Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

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  • เผยแพร่เมื่อ 21 เม.ย. 2016
  • The Mathologer sets out to make sense of 1+2+3+ ... = -1/12 and some of those other notorious, crazy-looking infinite sum identities. The starting point for this video is the famous letter that led to the discovery of self-taught mathematical genius Srinivasa Ramanujan in 1913 (Ramanujan is the subject of the movie "The man who knew infinity" that just started showing in cinemas.) Find out about how these identities come up in Ramanujan's work, the role of "just do it" in math, the rules for adding infinite sums on Earth and other worlds, and what all this has to do with the mathematical super star the Riemann Zeta function.
    You can download the jpeg of Ramanujan's letter to Hardy that I put together for this video here: www.qedcat.com/misc/ramanujans...
    (quite large)
    You can access a scanned copy of Ramanujan's notebook here: www.imsc.res.in/~rao/ramanujan...
    or check this out
    books.google.co.uk/books?id=O...
    If you want to watch some other videos that deal with these strange identities I recommend the following:
    • Why -1/12 is a gold nu... (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.)
    • Ramanujan Summation (James Grime's video (singingbanana & Numberphile) which aims at making sense of the formula at the heart of Ramanujan summation which I only flash briefly in the last part of the video.)
    • What does it feel like... (a very nice 3Blue1Brown video that makes sense of the identity 1+2+4+8+ ... = -1 in a way that is totally different from the one I am talking about in this video.)
    This week’s video is in response to a large number of you and my students at university asking me for my take on the whole 1+2+3+... =-1/12 business. Initially, the plan was to come up with one of my usual 15 minute long videos. However, after several unsuccessful attempts at not exceeding the magic Mathologer time limit, I realised that any “short” video like this would just be a clone of one of those wrong/misleading accounts of this topic that TH-cam is full of. So, rather than just give up completely on this project I decided to do what you should never do if you actually want people to watch your videos, namely simply go for it and not look at the clock. The result - a video that is an insane 35 minutes long in which I say all the things that I think need to be said and can be said only using elementary math to (just barely) do this amazing topic justice.
    Thank you very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.
    Enjoy!
    P.S.: If you know calculus and want to read up on all this some more, 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 original 1924 edition of the book). 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. The Hardy who wrote this book is the Hardy who I mention at the beginning of the video! 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.

ความคิดเห็น • 6K

  • @tahmidt
    @tahmidt 8 ปีที่แล้ว +8506

    Imagine this;
    A guy comes up to you and offers you $1 on day 1, $2 on day 2, $3 on day 3... all the way to $n on day n and he keeps doing this for the rest of eternity. You might think that he's giving you free money but a mathematician will quickly realize that he is trying to con you and steal a twelfth of a dollar.
    But now you know.

    • @ishwar8119
      @ishwar8119 8 ปีที่แล้ว +167

      +Tahmid Islam (Tanveer) Fine of $0.09Mathematician: That guy lost 2/3 of a cent because of this

    • @SyntakticSugar
      @SyntakticSugar 8 ปีที่แล้ว +36

      +Tahmid Islam (Tanveer) Nice one :P

    • @rasowa2958
      @rasowa2958 8 ปีที่แล้ว +187

      +Tahmid Islam (Tanveer) That's just what Federal Reserve and other central banks do.

    • @dixonbuttes
      @dixonbuttes 7 ปีที่แล้ว +273

      I know I'm 9 months late, but I wanted to let you know this is the best comment I've ever seen on youtube.

    • @ramirez9919
      @ramirez9919 7 ปีที่แล้ว +16

      Tah mid Tanveer, But why only 1/12 and why not any other figure

  • @kevnar
    @kevnar 2 ปีที่แล้ว +2372

    An infinite number of mathematicians walk into a bar. The first guy orders a beer. The second guy orders half a beer. The third guy orders a quarter of a beer the fourth, an eighth. The bartender just pours two beers and says, "You guys need to know your limits."
    I finally get that joke. Thanks.

  • @kevintan9483
    @kevintan9483 3 ปีที่แล้ว +576

    Every time I make a mistake on a maths paper, I'm going to hear that sound and be scolded and scared out of my skin by Ganesha descending from the ceiling.

    • @pranavchandrav6071
      @pranavchandrav6071 2 ปีที่แล้ว +5

      Jumpscare

    • @yedosti3092
      @yedosti3092 2 ปีที่แล้ว +5

      This comment made me jump out of my bed laughing😂😂. Truly insane😂😂

  • @aadityasingh5575
    @aadityasingh5575 3 ปีที่แล้ว +374

    I love how whenever Ganesha comes up we get a death threat

  • @donmoore7785
    @donmoore7785 4 ปีที่แล้ว +814

    I like how Ramanujan left out his bold assumptions, but the recipient of the letter knew exactly what he meant.

    • @maxwellsequation4887
      @maxwellsequation4887 3 ปีที่แล้ว +79

      Recipient was Hardy tho...

    • @abhaynatoo
      @abhaynatoo 2 ปีที่แล้ว +110

      it was THE ramanujan talking to THE hardy. no commoners here. so its understandable.

    • @vaibhavkrupakar240
      @vaibhavkrupakar240 2 ปีที่แล้ว +8

      Not an assumption, he proved it himself

    • @Alkis05
      @Alkis05 2 ปีที่แล้ว +35

      It wasn't an assumption. If you pause the video, he says that he explain further in what conditions those divergent equations make sense. Most pointedly, he understood they were divergent and he made it clear he was not talking about standard summations.

    • @stevethea5250
      @stevethea5250 ปีที่แล้ว

      @@Alkis05 timestamp?

  • @binayakthakur5122
    @binayakthakur5122 5 ปีที่แล้ว +1837

    It is like the software running the universe got overwhelmed and gave error - 1/12 Integer Overflow

    • @waywardson4472
      @waywardson4472 4 ปีที่แล้ว +33

      Binayak Thakur I was thinking along similar lines when he had all powers of 2 summed up to -1

    • @thesunexpress
      @thesunexpress 4 ปีที่แล้ว +25

      Actually probably the Universe spat out "Cannot compute! Error: 1/137 "

    • @bee_irl
      @bee_irl 4 ปีที่แล้ว +42

      -1/12, my favourite integer

    • @aklipsigman3451
      @aklipsigman3451 4 ปีที่แล้ว +15

      It's real number not integer

    • @vivanmakwana2253
      @vivanmakwana2253 4 ปีที่แล้ว +7

      it is not error it is a smarter idea of an indian and i am proud to be an indian

  • @sjegannath6295
    @sjegannath6295 ปีที่แล้ว +85

    It's important to note that this doesn't mean that the sum of all natural numbers is -1/12 but rather it's the solution to the riemann zeta function where this series occurs.

  • @guillermoh.k.2967
    @guillermoh.k.2967 4 ปีที่แล้ว +1969

    Remember: Ganesha knows when you stop paying attention...

    • @sanky1211
      @sanky1211 3 ปีที่แล้ว +16

      😂😂

    • @danielharris9403
      @danielharris9403 3 ปีที่แล้ว +242

      Someone had to address the Elephant in the room 👍

    • @096astiksharma8
      @096astiksharma8 3 ปีที่แล้ว +6

      @@danielharris9403 😂😂😂

    • @IbrahimKhan-gv6cw
      @IbrahimKhan-gv6cw 3 ปีที่แล้ว +2

      No, it does not. Just stop lying.

    • @nithishnithish504
      @nithishnithish504 3 ปีที่แล้ว +145

      @@IbrahimKhan-gv6cw we have a religious fanatic here

  • @rifkyalfarizy9945
    @rifkyalfarizy9945 8 ปีที่แล้ว +2756

    before i started watchibg mathologer i hate math and have bad grades
    after i found this channel, i love math, and still bad grades
    luv dis channel

  • @Mathologer
    @Mathologer  8 ปีที่แล้ว +821

    This week’s video is in response to a large number of you and my students at university asking me for my take on the whole 1+2+3+... =-1/12 business. Initially, the plan was to come up with one of my usual 15 minute long videos. However, after several unsuccessful attempts at not exceeding the magic Mathologer time limit, I realised that any “short” video like this would just be a clone of one of those wrong/misleading accounts of this topic that TH-cam is full of. So, rather than just give up completely on this project I decided to do what you should never do if you actually want people to watch your videos, namely simply go for it and not look at the clock. The result - a video that is an insane 35 minutes long in which I say all the things that I think need to be said and can be said only using elementary math to (just barely) do this amazing topic justice.

    • @MK-13337
      @MK-13337 8 ปีที่แล้ว +7

      I just finished watching this because I'm a time traveller. Great video!

    • @wkwmenen
      @wkwmenen 8 ปีที่แล้ว +27

      Jesus, that Indian God works as almost a screamer

    • @icefreezer7
      @icefreezer7 8 ปีที่แล้ว +1

      +Hououin Kyouma lol. me too. and nice name

    • @Mathologer
      @Mathologer  8 ปีที่แล้ว +12

      +Matti Kauppinen Fill me in on the secret of time travelling sometime. Would make for a great video I am sure :)

    • @Mindsway
      @Mindsway 8 ปีที่แล้ว +3

      great video ! the cesaro methode is cool :) But can we.. take the average of the average of the average... and so on to the infinite ?

  • @villagelog1966
    @villagelog1966 4 ปีที่แล้ว +822

    Ramanujan’s work in pure mathematics is now being used in engineering too. “In 1918, Srinivasa Ramanujan introduced a summation, known today as the Ramanujan-sum. He used this to express several arithmetic functions in the form of infinite series. For many years, this sum was used by other mathematicians to prove important results in number theory. In recent years, engineers and physicists have found applications of this sum in digital signal processing, especially in identifying periodic components of signals with integer periods,”

    • @rustalisin8950
      @rustalisin8950 3 ปีที่แล้ว +3

      Pls Help ..Any Polynomial may be completely determined by a part of it. Analytic function is uniquely determined by a small part ( sample ) of it. OK. How can a Eta / Zeta Analyt function be used to extract binary modulation from a high density set of timespaced sloping carriers (let all carriers be linear, thus parallel, with guard band) I can see this series extracting (defined) harmonic modulation using array summation to yield an entire constellation across a message timespan of say 12milliSec. given 512 symnbols in 12mS.

    • @RecliningFurniture
      @RecliningFurniture 3 ปีที่แล้ว +9

      Great, but what on Earth does all that mean? It is really not difficult to see why 1+2+3...etc does NOT equal -1/12 [but, incidentally, that 0.999...(0.9 recurring) DOES equal 1 (which I mention only to show that I don't have an issue with infinite numbers in calculations, where the calculations are actually grounded in logic)] . As that is so (and all you really need to know is that a series of plus numbers added together cannot logically equal a minus number unless you introduce a minus figure into your calculation, in which case it is no longer a series of plus numbers) I am not sure where that leaves the 1+2+3....series in terms of any practical application. Can anyone enlighten me on this, please?

    • @achyuththouta6957
      @achyuththouta6957 3 ปีที่แล้ว +42

      @@RecliningFurniture 1+2+3+4..... is indeed equal to -1/12 although the explanation given by Ramanujan is completely wrong but this is used in string theory and has merit. Ramanujan gave insane explanations to this theorems and equations but most of them are correct

    • @RecliningFurniture
      @RecliningFurniture 3 ปีที่แล้ว +14

      @@achyuththouta6957 Have to say I'm surprised people are still taking the whole -1/2 thing seriously. Mathologer has done another video about this (I'm not sure if it was before or after this one) where he completely debunks it. I don't know which proof you favour; the one I followed introduced plus and minus 1s and tried to make out these implied an average, when this was very obviously a completely different sequence - a mathematical sleight of hand. But, for the sake of argument, I would be interested to know where the logical fault lies in positing that adding only positive numbers to positive numbers must result in a positive number and cannot result in a negative one. I cannot personally fault the logic in that, but, as I say if the -1/2 sum is correct, there HAS to be a logical flaw in what I just said. Can you identify what it is, please? I would be extremely impressed (enlightened, even, in the truest sense) if you can.

    • @RecliningFurniture
      @RecliningFurniture 3 ปีที่แล้ว +4

      @jamesk479 Thanks for this. You will need a specific rule to assign a solution to sqrt (-2). Such a rule would not accord with any maths I know, but that's OK, because it would be a rule specifically dealing with minus numbers, and the point of the rule I referred to above is that it deals only with positive numbers. To test the validity of the c = 1+2+3....etc here it should help to first consider a much simpler sum. So let's look at c* = 1+2+3 (which seems as reasonable a sum to consider as anything not containing an infinite series). So, c in this case equals 1+2+3. Which equals 6. Now, going on to use Ramanujan's methodology, we multiply by this 4 and subtract the x4 number from the original number. According to the demonstration in this video, this should result in -3c = 1-2 +3. But it doesn't. What we actually get is -3c = -3-6-9 (which is -18, so c =6, as we already knew).
      The practice of missing out every other number in the demonstration when multiplying by 4, and then including numbers missed out when subtracting the bottom number from the top, is going to give a bogus result. What we can actually say about the 'c' in = 1+2+3....etc is that c must >6, because the infinite series following 3 contains only additional positive numbers. Similarly, we can say with absolute confidence that c >10, because we know the next number in the sequence is a 4, and 1+2+3+4 =10, and there are more positive numbers to follow (an infinite number of them). Taking into account the number after that, we have 1+2+3+4+5 = 15, so c must be greater than 15. And so on. Forever. It turns out there are an infinite number of things we can say about c. We know exactly what types of things they are, and none of them are that c is equal to - 1/12.
      *c here obviously does not stand for the constant in an infinite series as Ramanujan used it, it is just c.

  • @samtgamee3202
    @samtgamee3202 3 ปีที่แล้ว +249

    thanks to Ganesha I will never forget infinity can't be subtracted from itself.

    • @gulshansharma2131
      @gulshansharma2131 3 ปีที่แล้ว +5

      Why u can't subtract infinity from infinity ? Becoz u can't think up to infinity? Or u can't make sense about infinity ? Or u want to just follow others' work?

    • @gulshansharma2131
      @gulshansharma2131 3 ปีที่แล้ว

      @Sam please elaborate a little bit😀

    • @rishisingh1035
      @rishisingh1035 3 ปีที่แล้ว +9

      @@gulshansharma2131 u can't subtract infinity from infinity , but u can subtract 2 numbers tending to infinity and get 0

    • @beastgamer4932
      @beastgamer4932 3 ปีที่แล้ว +1

      @@rishisingh1035 we’re not talking about limits here ok?

    • @rishisingh1035
      @rishisingh1035 3 ปีที่แล้ว +9

      @@beastgamer4932 then u cannot subtract infinity from infinity

  • @parinitachakma765
    @parinitachakma765 4 ปีที่แล้ว +2477

    A simple stack overflow bug. God will patch it in the next update.

    • @capwilder2504
      @capwilder2504 4 ปีที่แล้ว +17

      Skylark Phoenix 😂😂😂😂

    • @rohitupadhyay1116
      @rohitupadhyay1116 4 ปีที่แล้ว +37

      There is no bug under his rule my friend

    • @andrewzhang8512
      @andrewzhang8512 4 ปีที่แล้ว +36

      'stack overflow'. EVERY PROGRAMMERS LOVE!!!!

    • @wliaputs
      @wliaputs 4 ปีที่แล้ว +30

      Rohit Upadhyay but i see bugs everyday

    • @rohitupadhyay1116
      @rohitupadhyay1116 4 ปีที่แล้ว +11

      @@wliaputs 🤣🤣

  • @PickyMcCritical
    @PickyMcCritical 7 ปีที่แล้ว +1799

    List of jumpscares:
    4:02
    9:28
    11:53
    22:50
    30:12
    31:57
    34:14

    • @ankitaaarya
      @ankitaaarya 5 ปีที่แล้ว +31

      PickyMcCritical 😂😂😂😂

    • @ekap1916
      @ekap1916 5 ปีที่แล้ว +14

      PickyMcCritical You ignorant knob!!

    • @biscuitsalive
      @biscuitsalive 5 ปีที่แล้ว +19

      PickyMcCritical terrifying

    • @vaishnavplays203
      @vaishnavplays203 5 ปีที่แล้ว +4

      Lol

    • @Akshaylive
      @Akshaylive 5 ปีที่แล้ว +51

      Thanks muck. This helped me prep.

  • @techsandbulls1869
    @techsandbulls1869 3 ปีที่แล้ว +121

    man who knew infinity
    now i understand why the title of his biography makes sense

  • @yashjobanputra3832
    @yashjobanputra3832 3 ปีที่แล้ว +96

    When he pauses for Hardy and then said "He is not dummy either", lol

  • @Nero-ox5tw
    @Nero-ox5tw 3 ปีที่แล้ว +1719

    This is why TH-cam is leagues better than Facebook, Instagram, Snapchat, etc.

    • @drbhaviify
      @drbhaviify 3 ปีที่แล้ว +30

      Yes agree

    • @ign_angry
      @ign_angry 3 ปีที่แล้ว +13

      i use all

    • @Subs1338
      @Subs1338 3 ปีที่แล้ว +6

      Why?

    • @thatkindcoder7510
      @thatkindcoder7510 3 ปีที่แล้ว +90

      @@Subs1338 Because TH-cam mainly teaches the objective truth, while other social media sites degrade your brain with attractive but biased false facts.

    • @dr.palsonp.h.d815
      @dr.palsonp.h.d815 3 ปีที่แล้ว +51

      @@thatkindcoder7510 "objective" "youtube" HAHAHAHAHAHAHAHAH

  • @NoobMasterX1
    @NoobMasterX1 6 ปีที่แล้ว +1180

    Don't wear headphone when watching this video,
    have a nice day

  • @felipelopes3171
    @felipelopes3171 4 ปีที่แล้ว +230

    I think Ramanujan was quite aware of what his sum meant. He mentions it's the "center of balance" of the series. You can get the -1/12 value using the Euler-Maclaurin formula with an expansion around 1/n -> 0. This is a pretty novel way to interpret the value of the zeta function.
    Anyway, about this confusing people in calculus, I think people learn much more math by analyzing where the -1/12 comes from than when they dismiss the formula.

    • @akanksha8311
      @akanksha8311 ปีที่แล้ว +3

      well said

    • @Entropy3ko
      @Entropy3ko ปีที่แล้ว +9

      The problem is that people do not understand how limits work, often
      Functions like F(x)= Sin(x)/x has a limit equal to 1 at x-->0, but the function itself does not exit at 0.
      So you can pin a value to F(0), but this does not mean the function at that point actually exists.

    • @Wallofdenial50
      @Wallofdenial50 ปีที่แล้ว

      Kind of a divide by zero accident

    • @abhishankpaul
      @abhishankpaul 7 หลายเดือนก่อน +1

      ​@@Entropy3ko people conveniently skip the word "approach" when studying limits and then complain when shit blows up

  • @aniketthakor
    @aniketthakor 3 ปีที่แล้ว +173

    Happy Ganesh Chaturthi :)
    Love and respect form India

  • @WolfPack-gi7br
    @WolfPack-gi7br 6 ปีที่แล้ว +542

    4:02 that scared the hell out of me lol

    • @darkdelphin834
      @darkdelphin834 4 ปีที่แล้ว +1

      Same here xd

    • @himanv
      @himanv 3 ปีที่แล้ว +37

      Ganesh is the remover of obstacles and the lord of knowledge and light-- so yeah, makes sense he would scare the literal hell out of you! lol

    • @sarojnayak8350
      @sarojnayak8350 3 ปีที่แล้ว +1

      @@himanv the sound was scary

    • @franklee8032
      @franklee8032 3 ปีที่แล้ว +3

      And he never answers the question posed.. what's the point of even showing it?

    • @jacksummer4041
      @jacksummer4041 3 ปีที่แล้ว +10

      I'm watching at 3am 😂 and i almost died

  • @Kevbotomy
    @Kevbotomy 7 ปีที่แล้ว +666

    On a scale of 1 to -1/12, how would you rate this convergent series?

  • @jaimeriveras
    @jaimeriveras 3 ปีที่แล้ว +56

    As in the case of quantum mechanics, I understand very little, but it’s enough to appreciate the beauty of it all. Amazing stuff.

  • @TommyAmbersonRD
    @TommyAmbersonRD 3 ปีที่แล้ว +89

    2:54 "keep it completely elementary" .
    My definition of elementary is clearly not the same as his.

  • @heyitsalex99
    @heyitsalex99 8 ปีที่แล้ว +70

    i havent watched the video yet, but thankyou for 3 reasons, 1. ramanujan 2. infinite sum of natural numbers 3. 30 minutes

    • @Mathologer
      @Mathologer  8 ปีที่แล้ว +27

      +heyits- alex Well, if you like Ramanujan, I'll probably do at least two more videos this year featuring his math :)

    • @heyitsalex99
      @heyitsalex99 8 ปีที่แล้ว

      +Mathologer yassss

    • @Mathologer
      @Mathologer  8 ปีที่แล้ว +12

      +Appleguysfriend A video on Galois theory would be nice (probably a 60 minute one though :)

    • @funcaogamma7663
      @funcaogamma7663 8 ปีที่แล้ว

      +Mathologer yes

    • @4Pssf2w
      @4Pssf2w 8 ปีที่แล้ว

      +Mathologer yes

  • @marksmod
    @marksmod 8 ปีที่แล้ว +927

    The elephant god of jump scares (aka. purple heart attack)

    • @McRaylie
      @McRaylie 8 ปีที่แล้ว +7

      +marksmod Ganesh?

    • @SomeoneCommenting
      @SomeoneCommenting 8 ปีที่แล้ว +38

      +McRaylie He means that every time that it appears the sound is VERY ANNOYING. I was using headphones when I was watching this video and it is a very unpleasant sound that makes you jump because it is unexpected and awkward.

    • @QuantumConundrum
      @QuantumConundrum 8 ปีที่แล้ว +21

      +marksmod Ganesh is secretly trying to murder all the mathematicians.

    • @Hect0rxP
      @Hect0rxP 8 ปีที่แล้ว +5

      hahahahaha all this comments have made me laugh so hard!!! hahahaha and yeah! freaking Ganesh! my heart almost stops >_

    • @shepaustad558
      @shepaustad558 8 ปีที่แล้ว +12

      Be kind

  • @devjeetnanda7698
    @devjeetnanda7698 3 ปีที่แล้ว +80

    The way lord Ganesha pops up with that sound.... It feels like he's giving some sort of mythological warning
    Edit: I forgot to mention while writing this comment that I was watching the video on Ganesh Chaturthi(weird YT algo right, for most Indians) and that my half yearly exams were a week away starting with MATHS as the first exam

  • @zainulabideen5895
    @zainulabideen5895 2 ปีที่แล้ว +91

    One Word for Ramanujan, "Genius of Genuis", He is a idol of motivation for math students, #Respect

  • @chrisdavis5698
    @chrisdavis5698 4 ปีที่แล้ว +36

    who else was baffled by how breath-taking gorgeous that handwriting was?? jeez.

  • @kcwidman
    @kcwidman 7 ปีที่แล้ว +903

    Oh my freaking goodness, I jumped right out of my seat with my headphones in at 4:00.

  • @rajendramisir3530
    @rajendramisir3530 2 ปีที่แล้ว +12

    Srinavaasa Ramanujan said every equation was a prayer for him. Ever since I learned about him in my Calculus 2 class 30 years ago, he has been my Mathematics role model. He approximated the value of 1/Pi to a few decimal places using infinite series.
    Srinavaasa Ramanujan gave our world his gift of genius and departed peacefully from this material world. It feels sad to loose men of great minds like him.
    Although he was not a trained Mathematician, he was able to enlighten our world of Mathematics with his genius of Mathematical deductions and profound insights. I am impressed at how he caught the attention of Professor GH Hardy of Cambridge University by his(Ramanujan) letter of theorems on infinite series that diverge( 1+2+3+ ... = -1/12.

  • @roughysk9851
    @roughysk9851 3 ปีที่แล้ว +35

    Ramanujan was genuinely a masterpiece

  • @jedus007
    @jedus007 4 ปีที่แล้ว +59

    Ramanujan was sheer poetry in Mathematics.

  • @Hecatonicosachoron
    @Hecatonicosachoron 8 ปีที่แล้ว +254

    Those interjections by Ganesha are terrifying

    • @user-ur2en1zq4f
      @user-ur2en1zq4f 3 ปีที่แล้ว +6

      Jay shri Ganesh

    • @HinduSherForever
      @HinduSherForever 2 ปีที่แล้ว +2

      "You are encapsulated by evil energies. Pray to Bhagwan Narsimha. Stay calm. Respect fellow people. Don't get into alcoholism.*

  • @ralphallengamboa9394
    @ralphallengamboa9394 3 ปีที่แล้ว +20

    This is much better than an intense film. That Elephant jump scares.. 😂

    • @MrDrgdf
      @MrDrgdf 2 ปีที่แล้ว +12

      Hindu God Ganesh.

  • @adityanair7159
    @adityanair7159 3 ปีที่แล้ว +34

    Jai shree Ganesha Cutest God 🙏😇
    The God of Wisdom .

    • @user-ur2en1zq4f
      @user-ur2en1zq4f 3 ปีที่แล้ว +7

      Jay shri Ganesh

    • @catwithsunglasses3949
      @catwithsunglasses3949 2 ปีที่แล้ว +10

      @@KhvLeD yea what’s wrong with that? I’m an atheist but even I don’t think anything is wrong with believing in multiple gods lmao.

    • @sttpt9217
      @sttpt9217 2 ปีที่แล้ว +1

      @Store Patternator 😂 lol we don't belive in man made religion like Islamism, Christianity ..

    • @superman5742
      @superman5742 2 ปีที่แล้ว

      @Store Patternator nothing...just carry on with our respective lives 😂

  • @andreguimaraes9347
    @andreguimaraes9347 8 ปีที่แล้ว +98

    The loud noise of the elephant thing coming up scares the crap outta me every time xD

  • @sergiin3
    @sergiin3 4 ปีที่แล้ว +69

    A man who knew infinity.
    Good book about Ramanujan's life.

  • @mohityadav21
    @mohityadav21 2 ปีที่แล้ว +5

    I got scared every time Ganesha appeared with that scary sound.

  • @user-gc6my9jg2c
    @user-gc6my9jg2c 4 ปีที่แล้ว +8

    I like your videos! Several times I've had a technical comment that you specifically addressed at some point later in your video. I'm reviewing topics that I already know. Your explanations are pretty good! I also appreciate that your animations are simple and enough.

  • @paulczar
    @paulczar 5 ปีที่แล้ว +401

    If this guy had been by math teacher is high school, I’d probably be a mathematician by now. Amazing what a good, passionate teacher can do for you.

    • @jacksummer4041
      @jacksummer4041 3 ปีที่แล้ว +14

      😂 yeah a mathematician who's trying hard to find contradictions to proof that originally do not have any contradiction

    • @angelc9818
      @angelc9818 3 ปีที่แล้ว +8

      he has been my teacher

    • @DocBree13
      @DocBree13 2 ปีที่แล้ว +1

      I feel the same

    • @ripjawsquad
      @ripjawsquad 2 ปีที่แล้ว +7

      @@jacksummer4041 isn't that what good mathematicians do

    • @AlexanderSuraphel
      @AlexanderSuraphel 2 ปีที่แล้ว

      @@angelc9818 I've read someone commenting the same. Which school was it?

  • @94D33M
    @94D33M 5 ปีที่แล้ว +251

    Next time when you get wrong in ur maths question, remember to tell your teacher about maths in another world, your answer is definitely right in atleast one planet in the universe

    • @wav372
      @wav372 4 ปีที่แล้ว +15

      If universe is infinite then your answer is right on the infinite amount of planets

    • @shimpiyaa
      @shimpiyaa 3 ปีที่แล้ว +6

      1 = 2 is right in our planet.
      Assume 1= 2
      1/0=2/0
      1×0=2×0
      0=0
      LHS and RHS are equal
      Hence proved.
      Infact any number is equal to any number.

    • @shoumikchakraborty3604
      @shoumikchakraborty3604 3 ปีที่แล้ว +8

      @@shimpiyaa Adding one more proof
      d/dx (X ^2) = d/dx(x) + d/dx(x) +d/dx(x) ... x times ....+d/dx(x)
      2X= 1+1+...X times +1
      2X=X
      Dividing X both the sides
      2=1

    • @hamiltonianpathondodecahed5236
      @hamiltonianpathondodecahed5236 3 ปีที่แล้ว +33

      the teacher would be like : then go on dat planet

    • @drbhaviify
      @drbhaviify 3 ปีที่แล้ว +1

      @@hamiltonianpathondodecahed5236 correct 😅😂😂😂😂

  • @shafisaqib
    @shafisaqib 4 ปีที่แล้ว +165

    4:02 If Ramanujan knew infinity that means he considers the outcome value a constant so basically he is subtracting two constants which is not a prohibition.
    *He was not bound by the concept of infinity like we are*

    • @iroh1796
      @iroh1796 4 ปีที่แล้ว +9

      Dude chill

    • @kennethmendoza1709
      @kennethmendoza1709 4 ปีที่แล้ว +42

      @@iroh1796 he seems pretty chill to me lol

    • @stuckonautomatic
      @stuckonautomatic 4 ปีที่แล้ว +22

      It doesn't make any sense, though. Because by treating infinity as equal constants you can just "prove" anything, even 8=0, 5=-2, 999=-123 just by shifting and subtracting infinities.

    • @achyuththouta6957
      @achyuththouta6957 3 ปีที่แล้ว +13

      @@stuckonautomatic The explanation given by Ramanujan doesn't make sense but the value does and it's used in string theory. 1+2+3+4.....=-1/12

    • @neonskie7008
      @neonskie7008 3 ปีที่แล้ว +3

      @@stuckonautomatic but infinity is also a constant,right?

  • @handsomenubian
    @handsomenubian 4 ปีที่แล้ว +10

    Now I'm at home in the curfew I have never thought I would watch a math video and enjoy it like I have just done.

  • @Eric06410
    @Eric06410 7 ปีที่แล้ว +223

    He does this to show off his t-shirt collection

    • @Mathologer
      @Mathologer  7 ปีที่แล้ว +53

      There are easier ways to show off ones t-shirt collection :)

    • @gourabdas8560
      @gourabdas8560 5 ปีที่แล้ว +1

      😂😂😂

    • @wolframalpha8634
      @wolframalpha8634 5 ปีที่แล้ว +1

      😂😂😂

    • @bharthyadav6794
      @bharthyadav6794 4 ปีที่แล้ว

      Lol

    • @sillybears4673
      @sillybears4673 4 ปีที่แล้ว +2

      He is laughed at this comment because all his shirts are awesome and related to the videos usually lol

  • @michaelwinter742
    @michaelwinter742 7 ปีที่แล้ว +114

    Interestingly, this video is the zeta function output of all the videos on TH-cam being added together.

  • @vaibhavtiwari8865
    @vaibhavtiwari8865 3 ปีที่แล้ว +56

    Remember Ramanujan don't have any formal education even after that He was a Genius ❤️

  • @ArigatoPlays
    @ArigatoPlays 4 ปีที่แล้ว +31

    Man, I was really following the video understanding everything, being convinced at the end of this I'd understand the Riemann Zeta function only for you to hit me with that 32:27 lmao

  • @slappy8941
    @slappy8941 4 ปีที่แล้ว +387

    LOL I like the shirt; "JUST OVER DO IT". This describes the German approach to engineering.

    • @Mal-Function4
      @Mal-Function4 4 ปีที่แล้ว +9

      we aren't that crazy... look at the russian uragaan-class guard ships... THEY overdid it on the weight distribution

    • @gladtobeangry
      @gladtobeangry 3 ปีที่แล้ว +10

      True. I used to live close to the german border near Aachen. I remember walking through a park there one time and thinking to myself "what are all these bulky stone monoliths lining the paths?". So I checked. Turns out that it were little lamp posts. If a dutchman had built those lamp posts, they'd have been made out of plexiglass, be covered in birdshit after day one, and be kicked into pieces by vandals after day two, after which we'd decide the park probably doesn't need lights. In Germany, they'll still be attached to the debris of earth when we get finally sucked into the supermassive blackhole.

    • @marlobardo4274
      @marlobardo4274 3 ปีที่แล้ว +3

      @@gladtobeangry love your comment about German Massivbauweise

    • @iaroslavakornach
      @iaroslavakornach 2 ปีที่แล้ว

      hahah just noticed it! I want that t-shirt now

    • @srinathtankasala
      @srinathtankasala 2 ปีที่แล้ว

      @@iaroslavakornach did you find it? could you send me a link to buy?

  • @DustinRodriguez1_0
    @DustinRodriguez1_0 7 ปีที่แล้ว +151

    If given access to a time machine, my first stop would be to visit Hardy when he firsts open and reads that letter from Ramanujan. I can't even imagine what the next few hours and days of his life must have been like. He probably thought he was losing his mind.

    • @Metalhammer1993
      @Metalhammer1993 6 ปีที่แล้ว +27

      Dustin Rodriguez nope he actually read it, showed it colleagues and set everything into motion Ramanujan got financial support and transport to England. Harvey was baffled someone with no formal training could deduce all that. but the content of the letter at best slightly surprised him. the shocker for Hardy was Ramanujans talent

    • @dscruiter
      @dscruiter 6 ปีที่แล้ว +16

      I would have made certain Ramanujan's health would be okay. Then we could have enjoyed his brilliance so much more and witness more math miracles.

    • @tsresc
      @tsresc 5 ปีที่แล้ว +4

      @Tangent of circle. Thanks for giving me the idea. 😉
      I'll teach him a few things in exchange of being my mathematician.

    • @zoetropo1
      @zoetropo1 5 ปีที่แล้ว +2

      Dustin Rodriguez: if given access to a time machine, your first stop would be the explosion when you turned it on. That’s what happens when a backward-going time machine occupies the same space-time as a forward-going one.

    • @chandrasinghrawat622
      @chandrasinghrawat622 5 ปีที่แล้ว +1

      Certainly

  • @priyanshuindra4648
    @priyanshuindra4648 4 ปีที่แล้ว +9

    You always make great content for viewers with your hard work. We appreciate that.

  • @crewrangergaming9582
    @crewrangergaming9582 10 หลายเดือนก่อน +6

    Ramanujan was no doubt a god-send, whose mind formed in such a beautiful way that these came to him out of nowhere. It is spiritual, it came to him by itself, as if Universe conspired to make him aware of these nuances of maths in the Universe.

  • @DaUsher
    @DaUsher 7 ปีที่แล้ว +379

    Therefore, 1 > 1+2+3+4+5+...

    • @chillphil967
      @chillphil967 7 ปีที่แล้ว +5

      You jerk! lol

    • @jimbean4751
      @jimbean4751 7 ปีที่แล้ว +41

      and that's why 0 isn't a natural number :)

    • @bradenweber3654
      @bradenweber3654 7 ปีที่แล้ว +36

      That's only using the Cesaro convergent, which deals with averages rather than sums. Such could make sense in the regular mathematical system of an alien planet, but we decided our system would be different. That doesn't stop mathematicians from find answers outside of our mathematical system though.

    • @fdagpigj
      @fdagpigj 7 ปีที่แล้ว +14

      Unless I misunderstood, the Cesaro convergent only deals with the averages which are still positive, it's the analytic continuation of the Riemann function that gives the sum a negative value.

    • @chizhang2765
      @chizhang2765 6 ปีที่แล้ว +4

      I find the use of word "alien" quite confusing. Isn't it just some sort of fun experiments with maths? Or do they describe actual physical realities in some way, that addition→finding converging point of average of partial sums would actually be useful in simplifying physical equations in certain cases? Please do tell me more. I would be really grateful.

  • @RamirodeSouza
    @RamirodeSouza 8 ปีที่แล้ว +57

    *WARNING*: Ganesha will scare the shit out of you.

  • @garymartin9777
    @garymartin9777 ปีที่แล้ว +2

    the error is the residue term -- infinity -- cannot be subtracted from itself. It is an undefined operation like division by zero. so the method is invalid.

  • @malzcuatro3379
    @malzcuatro3379 4 ปีที่แล้ว +108

    Trying to understand the genius of Ramanujan. Four minutes into the video:
    "Well, Rananujan somehow sees that..."
    I guess not today...

    • @acvarthered
      @acvarthered 3 ปีที่แล้ว +7

      Allow me to summarize. Even geniuses come up with dumb ideas.

    • @salvaalveal3848
      @salvaalveal3848 3 ปีที่แล้ว +5

      Geniuses are always ridiculed for having "dumb ideas", just ask Cantor.

    • @RobBCactive
      @RobBCactive 3 ปีที่แล้ว +1

      He showed the reason for that insight later in the video, where the series was convergent it's simple pattern matching but ignoring the validity conditions

    • @Artaxerxes.
      @Artaxerxes. 3 ปีที่แล้ว +4

      @@acvarthered believe me. You're not intelligent enough to call it dumb. I will readily consider it if Grigori or Terrence Tao call it dumb. Just not you pal. Because there have been plenty of dumb people who ridiculed at geniuses

  • @jwinburn
    @jwinburn 5 ปีที่แล้ว +218

    Ramanujen once wrote just for fun
    that the sum of the numbers from one
    was not aleph naught
    as we might have all thought
    but one twelfth times negative one

    • @calebberhow2203
      @calebberhow2203 4 ปีที่แล้ว +11

      This is the best math poem I have ever read. (Haven't read many, but I had a laugh.)

    • @gaymerjerry
      @gaymerjerry 4 ปีที่แล้ว

      aleph null isnt the sum of all the natural number aleph null is the total number of natural number

    • @petrie911
      @petrie911 4 ปีที่แล้ว +3

      @@gaymerjerry In cardinal arithmetic, the sum of all natural numbers is indeed aleph null. In ordinal arithmetic, it's omega, which is equal to aleph null in the most common formulation of set theory.

    • @gaymerjerry
      @gaymerjerry 4 ปีที่แล้ว +4

      @@petrie911 i dont think you know what cardinal and ordinal means if you said that
      cardinality literally mean sizeof or absolute value while ordinal means ordered lists
      you can have -omega but -aleph null is nonsense
      aleph null is the amount of counting numbers there are while omega is ordering them then adding another one at the end of the list (as adding another one at the beginning of the list still cant really make omega as ordinal infinity is communitive)

    • @gaymerjerry
      @gaymerjerry 4 ปีที่แล้ว +1

      @@petrie911 and also its not called cardinal arithmetic "Cardinal numbers" are a generalization of the natural numbers to describe sets of infinite size in set theory thats it if you ever put on any math test that all natural numbers add to a cardinal number you will get 0 points because the act of adding number is ordinal numbers
      if you were saying you can combine 2 sets to get a larger set you can do that to prove 2 * aleph null = aleph null
      you have the set of {0,2,4,6,8,10,12,14,16,....} and {1,3,5,7,9,11,13,15,...} now according to standard axioms if a set is infinite but can still be made into an ordered list its size is aleph null set one is clearly listed where each term matched to 2x and set to each term matches to 2x+1 and the fact i could put a ... to imply more number further proves its an ordered list so combine these 2 sets of size aleph null creates {0,1,2,3,4,5,6.....} which is the natural numbers which is the set that aleph null is based on but can also map each term to x
      so combining these 2 sets we show 2 * aleph null = 0

  • @HeinrichTsanov
    @HeinrichTsanov 8 ปีที่แล้ว +793

    The elephant god jumpscared me for many times...

    • @KL-sq9hg
      @KL-sq9hg 7 ปีที่แล้ว +64

      his name is lord ganesha well dont say like he is bad i and many more than a billion people around the world worship him

    • @ullqiorracifer9935
      @ullqiorracifer9935 7 ปีที่แล้ว +16

      +Firicious Gaming- Clash Royale and More i dont think everyone in india is a hindu

    • @nalawade
      @nalawade 7 ปีที่แล้ว +26

      around 80 % are

    • @KL-sq9hg
      @KL-sq9hg 7 ปีที่แล้ว +13

      ***** well i said around the world just google it

    • @autodidactusplaysjrpgs7614
      @autodidactusplaysjrpgs7614 7 ปีที่แล้ว +1

      Stimulus and response

  • @UMESHPILANIA
    @UMESHPILANIA 3 ปีที่แล้ว +7

    Ramanujan had Vedic mathematics education, Many Gurukul students still get ancient Indian Vedic mathematics education and they can do wonders, Aryabhatta, Brahmgupta etc have studied the Vedic mathematics, It works on a completely different level, even Prof. CK Raju has researched on this topic!

  • @AshutoshSingh-qt1up
    @AshutoshSingh-qt1up 3 ปีที่แล้ว +10

    'Let C - a constant" the secret lies in this.

  • @PaulKruskamp
    @PaulKruskamp 8 ปีที่แล้ว +153

    I did the maths and came up with 42.

    • @JakeIsEpicHavard
      @JakeIsEpicHavard 8 ปีที่แล้ว

      😐

    • @PaulKruskamp
      @PaulKruskamp 8 ปีที่แล้ว

      EpicGuyRandom you don't get it.

    • @JakeIsEpicHavard
      @JakeIsEpicHavard 8 ปีที่แล้ว +9

      +Dean Thorton no i do 😂 but that is the answer to everything ...

    • @PaulKruskamp
      @PaulKruskamp 8 ปีที่แล้ว +1

      EpicGuyRandom lol, so silly

    • @perryt2039
      @perryt2039 8 ปีที่แล้ว +9

      I did it and came up with 69.6969696969696969696969...

  • @Poor_Vampire
    @Poor_Vampire 5 ปีที่แล้ว +49

    I never knew Ramanujan was SUCH A GENIUS !
    Thanx to mathologer.

    • @u.v.s.5583
      @u.v.s.5583 3 ปีที่แล้ว +6

      He actually could do much much more than this!
      But don't read this comment any further or you will regret it.
      Remember, I warned you. Stop reading this comment.
      Really.
      Ramanujan was such savage genius that he even caught in London Tbc instead of Covid.

    • @gumnaam4302
      @gumnaam4302 3 ปีที่แล้ว

      @@u.v.s.5583 Exactly, the man who knew infinity catches TBC in the heart of the nation that looted and pillaged more than half the world and was still grappling with TBC!! So much for being a pomp regime. Such a shame!!

    • @shubhama891
      @shubhama891 3 ปีที่แล้ว +4

      He actually wrote many formulas and assumptions in last year of his life. Researches are still going on. Many of his formulas are still used to find the black hole😲😲

  • @pramodvora2067
    @pramodvora2067 3 ปีที่แล้ว +8

    Congratulations!! Your attempt at this is indeed very successful. Many many thanks for this explanation both here and other planets!! We know our maths is just an approximation as we are not perfect. If we get enlightened, we will see things very clearly. This is the inspiration to lead the kindly light.

  • @1nd93dk3
    @1nd93dk3 4 ปีที่แล้ว +8

    I reached the -1/12th level of enlightenment

  • @jimmyalderson1639
    @jimmyalderson1639 8 ปีที่แล้ว +18

    It's hard enough learning this, just imagine how hard it was to solve in the first place

  • @HariPrasadindependantphysicist
    @HariPrasadindependantphysicist 8 ปีที่แล้ว +113

    For anyone who wants to know what is the number shown in his shirt (from 16:53 to 26:09), its the expansion of *pi* in base 3 = 10.01021101222201.........

  • @Christian_Martel
    @Christian_Martel ปีที่แล้ว +3

    Mathematics are similar to these granular tests we do at engineering university. Out of a boring standard soil, you’ll always all sorts of gems at every filtering layer…
    From the natural numbers to Ramnujan summations, through fractions, irrational numbers and the complex domain, a wonderful world of discovery!

  • @humanidrome
    @humanidrome 2 ปีที่แล้ว +5

    This video took me on an interesting tour: up the insane-o-meter to the fourth degree, down to the first again, and at the same time up to the fourth level of maths enlightenment. Thank you Burkard & Ganesha

  • @philippedavid0
    @philippedavid0 8 ปีที่แล้ว +39

    Great video, but man you made me jumpscare with those " *BOOM* Elephant speech bubbles" !

    • @mtomazza
      @mtomazza 8 ปีที่แล้ว

      +Philippe David me too

  • @slouch186
    @slouch186 8 ปีที่แล้ว +31

    the sound that plays when ganesh appears to say something keeps startling me

    • @khushnoodnaqvi3793
      @khushnoodnaqvi3793 8 ปีที่แล้ว +3

      +slouch Yes, OP. Pls remove the horrible ding sound.

    • @bonbonpony
      @bonbonpony 8 ปีที่แล้ว +8

      +slouch But it should! You should be scared when doing such an insanely wrong step in the Great Ganita*. The Elephant God is there to remind you of that.
      (*Ganita = Sanskrit word for Mathematics)

    • @pranavzarekar8369
      @pranavzarekar8369 6 ปีที่แล้ว +1

      roar falcon well that's not true

    • @pranavzarekar8369
      @pranavzarekar8369 6 ปีที่แล้ว +1

      the mathematics of ancient india and hindu mythology is actually related to is science , it's just that theories aren't been explained and we are still unable to understand coz it's too fuckin advance for us . the verse of an ancient book contains the distance to sun which was later later found out by scientist .

    • @bongo990
      @bongo990 6 ปีที่แล้ว +2

      Pranav Zarekar you are saying dumb shit here.

  • @Wow-vu8sf
    @Wow-vu8sf ปีที่แล้ว +3

    Thank you for making these really high quality mathematical videos

  • @ATLTraveler
    @ATLTraveler 3 ปีที่แล้ว +7

    You should go over his theory on how to calculate the number of primes within a given integer, this is what really impressed Hardy.

  • @arnabpaulchoudhury8455
    @arnabpaulchoudhury8455 5 ปีที่แล้ว +56

    Lord Ganesha surely knows his stuff... :D

  • @UltraRik
    @UltraRik 7 ปีที่แล้ว +20

    Thank you for teaching us the complex math of blue aliens

  • @TenzinLundrup
    @TenzinLundrup 3 ปีที่แล้ว +6

    I saw the Ramanujan sum mentioned in a talk on quantum field theory.

  • @YEC999
    @YEC999 3 ปีที่แล้ว +5

    The Ganesha animation is like Pixar spent 2 years to make it perfect. It really gives me the chills when she comes.

  • @MemberHomei
    @MemberHomei 8 ปีที่แล้ว +454

    I get a shock each time the elephant god appears! You should have toned it down a bit

    • @bonbonpony
      @bonbonpony 8 ปีที่แล้ว +49

      +MemberHomei One does not simply tone down a goddamn Elephant God :P

    • @keyar87
      @keyar87 8 ปีที่แล้ว

      +Bon Bon Hahaha :P

    • @StrategicGamesEtc
      @StrategicGamesEtc 8 ปีที่แล้ว

      +Bon Bon What about a bugbear? :D

    • @bonbonpony
      @bonbonpony 8 ปีที่แล้ว +1

      StrategicGamesEtc What about him? The mead tasted good ;J

    • @bonbonpony
      @bonbonpony 8 ปีที่แล้ว

      Bhaswar Roy Ki?

  • @Bleubear3
    @Bleubear3 8 ปีที่แล้ว +6

    How did I even get here. Autoplay set me up. I gave it a go, I'm at 16:31 and I give up LOL
    "This makes zero sense to me."
    That's all I've been saying the past couple of minutes. I'll let you mathematicians be. You're doing us a great service.

    • @Mathologer
      @Mathologer  8 ปีที่แล้ว +3

      +BleuBear Well, since you made it to 16:31 you get my seal of approval anyway :)

  • @Nevermind445
    @Nevermind445 2 ปีที่แล้ว +1

    Ganesha appearing with the horror sound is basicaly a jumpscare

  • @xeroxsaw1303
    @xeroxsaw1303 2 ปีที่แล้ว +4

    4:02, I never thought I would ever be jump scared on a math video

  • @pierineri
    @pierineri 8 ปีที่แล้ว +57

    Of course, green aliens have three fingers, that's why they use base 3 ;)

  • @mylord6868
    @mylord6868 7 ปีที่แล้ว +71

    i am hindu and i am totally ok with Ganesh thing, and i am not going to Charlie hebdo office😀.
    btw nice explanation professor👍👍

    • @hank1519
      @hank1519 5 ปีที่แล้ว +1

      A little too soon for the joke, I fear.

    • @DharamG
      @DharamG 4 ปีที่แล้ว +1

      My lord, Who is asking you what you are? U can't give any certificate pretending to belong to a community

    • @BBCBullshit
      @BBCBullshit 4 ปีที่แล้ว +1

      @@deka0014 😂😂😂😂😂😂

    • @alvarogoenaga3965
      @alvarogoenaga3965 4 ปีที่แล้ว +1

      Cool. After all, all deities are probably and possibly products of some people's imaginations.

    • @alvarogoenaga3965
      @alvarogoenaga3965 4 ปีที่แล้ว

      @@wolfx1654 .What are you saying, heathen? No, not my deity. Mine is 100% real.
      J/K

  • @ahmed51988
    @ahmed51988 ปีที่แล้ว

    Finally a video that actually fully delivers on what it promises in a serious way about this topic

  • @BritishBeachcomber
    @BritishBeachcomber 3 ปีที่แล้ว +2

    The real beauty of math is when you reach a dead end when trying to find a proof, you can often solve it by applying a seemingly unrelated field.

  • @AaronBruffett
    @AaronBruffett 8 ปีที่แล้ว +17

    Mathematician Love poetry:
    How do I love Thee
    let me count the ways
    -1/12 ways

  • @carlosffm
    @carlosffm 8 ปีที่แล้ว +6

    It is actually nice to see a video that so elegantly shows the beauty of math, and in such a simple and fun way too, thank you very much

  • @NicholasShanks
    @NicholasShanks 2 ปีที่แล้ว +3

    Those loud bangs when a footnote appears are terrifying when you wear headphones.

  • @smritidipa
    @smritidipa 4 ปีที่แล้ว +53

    I think you should give a image of NAMAGIRI the Hindu goddess on whom "Ramanujam" ( actual name not Ramanujan) had faith.

    • @hello123s
      @hello123s 3 ปีที่แล้ว +2

      @Adarsh Jha it is.. She is a feminazzi.. Who just wants credits for no reason..

    • @stuntxo3968
      @stuntxo3968 3 ปีที่แล้ว

      Correct

    • @anshul6168
      @anshul6168 3 ปีที่แล้ว +1

      He had faith over all Hindu Gods
      In Hinduism you can worship any god but that doesnot mean people who worship Devi dont have faith in Ganesha
      Ganesha is known as obstacle remover

    • @samchaco2
      @samchaco2 3 ปีที่แล้ว +1

      Right? Its so poor research, he actually credits Goddress Namagiri for revelations. How easy would that have been to quote.

  • @AnneoSeneca1993
    @AnneoSeneca1993 6 ปีที่แล้ว +16

    I'm a PhD student in Theoretical Physics and I found this video really helpful and entertaining, thank you so much! :)

  • @swissyodeler6970
    @swissyodeler6970 6 ปีที่แล้ว +52

    4:01 Watch this in a dark room late at night.

    • @shivansh5579
      @shivansh5579 4 ปีที่แล้ว +2

      with that sound its effect is increasing😂😂

    • @joseXPOP101
      @joseXPOP101 4 ปีที่แล้ว

      Doing that rn Chief

  • @teressacooks7928
    @teressacooks7928 4 ปีที่แล้ว +9

    2:43 the most telling and interesting of this entire segment👀! Insight into Ramanujan himself (see graphology) ✍

  • @HDitzzDH
    @HDitzzDH 4 ปีที่แล้ว +8

    7:28 Correct me if I'm wrong, but when it comes to the geometric series the absolute valur of r must be strictly

    • @u.v.s.5583
      @u.v.s.5583 3 ปีที่แล้ว +5

      But now imagine you are doing a hard physics problem and get this sum as the answer, and you know the sum exists. Do you say, no, the sum does not exist, or do you try to generalize the very concept of the sum? Of course, you generalize the concept of the sum, and this is what one does here. College calculus is out at this point.

  • @rajeshkoppa2367
    @rajeshkoppa2367 6 ปีที่แล้ว +95

    True knowledge comes from humblest of origin.....

    • @rosaliacastro1551
      @rosaliacastro1551 4 ปีที่แล้ว +11

      Not necessarily.

    • @KodamatiUdayaPrabhuKiran
      @KodamatiUdayaPrabhuKiran 4 ปีที่แล้ว +5

      @@rosaliacastro1551 necessarily

    • @jovian304
      @jovian304 3 ปีที่แล้ว +3

      @@KodamatiUdayaPrabhuKiran not necessarily.

    • @KodamatiUdayaPrabhuKiran
      @KodamatiUdayaPrabhuKiran 3 ปีที่แล้ว

      @@jovian304
      I guess your name says you are dumb and arrogant

    • @jovian304
      @jovian304 3 ปีที่แล้ว +5

      @@KodamatiUdayaPrabhuKiran Well I know meaning of ur name is sunshine. There's nothing wrong in having name as "sunshine". Just don't judge others.

  • @dance1211rec
    @dance1211rec 8 ปีที่แล้ว +86

    christ sake the elephant keeps giving me a heart attack everytime he appears

    • @Mathologer
      @Mathologer  8 ปีที่แล้ว +20

      +dance1211 Well, it's a long video, so I thought I better have a wakeup call every once in a while :)

    • @AnstonMusic
      @AnstonMusic 8 ปีที่แล้ว +7

      +Mathologer
      Please, no more. I'm afraid of it popping up. :(

    • @Morgalucci
      @Morgalucci 8 ปีที่แล้ว

      I felt a cold shiver through my body into my feet when it first came up.

    • @pronounjow
      @pronounjow 8 ปีที่แล้ว

      +Mathologer It's actually taking me a lot longer to finish the video because I have to take a break to calm myself down every time the elephant shows up, and it's kind of hard to focus because I'm too scared of when the next one will pop up...
      It's also surprisingly hilarious in a twisted way XD !

    • @Asdfghj87
      @Asdfghj87 8 ปีที่แล้ว +1

      +dance1211 agree. @Mathologer: the elephant "boom" noise is way too loud. Thanks for the video though, awesome content as usual.

  • @adharshmanikoth3381
    @adharshmanikoth3381 3 ปีที่แล้ว +17

    When you are such a pro, that you can write whatever you want on the otherside

  • @AdrienLegendre
    @AdrienLegendre 11 หลายเดือนก่อน +2

    Thanks for an excellent presentation. A related area that I am reading about now is Borel-Laplace summation and transseries. It is amazing that Ramanujan uses grade school arithmetic to perform the difficult task to extend the Riemman zeta function in the complex plane to z= -1. Another approach for the early part of the video: f(x)=1/(1+x) = 1-x+x^2-x^3+..., take the derivative df(x)/dx= -1/(1+x)^2 = -1+2x-3x+4x..., and set x=1 so result is 1/4=1-2+3-4+...

  • @SeleniumGlow
    @SeleniumGlow 8 ปีที่แล้ว +21

    The Ganesha entry sound FX is dramatic and scary. I kept spilling my beer every time it chimed.

    • @Mathologer
      @Mathologer  8 ปีที่แล้ว +5

      +Selenium Glow Hehe, so my friend the elephant did succeed in getting peoples' attention :) But seriously, just a bit of an oversight during editing the video to not also limit the peaks of this entry sound just like the rest of the audio.

  • @MahipalSingh-nv1bq
    @MahipalSingh-nv1bq 4 ปีที่แล้ว +45

    whenever such a sum appears anywhere in physics - I explicitly emphasize that not just in string theory, also in experimentally doable measurements of the [Casimir force] (between parallel metals resulting from quantized standing electromagnetic waves in between) - and one knows that the result is finite, the only possible finite part of the result that may be consistent with other symmetries of the problem (and that is actually confirmed experimentally whenever it is possible) is equal to −1/12.
    It's another widespread misconception (see all the incorrect comments right below your question) that the zeta-function regularization is the only way how to calculate the proper value.

    • @maxpower8460
      @maxpower8460 4 ปีที่แล้ว +7

      Hey I'm actually super curious to know more of what you mean! Any source I could dig in more? Can be an academic paper too.

    • @igoranisimov6549
      @igoranisimov6549 2 ปีที่แล้ว

      Last time I heard string theory did not get experimental validation.

    • @irokosalei5133
      @irokosalei5133 2 ปีที่แล้ว +1

      @@igoranisimov6549 R e a d b e t t e r b e f o r e c o m m e n t i n g

    • @igoranisimov6549
      @igoranisimov6549 2 ปีที่แล้ว

      @@irokosalei5133 I am professional physicist for the last 40 years. Am I talking to some kid who likes "anime"? Try doing something else in your life (sorry if I did not space every letter, don't have much time for cool things)

  • @TheJohnskinner
    @TheJohnskinner 3 ปีที่แล้ว +10

    Props to anybody who can understand this type of math , as for myself, I have no idea what’s going on but I watched the whole video,
    Absolutely mind boggling

  • @santisica
    @santisica 2 ปีที่แล้ว +1

    I made it to the end countless times appreciating its beauty.