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

Embed

**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".

Андрей Смирнов2 hours agoСумма 2-х или более расходящихся рядов может к чему-нибудь и сойтись... Например к -1/12... ))))

Joshua Reed3 hours agoWOAH! 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 Reed3 hours ago15 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 Kumar6 hours agoSo, if this video was infinitely long, the number of annoying giggles in the background would diverge to positive infinity?

David Beaumont10 hours agoBest visualisation of the Riemann Zeta function and analytic continuation you'll ever see: thexvid.com/video/sD0NjbwqlYw/video.html

Abdullah AboMuhammad11 hours agoI only unDerstooD first half of the viDeo. anDthen my brain mal functionD

Rui Dias13 hours agoI 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 Raphael15 hours agonow explain the meaning of your T-shirt? ...

wassermeister22 hours agomath vs physics *eats popcorn*

JAGADEEP J LDay agoRamanujan :-- The man who knew infinity.

😍😘😘😘😘😘😘

domino2515Day agoSo, 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 KhatiDay agoSo 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 Bear2 days ago23:16

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 Bear2 days agoI 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?

1234Daan43212 days agoInfinity + 1/12 = 0

Roman Fedyashov2 days ago34:50 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 Иванов3 days agoI 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 Kalita3 days agoThen why the summation of 1+2+3+4+5...= -1/12 is used in string theory in physics ??? Answer me

Mathologer3 days agoIt'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 Меляйкин3 days agoОгромнейшее спасибо за перевод.

Razor 14 days agoHey he didn't use 1+1-1+1-1+1-1....as g.p he has explained it in another video....

Cobb Butterscorn5 days ago1-1+1-1+1-1... = 1/2 = 0 marks

Kapitan Candy5 days ago2x=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 Nominandum5 days agoWhy 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 Ochoa6 days agoMate, i love every t-shirt that you use in your videos, they're something hilarious.

edouard Bail6 days ago^{+1}except you're the one who is wrong on that case.

Dirk-Ulrich Heise6 days agoI heard about that numberphiles -1/12 thing and wondered what they did. Thanks for the explanation. They're physicists? That explains it.

Manuel Odabashian6 days agoHas the zeta function been proven?

Jeremy Nathan6 days agoI 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.

picampicam6 days agoIn 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.

Mathologer4 days ago^{+1}Maybe consider actually watching the video? :)

Nishan de silva6 days agoyou should cut out the sarcasm. Takes away from what you say. But I want to say your videos are very interesting.

Darth Drake7 days agoWe live in a society

Jabrane Amami7 days agonumberphile is not a certified mathematical institute. you didn't need to do all this, mathematicians will know the difference.

Mathologer4 days agoThis video is not aimed at mathematicians but at the millions of people won't know the difference unless someone tells them.

Josh Wilkinson7 days agoI'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 Scrocca8 days agoreminds 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 Syrup8 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 Jankovec8 days agoFor the puzzle, I got 2/3... how bad is it?

Green Sombrero9 days agoR+a+m+a+n+n+u+j+a+n = -1/12

Mathologer3 days agoAlways actually a good idea to watch a video before commenting on it :)

thexvid.com/video/YuIIjLr6vUA/video.html?t=2316

Ondřej Karbaš9 days agoMaths.. the only subject in the world you can pay attention to for forty minutes and still be entertained

Johnson Barnaby9 days agoi 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

Harpreet Singh9 days ago^{+2}thexvid.com/video/XFDM1ip5HdU/video.html

Ruben J10 days ago^{+1}That yellow infinity looks like a giant bow

Shiny Cupcake10 days agoWrong. 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 Sorath8 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 Cupcake8 days agoOh 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 Sorath8 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 Cupcake9 days agoWhy?

Herald of Sorath9 days agoPlease 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.

inox1ck10 days agoSo 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 spirit10 days ago5:32 black shirt

Frimchin10 days agoJust dont watch numberphile when james grime isnt on the thumbnail...dummies

mEmE sTeAlEr10 days agoThis is the math professor version of a TheXvid callout.

Fahad bin Islam10 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.

moo3heril7 days agoCheck the second term of your partial sum averages. It should be (1+0)/2 = 1/2. That should get you started

The Dancing Vegan Atheist10 days agoHow does 1/2 plus 1/4 plus ETC. converge to 1? Thanks for any help!

The Dancing Vegan Atheist5 days agoEliza K Yes, they say that, but I still don't know why.

Eliza K5 days agoIf 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 Atheist6 days agoI'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 K6 days agoTake 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.

carado11 days agofunny you say that while wearing a t-shirt that confuses ⇒ for =

Paul v11 days agoI’ll believe whoever wins a fist fight!

Shrimat Kapoor11 days agoAfter doing some real analysis, I realised Numberphile fooled me when I was naive

Александр Каренин11 days agoВ 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 Schuster11 days agoI love his laugh...

jlh530i111 days agothe guy commenting in the background detracts from the quality of the video.

Some Guy11 days agowouldn'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 K6 days agoFrom what I understand, it is alternating between 0 and 1. So it depends where you 'stop' your series.

Abdelmoutaleb Kandil12 days agoif 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 Kandil11 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

Mathologer12 days agoMath is simple? Most people would disagree with that statement. Did you actually watch the video before you wrote this?

Sebastian Kranzinger12 days ago^{+1}friend: *makes a racist comment in class*

me: 5:25

Azure Flash12 days agoThat 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 Ellis13 days agoAnd onward, towards the distribution of primes

Russeljrjs OwlyLife13 days agoNot to offense anyone but this video never fail to make me sleep every night

Daniel Gomes Machado Junior13 days agoFINALLY, 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 Martinez13 days ago^{+1}Who cares/

Aaron Stone13 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.

cngbuddah14 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?"

Tom Walter11 days ago'Bury the lede' FYI

Keisyuu O14 days agoThis is really brilliant! and I love the timings that you changes your T-shirt!

Princeofcups Poc14 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 Bennack14 days agoThe camera man should keep his comments to himself.

Timothy T15 days agoWhy if we put 0 in the z gunction we get a -1/2?

1 subs with no videos15 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.

Mathologer15 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.

JamesJoyce1215 days agoif 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 Coppola15 days agoisn't that the same answer the analytic extension of the riemann zeta function yields?

Aurongroove15 days agoThis was exactly what my instinct told me when I watched the Numberphile video!

Vincent Lextrait15 days agoG. H. Hardy has indeed turned in his grave with that Numberphile video. They slipped into pre-Hardy-lack-of-rigor...

John Brownridge16 days agoInfinity 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 Kitrid16 days agoSo, 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 Sorath11 days agoNot 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 J16 days agoThe 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

ManuJulianShulian16 days agoYou 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.

Mathologer16 days agoListen to what exactly I say :)

Danish Kamaal16 days agoThat last part. You really left me sleepless there.

alex tworkowski16 days agoThey'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 Tseung16 days agoall, i am know why numberphile is wrong

Wai Shing Tseung16 days ago0.5+0.25+0.125+0.0625+0.03125+…=1,*1+2+3+4+5+6+…=○○

angenogu16 days ago''What if it was possible to define a super sum'' -> *T-Shirt evolves to a Super T-Shirt*

Pilletta Doinswartsh17 days agoI have only one question. why are you staring at my chin?

Jens Philip Höhmann17 days ago18:50ff The 2nd series? I think it's rather a sequence.

Alexis Ramis17 days ago^{+1}Dr. Zola sounds pissed in the background

Alf Lacis18 days agoI 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 Sedlický18 days agoWhat 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 Sedlický17 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...) :)

Mathologer18 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 bhinwal18 days agoThen why this result is used in string theory?.??????????????

Mathologer18 days agoSigh, please check through the comments. That nonsense is worth another debunking video :)

n5sdm19 days agoFail.

bonnome219 days agoWell, can you explain the Casimir effect that uses the zeta(-3) does lead to the correct answer?

Mathologer18 days agoSure 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? :)

LordFvckingHorst19 days agoTo 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).

tubehepa19 days agoNot necessarily over 6 million people, rather *views*?

nick hadloc20 days ago"why are you the way you are?" -Michael Scott

Endrit Shabani20 days agowell 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

Jay20 days agoThe real question is: when are you gonna release a *diss track* ? 😁

leonard TheReal20 days ago8:23 the answer has to be 0.999.... so neverending because it never gets to 1 it always stays below

Curtis Rahman21 day agoshouldn't s - s2 = 0.25

ajsdoa21 day ago20:00 should be + there after 7.

abu abdulah21 day agoYour experience make maths easy to understand thanks sir

Desiree Disco22 days ago^{+1}🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽🙌🏽 thank you. Math grad and that video bugged me