of the equal sign. indicating that there is a complicated connection between -1/12 and 1+2+3+... but that this connection is NOT an equality :)

  • MoVieFaN world
    MoVieFaN world 11 days ago

    46 is my roll number
    Look If it help you

  • Alex
    Alex 11 days ago

    I'm not a math guy and I would think that [1-1+1-1+1-1+1...] is equal to zero, because if you add all the positives you get infinity, and if you add all the negatives you get negative infinity, so you have infinity minus infinity... which should be zero! Did I mention I'm not a math guy? LOL

  • Liviu e
    Liviu e 11 days ago

    Seems like modern ape forgot how it all started few thousand years ago(.at least).
    Math is a "numerical" representation of nature (aka physics).
    Is just math counting and ecuating what "is" or physics trying to prove what math calculated there should/must be, one trying to catch the other at some point, nothing more.
    In no reality adding more and more apples will not be equal to lacking a "seed" of an do not need math to realize you're going to " a lot of apples" ...if "your" math is pointing you to lacking something then your "kung fu" is damn wrong, you need to forget all you think you know and start all over again by counting fingers.

  • Vishal Dev
    Vishal Dev 12 days ago

    I like how 1 atomic mass unit is equal to 1/12 the mass of Carbon-12 atom

  • Akshay Chaudhari
    Akshay Chaudhari 12 days ago

    Suppose in a match of cricket,batsman play infinity balls and score should be

  • Akshay Chaudhari
    Akshay Chaudhari 12 days ago

    Infinity can be either odd or even,it cant be the combination

  • 21st Century Poops
    21st Century Poops 12 days ago

    math beef incoming

  • 21st Century Poops
    21st Century Poops 13 days ago

    i dont get anything lol

  • VA
    VA 13 days ago

    Ramanujan's summation is bullshit

  • Parth Raut
    Parth Raut 13 days ago

    1+2+3......=-1/12 given by great mathematician Ramanujan is used in string waves and quantum science . It is quite interesting result but many mathematician approved to this bcoz nothing was wrong with method

    • Not Broihon
      Not Broihon 7 days ago

      No. The *Ramanujan Summation* of this sum is -1/12. But saying this DIVERGENT series is equal to -1/12 is wrong. Especially if you do it like they did on Numberphile. Using these kinds of manipulations to a divergent series can basically give you any result. With similar methods you can prove that this sum is "equal" to -1/8 and -1/9. And no, it's not used like that in string theory. What they did on Numberphile was showing a page (completely out of context) which stated that the sum is "related" to -1/12. There isn't even a = but an →. Watch their video again and read what it actually says on the page they show. What's used in physics is the complex relationship between the sum of all positive integers and -1/12 and not the fact that those two are equal. This sum diverges to positive infinity when doing regular algebra.

  • Александр Ильин

    Thank you for Russian subtitles!

  • Reda Alnoueimi
    Reda Alnoueimi 13 days ago

    5:38 I SEE AMSTERDAM!!!

  • Supremacy 98
    Supremacy 98 13 days ago

    These qns should be given to primary school students,to show and teach them what not to do in their exams

  • Aaron Bell
    Aaron Bell 14 days ago

    Mine is a question: Had the numberphile guys qualified their sums with specialized quirky names, would they then have a specialized quirky proof of a quirky sum? I am not being whimsical or cynical when asking this. Could there be something to the madness? I mean, it appears that, in some quirky sense, mathematicians have reached the same result.

  • Aisir
    Aisir 15 days ago

    *equating endless series to calculable number*

  • Андрей Бережной

    это называется НЕ математика, а манипуляция с цифрами, вот к примеру 1+1 = 2, а уже 1 - 1 = 0. Вот видите. А если теперь 2 + 0 = 2, и при этому же 2 - 0 = 2 - вот видите! - это называется манипуляция.
    И вот почему, если к числу больше 1, добавить любое число больше 0 - и в любом количестве - полюбому получится в ответе число более 1.
    Как? к числу = 1 прибавляя до бесконечности все положительные числа, мы имеем число 1/12, что является меньше первоначального????? - это просто БРЕД. Это типа: Я тебе должен 153у.е, поэтому, вот смотри, давай посчитаем: 1 + 2 +...+17 - так что теперь ты мне должен (знак минус долга одного превращает в долг другого), аж 1,09 - так что ли получается?
    Поэтому я тебе должен 153 = ты мне должен 1,09

  • Xen Xander
    Xen Xander 16 days ago

    I thought the first sum would be '1'.
    1 - 1 + 1 - 1 + 1 - 1 ...
    If you put parenthesis around it creatively, you can get:
    1 - (1 - 1) - (1 - 1) ....
    In this, you cancel everything out, as everything else becomes a zero. Thus 1 - 0 - 0 ....
    I thought it would just be 1.

    • Mathologer
      Mathologer  13 days ago

      If you are happy with 1 - 1 + 1 - 1 + 1 - 1 ... = (1 - 1) + (1 - 1) + (1 - 1) ... = 0, how about adding in a different way brackets like this 1 - 1 + 1 - 1 + 1 - 1 ... = 1-(1-1)-(1-1)-... = 1 ? :)

  • Satvik Dasariraju
    Satvik Dasariraju 17 days ago

    Thanks for fixing this blatant error!

  • Tanel Kagan
    Tanel Kagan 17 days ago

    I don't see anything wrong with throwing out fun and paradoxical puzzles, especially when they are just at the edge of people's understanding and get them thinking. Of course if it gets to the point where people are relying on supposed formulae for the purposes of their exams, or important calculations, then we have a problem.
    Otherwise, what makes maths such as this so interesting is that it uses fallacies that challenge what we know. Anyone can sit down and work out the answer to a "real" equation, but it's not exactly an engaging party trick!

  • Goria Akash
    Goria Akash 17 days ago

    Isnt the first series a {sigma}(-1)^n which is an alternating series ??

    • Not Broihon
      Not Broihon 7 days ago

      Yeah, it is. It's simply wrong to assign a value to it like they did on Numberphile. You can't do these algebraic manipulations with a divergent/alternating series. You'll get a result, sure, but it's simply bs. Sorry Grandi.

  • Apollyon78
    Apollyon78 18 days ago

    -1/12th is a mathematician's heroine

  • Varadaraj Curam
    Varadaraj Curam 18 days ago

    Very nice. Gave lots of clarity on how to view divergent series. Thanks

  • Chris Feige
    Chris Feige 18 days ago

    numbers have an end. scientific truth!

  • Naeem Ullah
    Naeem Ullah 18 days ago

    Or less.... Hahaha

  • Max White
    Max White 18 days ago

    At 26:54 I can’t stop hearing chungus

  • عباس سعد
    عباس سعد 18 days ago

    GREAT 😍😍😍😍

  • PatriotsUnited
    PatriotsUnited 19 days ago

    This argument people are having is ridiculous. This is common sense. That other shit was obviously nonsense to me I don't get how they fooled so many people.

  • Krishnakanth Chittharu

    Got good

  • Akash Chowdhury
    Akash Chowdhury 19 days ago

    Hey, these tricks are just mindblowing. Here, I would recommend you to join LearnPick [ ] for local tutoring service in Bahrain.

  • Matrixar
    Matrixar 20 days ago

    I think that a 1 to -1n sum is 0

  • Sokaren Art
    Sokaren Art 20 days ago +2

    but... wait... don't we have random Axioms(Postulates) just laying about all over mathematics? who's to say that this is not true? 1+2+3+4+5+6+... could equal Pi for all we know or even Euler's number. but what do i know we have the axiom of infinity yet haven't really proved anything to be infinite except our imagination.

    • Sokaren Art
      Sokaren Art 18 days ago

      @OfficialUL then how come lots of new modern mathamatics are constantly being changed argued disproved and or proven? Axioms may be precise and consistent, but only in the made up world of mathamatics, if I wanted to take the time I could develop an axiom that states there is a finite end to the naturals and that all infinities don't exist. Once an axiom is tested and proved by the ways and or other ways that the person who made it did, then everyone will take it as it exists. But why should we trust axioms because they are 'proof' of things? Just counting seems easy until you divide or cube root or do uniform circular motion calculations (and don't even go to quantum mechanics)
      Also even though I maybe wrong ( I'm still in highschool give me a break) I'm not here to say who's right , even if people were getting confused ... Think about it , numberphile uploads a video that gets people interested albeit a wrong video, but the people who actually care will look and find out he's wrong , and in the process they could stumble on to something interesting and then they would share that, but this video , although good natured, ruined the fun of us solving it ourselves.

    • OfficialURL
      OfficialURL 19 days ago +1

      You're seriously misunderstanding axioms. In modern mathematics, we have very few actual axioms, nine to be precise, and the others are just suppositions to models, most famously Euclidean geometry. Axioms are precise, mathematical statements, and are supposed to be consistent. Stating that this sum equals anything axiomatically is not just inconsistent with actual math, but literal nonsense, since you'd have to precisely define your notions of sums in the first place, as they don't work as such in a standard way.

  • George Quilitz
    George Quilitz 20 days ago

    Answer to the question about contradictions if S was convergent.
    S = 1 + 2 + 3...
    1 + 2 + 3 ...
    - [1 + 2 + 3...]
    = 1 + 1 + 1 + 1...
    -[1 + 1 + 1 + 1]
    (S - S) - (S - S)
    (S - S) - (S - S) = 0
    0 = 1

  • Jonathon Jubb
    Jonathon Jubb 20 days ago

    Nicely done, Sir. Accuracy combined with respect. Thank you.

  • Josh Freeman
    Josh Freeman 21 day ago +2

    Awesome video !!

  • BlazzedTroll
    BlazzedTroll 22 days ago

    How much of an analytic function is required to formulate the continuation? You say "a chunk" if it's a continuous function. So given that the chunk is not a point then it must be infinite in information and that all boils down to exactly one and only one analytic function? Can you do a video on extracting the full analytic function from one portion of it and how do you write that portion if not by the entire function. It seems that the only way to describe a portion of an analytic function would be to write the analytic function and contain with limits. This seems like circular logic and I must be missing something. We can draw segments of a function, but how are those segments represented analytically?

  • Matej Grega
    Matej Grega 23 days ago

    Isnt infinity just an idea?

  • Fanamatakecick
    Fanamatakecick 23 days ago

    Something I noticed (I’m currently at 15:23), is that there is a pattern between the partial sums and the “sum” of the series.
    For example;
    1-1+1-1+1-1+1...= 1/2
    1-1 = 0 + 1 = 1 - 1 = 0....
    Half the time it is 0, half the time it is 1
    1-2+3-4+5-6...= 1/4
    1-2 = -1 + 3 = 2 - 4 = -2 + 5 = 3 - 6 = -3 + 7 = 4....
    A quarter of the time, the answer is -even, +even, -odd or +odd

    • Fanamatakecick
      Fanamatakecick 21 day ago +1

      I was just saying I noticed the pattern and the coincidental chance it was also the alleged answer

    • inyobill
      inyobill 21 day ago +1

      The conclusion that the sum of integers is equal to -1/12 is clearly false, therefore the proposition that it was based on, namely "1 -1 +1 -1 … = 1/2" is false. I. e., proof by contradiction that the sum of ones and negative ones NOT equals one half.

  • Aaron B.
    Aaron B. 23 days ago

    Who keeps talking off camera? :-/ they're kind of a dweeb

    • inyobill
      inyobill 21 day ago

      Or not, as the case may be.

  • lilla novak
    lilla novak 23 days ago +2

    me : * writing down what Numberphile said in their video *
    my teacher when they’re correcting my test : 5:25

  • Mido Reigh
    Mido Reigh 24 days ago

    Numberphile have addressed this in their later videos. One of them is this
    I could have subscribed to your channel, but I didn't. Because you promote your channel with so much negativity. That's not required.

    • inyobill
      inyobill 21 day ago +1

      "So much negativity"? Surely not. Numberphile are posting on a public forum. Given this, they should expect comments. In particular when they post a video that is as misleading as the subject video. Have you contact with Maths? This is what happens, and this is how the best truths we can achieve are pounded out.

  • Juven Ayudtud
    Juven Ayudtud 24 days ago

    I don't understand why you shift everything over? at 41:43.... The abstract space you created to multiply the 1/2 to the 1/4th gets shifted over by the 0. I feel like a distortion occurs. Why don't you subtract the 1/2 from the 1/4th?

  • Juven Ayudtud
    Juven Ayudtud 24 days ago

    Shifting the terms by one term is the same as adding a zero as the first term of the series- so if you moved it two terms would the second summation look something like -1 + 0 + 1 or would 0 + 0 + 1 be also correct. Is the moving of the term fixed by the sequence of enumeration?

  • mjgayle52
    mjgayle52 24 days ago

    thank you!

  • Samuel RPereira
    Samuel RPereira 24 days ago +1

    I knew it. Finally some common sense in this topic.

  • Magnus Schr
    Magnus Schr 26 days ago

    Which program are you using? :D

  • ThË ûñDëæD kīñG
    ThË ûñDëæD kīñG 26 days ago +6

    I was watching 8 mile ending rap battles and this came up

    Not disappointed this is a very mathematical diss track

  • n4n0ch1p
    n4n0ch1p 27 days ago

    1+0+1+0+1+0... = 1/5

  • Sabin O
    Sabin O 27 days ago

    What's the sum of 1/2+3/4+5/6+7/8...

  • Emilio Zaera Vidal
    Emilio Zaera Vidal 29 days ago +1

    Thanks, I just sensed right away that video was pure Bullshit

  • T A R S
    T A R S 29 days ago


  • vsm1
    vsm1 29 days ago +1

    I've spent 2 hours to watch 42-minutes-long video. a top-notch content, liked and subscribed

  • cal kane
    cal kane 29 days ago +1

    I'm so glad this video exists. Numberphile videos have been pissing me off immensely recently but I thought it was just me making a mistake. Have Numberphile responded to this video?

  • Mihey -38
    Mihey -38 29 days ago

    wow wow, take it easy, how does an area can be equal to the negative number?? 41:19

    • Mihey -38
      Mihey -38 29 days ago +1

      Clear, thank you

    • Mathologer
      Mathologer  29 days ago +2

      In calculus any area below the x-axis is considered "negative area" :)

  • Rocksolid64
    Rocksolid64 Month ago +1

    The series is an ever increasing triangle. Never can be negative!

  • Baul Tojokhan
    Baul Tojokhan Month ago

    You lost me at the number 1

  • Marcus International

    So ramanujam was not genius but confused math enthusiast looking for mentor in europe.

  • Brian Yentz
    Brian Yentz Month ago

    This video does a great job explaining what numberphile missed without seeming like it's desperate to feel better like a lot of "debunk" videos do, huge kudos on that, really! But every time the (I'm assuming) camera guy opened his mouth I had to fight to not leave the video he was so irritating.

  • Wilson Psotka
    Wilson Psotka Month ago +1

    Finally found someone smart enough to prove common sense