This is the math equivalent of a diss track.

@goyonman9655

5 жыл бұрын

Math Battle 😂😂

@bilalkhares9337

5 жыл бұрын

loooooooooool

@jaytan531

5 жыл бұрын

Universal Kombat dont you mean -1/12 more important things

@nowonmetube

5 жыл бұрын

Yeah but the only misconception he got is that value = sum Which is not the case. Edit: To be fair, the numberphile video explained it horribly wrong if I remember correctly. They made an updated video called "why - 1/12 is a gold nugged" that one's much better in explaining.

@nowonmetube

5 жыл бұрын

@Multorum Unum 😐

Never I thought I would see the day that a maths channel gets exposed by another maths channel

@chrisven899

4 жыл бұрын

@Mika Hamari Could you somehow explain it to me? I am a high school student and my basic logic skills say that it is impossible to reach a negative result with positive additions. (Also english isn't my native language, so excuse some grammar or vocabulary mistakes).

@chrisven899

4 жыл бұрын

@Mika Hamari So, is there a fault on the calculations?

@ElectroMathExp

4 жыл бұрын

yes they had a contradiction . the series doesn't converges .but they assumed it does converges and they used the properties of convergent series to find -1/12 .which is impossible since we are summing a positive integers . and the correct answer is that the sum approches infinity when n goes larger and larger .but what is more interesting is some how -1/12 is related to the series and it has applications in string theory and quantum mechanics even though it came from wrong assumption

@lupsik1

4 жыл бұрын

Mika Hamari You can disprove convergence of all of those with all basic tests like D’alambert, Cauchy, Integral test and Leibniz for the +/- series, which are tools people learn on the 1st year of technical college. Really scary how few people talked about how flawed the numberphile video was

@supersonicgamerguru

4 жыл бұрын

@@lupsik1 I think the big thing is that the majority of people are divided into two categories: People that have seen this all before in math classes but forgot some of the specifics and caveats, and people who haven't and trust professional mathematicians more than their own intuition. The latter group are the ones that would have been confused and bugging all the other math channels to explain it or something, which is what caused any of this. In reality, the numberphile video isn't "debunked", just properly contextualized and constrained. The issue with people bothering other math channels about the confusion is really the full extent of any damage that could have been done, at least that anybody should care about. If you're taking stuff from a youtube video and using it as the sole justification for anything you do on any math exam or really anything ever, then you have a bigger problem.

I could swear, when I took number theory, one of the first homework problems was proving that the sum of two natural numbers is another natural number.

@spiderjerusalem4009

2 жыл бұрын

how did that go?

@praharmitra

2 жыл бұрын

Two, yes. Finite, yes. Infinite? No.

@scinary7052

2 жыл бұрын

@@praharmitra if 1+2 is natural, then the result, 3+4 must also be natural. It'll always be natural even when you do it infinite times.

@l.w.paradis2108

2 жыл бұрын

@@praharmitra 1. Every partial sum is, by recursion, the sum of two natural numbers, and hence must be a natural number. 2. The set of all partial sums is countably infinite.

@praharmitra

2 жыл бұрын

@@l.w.paradis2108 I don't understand what your point is. Rational numbers are countably infinite. The infinite sequence 3, 3.1, 3.14, 3.141, 3.1415, 3.14159, ... is a sequence of rational numbers and each element of this sequence is a rational number. Yet, the limit of this sequence is pi which is not a rational number. Same goes for the sequence 1, 1+1/2^2, 1+1/2^2+1/3^2, 1+1/2^2+1/3^2+1/4^2,... where every element is a rational number but the limit is not.

39:20 Also; even Ramanujan, for all the formal education he lacked, didn’t call the identity: ”Sum”, in his personal notes. He used the notation: ”c”, for: ”Constant”.

@samueldeandrade8535

8 ай бұрын

Kinda po-tei-to, po-tah-to. But, yeah, was a careful move.

@PC_Simo

8 ай бұрын

@@samueldeandrade8535 I agree. It *_IS_* a kind of a small thing. But a lot of people just want to misunderstand others, and will take any excuse to do so, however minor. That was a careful and smart move, to disarm such people.

Things are heating up in the Math community of KZread.

@pentacles__

6 жыл бұрын

Things about to get lukewarm up in this piece

@proghostbusters1627

6 жыл бұрын

Waiting for Numberphile's response.

@turtle7562

6 жыл бұрын

keemstar and scarce will be all over this in no time.

@CoryMck

6 жыл бұрын

I'm waiting for the disstrack

@doubtfulguest5450

6 жыл бұрын

The maths drama is the best drama. These guys don't mess around. Watch out for the diss equations - they can be savage.

Another way to put this is this: the sum of all positive integers equals -1/12, for very specific definitions of the words "sum", "positive", "integers", and "equals".

@chetricker

3 жыл бұрын

Mainly sum and equals but yeah

@KRYMauL

3 жыл бұрын

Or just use lim x-> 0 x+1 bc 0+1 = 1 the series is divergent.

@baruchben-david4196

3 жыл бұрын

Also, 1/12

@jensrenders4994

3 жыл бұрын

No, only sum.

@90800905675

3 жыл бұрын

Very much agree with this one, context is everything

Thanks. I never understood Numberphile's assumption that an infinite series can have a fixed value like 1/2. It seemed arbitrary to assign a value but the presenter acted like it was self evident.

@raimundomuthemba766

Жыл бұрын

Bro it was so poorly explained it seemed like they were just randomly throwing in series that would conveniently result in the desired -1/2. Laziness and math do not go hand in hand. Ever. Even on KZread... I was fortunate to immediately go into the numberphile comment section and see someone recommend this video.

@osmarfreitas8646

Жыл бұрын

The sum of an infinite series of numbers can be a fixed value if it is convergent (e.g. 1/2 + 1/4 + 1/8 + 1/16 + ... = 1) as the video explains

@osmarfreitas8646

Жыл бұрын

@@candylover6419 search for "sum of convergent series"

@anomaliecosmos

7 ай бұрын

Arguably it is assumable for some cases, because it is *true* for some cases - convergent series, as another reply states. But something does have to be a convergent series for things only true about convergent series to be true about it, so you have to at least have an intuition for whether a series will converge if you don't know for sure - and while my own test isn't 100% accurate, it DEFINITELY rules out series whose terms *increase rather than decrease*. My point being I agree that here was not the place to act like that was a given.

@l.w.paradis2108

6 ай бұрын

You did this in grammar school when you divided 1 by 3 and got 0.3333 . . . and so on to infinity. This means 3/10 + 3/100 + 3/1000 + 3/10,000 + . . . + 3/10^n + 3/10^(n +1) . . . for all *_N_*

man, we really need new video for this "Does -1/12 Protect Us From Infinity? - Numberphile"

Numberphile is like the fun uncle. Whereas Mathologer is the Dad who smacks you on the head and says "get real son"

@MrOllitheOne

4 жыл бұрын

i^2

@aaronleperspicace1704

4 жыл бұрын

@@MrOllitheOne = -1

@MrOllitheOne

4 жыл бұрын

shit just became real

@AlgyCuber

4 жыл бұрын

hey i, get real! i : (grabs friend)

@balsoft01

4 жыл бұрын

In a matter of fact, Mathologer told us to quit being real and start seeing imaginary! It's Numberphile who tried to project the power of complex and imaginary to the simplicity of real, hereby resulting in nonsense.

"For every difficult problem there is a solution that is simple, easily understood, and wrong." H L Mencken

@otoyana

4 жыл бұрын

This sounds relevant only when you don't know who the author of the quote is.

@poogmaster1

4 жыл бұрын

Minakami Yuki What’s wrong with Mencken?

@sottallu

4 жыл бұрын

The original solution is also simple and easily understood by mathematicians of this era. Does that mean that even the original solution is wrong?

@dk6024

4 жыл бұрын

@@sottallu It asserts such "solutions" exist but makes to claim as to which "solutions" those are. It's merely a warning not to be fooled by simplicity.

@patjvr

4 жыл бұрын

Kinda like the opposite of Occam's razor

Having rewatched this for nostalgia:) it really reminds me of early math education in primary school, where you just get told stuff with no justification and even though most of the methods you learn there are common sensical, the point of math is to connect common sense with rigorous logic. And pretending something makes sense out of the blue is a really hard thing to unlearn and i think that sets a bunch of kids up to hate maths. Which is really a sad thing.

@misanthrophex

11 ай бұрын

Not much philosophizing in primary school math though... Some people just don't like math, some people just don't like poetry. Some like both.

@pugsnhogz

10 ай бұрын

​@@misanthrophexI have a BA in creative writing/English and now as a tutor, I also teach marh I can say with confidence that if primary school math involved more "philosophizing," the number of kids who "just don't like" it would drop significantly

@Acetyl53

10 ай бұрын

@@misanthrophex Arguing for uncaused causes.

@scott1564

10 ай бұрын

@@pugsnhogz I would strongly argue it would be the opposite. The mere seconds (if that) of attention span these kids have precludes virtually any form of philosophizing as it relates to much of anything, especially math. Putting that aside, they probably wouldn't get it anyway. These are, for the most part, people who, when presented with math word problems, freak out. I've never understood why anyone would have an issue with word problems, but then again, I've never had an issue with math. I had to study for Calculus, etc. but very little in math classes prior to that.

@One.Zero.One101

9 ай бұрын

The reason many teachers don't explain the equation is because they themselves do not know the explanation of the equation. They just pull out the book and tell the kids to memorize the equations and methods, and this is a very boring way to learn math.

I have a lot of respect for Eddie Woo who also did the -1/12 proof. I knew there was something wrong with his strategy, and now I know exactly what it is. Thank you.

@Entropy3ko

2 жыл бұрын

I just find it a bit dishonest (or very sloppy) they do not specify when the "super sum" (which is called I think Cesaro Summation), which assigns values to some infinite sums that are not necessarily convergent in the usual sense. The term "summation" needs also a big asterisk, since it's not the conventional sum you learn in primary school. In fact it's a swindle... the "Eilenberg-Mazur swindle", hehe

@yasyasmarangoz3577

2 жыл бұрын

I don't think you did.

@andreicecold4379

2 жыл бұрын

@@utkarshsaini5650, not even Ramanujan, it was Euler who first proved it, in the 1700s. This math has been around for years and there are multiple branches of physics-based around it, so if this video was accurate, which it's not, it would be one of the largest revelations for complex physics in the past 100 years

@jacobpeters5458

2 жыл бұрын

mathologer is great. as he points out, the shift in S2 is the culprit. if you did 3S2 where the last line got shifted back to the left, you get S2=-1/4, an S=1/12; also if you shift the 2nd line in 2S2 to the right twice instead of once, you get 2S2=-2S2-1, which also makes S2=-1/4

@hutsku1860

Жыл бұрын

To be fair, he never said that this result was true, at last with the standard definition of a sum. He just redemonstrate the result to make people think about the mathematical logic, never saying if it's true or not

Forget Logan Paul and Shane Dawson, numberphile vs mathologer is the real youtube drama of 2018

@steliostoulis1875

6 жыл бұрын

There is no drama just mistakes

@alephbunchofnumbers

6 жыл бұрын

Don't forget #shitholegate lmao Or rather, don't forget to forget it

@carbrickscity

6 жыл бұрын

Numberphile just made the mistakes of picking Physics professors instead of real mathematicians to present some of their videos.

@frankschneider6156

6 жыл бұрын

The interesting thing about it is that physicists often really don't understand the deep subtleties of the maths they apply, abuse the maths in a way that makes every mathematician cringe, and get out a result, which is exactly in-line with how nature behaves (just think of normalization in QED).

@cunningwolf4516

6 жыл бұрын

DavidSmyth666 so this is what future arguments look like

Your German accent automatically raises your math credibility by 3 points.

@Mathologer

5 жыл бұрын

:)

@AbhijitZimare1

5 жыл бұрын

If it was Asian, it would be +100

@schrodinger6991

5 жыл бұрын

@@AbhijitZimare1 i don' belive you

@user-kx7do4fh2j

5 жыл бұрын

One of my favorite mathemathians is Cantor. He was German. Too bad he died a broken man because he was bullied because of his theory about cardinality.

@paulcasino9511

5 жыл бұрын

I thought it was Indian

The best complex logics/math film I have ever seen. By “complex” I mean “consisting of many, sometimes, non-trivial elements”. If I confess I am awarded Best University Lecturer for many years, it is only to pay tribute to the quality of this film - to keep things so ordered and clear is SIMPLY AMAZING! I do appreciate the apologies for not explaining why complex numbers needed to be introduced (but no fully explained) when analytical functions were being talked about. It gives a lot of security to a lay listener that all vital things were introduced even if no all were fully developed. Yes, the content still can be completely wrong (I am not an expert to judge) but it is certainly “CONSISTENT and COMPLETE” - in contrast to the film it was commenting. The detailed and well paced debate with the statements of Numberphile content were excellent. Well, it was really impressive. I do not subscribe to any channels and social media but believe me, I will be watching you regularly!!! Well done (you know it 😊).

@jceepf

Жыл бұрын

Absolutely agree with you, I am a professional physicist so I can judge this video with some degree of expertise. It is absolutely brilliant. I was wondering how he would justify analytic continuation.... he succeeds even for a high school level educated person in my view. I am still dazed by the level of pedagogical expertise.

@margodphd

5 ай бұрын

I have a slight suspicion who You are, and If I am correct - we might have passed eachother a few times on Madalinskiego. My late father spoke very highly of You. Odd, getting teary eyed under math video, of all things.. With the current level of growing mistrust of science, I am eternally grateful for those smarter than me being on guard for falsehoods. I understand the desire to simplify complex subjects but this is unacceptable, not because it's a mistake -as these happen to best of us, but because it seems to be almost consciously feeding into the "stupid scientists, power to the simple minds, they are hiding truths from you" type of the political climate and I viscerally hate anything that creates artificial divides between people, some of whom perhaps could be lured into the dark side of learning and reason still. Thank You, Mathologer.

@jeffbguarino

3 ай бұрын

Yes but he still assumes induction is valid forever and it isn't . The universe will stop you at a large number. You can't count forever. It is impossible. Physics will stop you from adding "one" to some large number and that will be the biggest number possible. You can't escape the universe.

As someone who holds a PhD in analytic number theory, I appreciate the exposition here. The ideas are clearly presented and give a relatively complete explanation of the phenomenon occurring with -1/12. The explanation of analytic continuation was particularly nice, as this is a concept that's definitely tricky to pin down if you want to get into the technicalities around it. Glad to see some quality mathematics communication concerning the infamous Numberphile video.

@user-yi5cc9wn5c

6 ай бұрын

Can I ask you something?

@joshuastucky

6 ай бұрын

@@user-yi5cc9wn5c sure

*start of video* "This is a serious video so I'm wearing black" *later* Zombie + Human = 2 Zombies

@lokithecat7225

4 жыл бұрын

You forgot; "Und now we discuss Supersum" and switches into Black Superman shirt.

@RalfsBalodis

4 жыл бұрын

One does not simply change t-shirt 4 times in a video and gets away with it... oh wait. He did.

@alexandren.9346

4 жыл бұрын

@- RedBlazerFlame - The Zombie is like an Extension of the normal world: Your mathematical rules don't work here, human! 😈 Or you could say: This is the value you expect. The human is "converted" into a zombie, which actually makes sense

@MsJavaWolf

4 жыл бұрын

@- RedBlazerFlame - Other types don't have the exact same properties as numbers.

@mahmoodemami7466

4 жыл бұрын

Obviously the. Total of positive numbers is not equal to a negative number. There is at least one step wrong . It should be found.

Numberphile on Schrödingers cat: The cat is half dead, meaning it's probably in a coma.

@blizzbee

5 жыл бұрын

poor cat

@Dondala

5 жыл бұрын

thats right what it is, he calculated an expected value, not a sum :-)

@nichitacruceanu9540

4 жыл бұрын

Lmao

@Alex-hj2jd

4 жыл бұрын

No they meant the cat is alive and dead. It was in a state of quantum uncertainty. Unless observed the cat is alive and dead not half dead.

@potman4581

4 жыл бұрын

@@Alex-hj2jd Yes, we know. It's a joke.

With the new numberphile videos, I think this topic needs an update. :D

@ArnavTHR

3 ай бұрын

which new vid

@Tekay37

3 ай бұрын

@@ArnavTHR the one about -1/12 protecting us from infinity.

@v2ike6udik

3 ай бұрын

2i/24, open your mind, open your mind. You live in a hologram. All who believe in infinite series are duped by reps. You know... Tiles. Reps-tiles.

@v2ike6udik

3 ай бұрын

More data after contact. Cant share. ReptileAI deletes.

@v2ike6udik

3 ай бұрын

Dang, already removed even the thing before that. Lets try it bitbybit.

Wow, did not know about the sequence 1-1+1-1… not having a sum. Though it makes sense when u consider that one cannot evaluate oscillating functions, e.g. sinx or cosx, as they go to infinity.

@ScratRedemption

2 жыл бұрын

Indeed. The first thing i thought of when i saw that sequence was sin(x) which has no limit according to calculus.

@mcjon5477

Жыл бұрын

I thought it would be s={0,1}

@vgautamkrishna5197

11 ай бұрын

​@@mcjon5477well sum should be a single value so you can't say it has a sum if it gives 2 different values

@viktorsmets29

2 ай бұрын

That's what we call adherence points. These are points for which there exists an infinite subsequence with that point as its limit.

Numberphile (Brits): It’s -1/12th Mathologer (Germans): Halt mein Bier

@leonhardeuler6811

4 жыл бұрын

*-1/12th

@MattixHQ

4 жыл бұрын

It's '' halt mein Bier''*

@kristoferkoessel4354

4 жыл бұрын

MattixHQ Sorry guys 😂 you get the point...

@kristoferkoessel4354

4 жыл бұрын

MattixHQ wait but halt=stop right? Halte=hold? Or am I just retarded please tell me...

@M3tag

4 жыл бұрын

@@kristoferkoessel4354 Halte would be correct too, but it is more formal, which doesn't make much sense in this context. And Halt also means stop. In English there is a similar relationship of words. If somebody tells you to put something on hold you will probably stop doing something. Or if you are supposed to hold a door open for someone you also stop the door from moving. So Halte makes sense and the person you are talking to will understand you, so it is not a real issue. That rule also does not only apply to Halte. The e is often dropped from the verb, if you are telling somebody to do something, I can't even think of a word right now where it usually isn't dropped

"And this is where Numberphile takes a bow... BUT" - 35 minutes left.

@amogorkon

3 жыл бұрын

...and then the real fun stuff starts!

@user-dg9eb4mc9t

2 жыл бұрын

@@amogorkon ...and then the imaginary fun stuff starts!

@anshumanagrawal346

2 жыл бұрын

@@user-dg9eb4mc9t lol

@RichConnerGMN

2 жыл бұрын

nice pfp

@jakeenvelopes9561

3 ай бұрын

Yeah, I actually couldn't watch it. I'm ten minutes in and all he's done is slag off the numberphile video and it's been boring for a solid five minutes. I'm out.

Wonderful stuff! The second half was way above my mathematical pay-grade, but I still understand much more than I did before. Great work! I had been duped by the -1/12 stuff.

@wideeyedraven15

Жыл бұрын

Dupe isn’t the right word; this isn’t even necessarily a real rebuttal of the -1/12 sum. The result is controversial and this is a good argument against the result (which is counterintuitive which in itself isn’t meaningful). The whole thing, the controversy and the result, are more indicative of the clumsiness, errors and even perhaps uknowability of logic, math and the implicative language of trying to state it. The terms are very slippery and we get strange results in our minds when we try to manage it all. The argument made here is one, a robust and hardy one but it is no more ‘correct’ than other views.

@LeNoLi.

4 ай бұрын

you haven't been duped. -1/12 is a meaningful value assigned to an infinite series. this "sum" is not an actual sum in the traditional sense, but it was derived using real methods. in the context of a youtube video teaching about infinite series, numberphile was correct. in the context of a mathematics course that requires rigor and proper definitions, it was incomplete. we know that -1/12 works because it can be used in real world applications of physics.

@AmorLucisPhotography

4 ай бұрын

@@LeNoLi. This last comment is what really interests me. What does "-1/12 works" or its utility in real world physics tell us about mathematical truth? I have in mind the use of infinitesimals, in Newtonian calculus - i.e., before the introduction of a "limit". These "ghosts of departed quantities" (as George Berkeley memorably called them) "worked" in physics, despite being, at core, inconsistent. This suggests to me that having real world applications in physics really doesn't necessarily tell us much.

@sloaiza81

3 ай бұрын

The irony. You are being duped by thinking that we were duped. Terrence Tao just should that the -1/12 is valid and their is another numberfile vid on it.

@AmorLucisPhotography

3 ай бұрын

I think you misunderstand. By "duped" I mean that I misunderstood something about the proof. I in no way intended to suggest that it is not "valid", in its own terms, but simply that I misunderstood the terms of the proof.@@sloaiza81

This was like one of the first things they covered in undergrad, the series that alternates positive and negative 1 they told us to think about as a digital switch, it's either on (1) or it's off (0) and it can always be made to be in one of those states by adding an extra term but it can never behave like an analogue switch and be in a state that is some measure of two values it takes. Really helped me to understand why its sum cannot be assigned a value. This video made more clear outside of thay intuition.

Y'all so focused on James vs Tati vs Jeffrey while this right here is some high quality tea

@matthewboyea3860

5 жыл бұрын

Thats a quality evaluation, Fonn the Human

@alexwang982

5 жыл бұрын

Quali-tea

@user9287p

5 жыл бұрын

@@alexwang982 Shh.... you are not welcome here. You are not # e^(pi•i) after all.

@torontobud8902

4 жыл бұрын

Omg sisterrrrrr

@ashierapreston

4 жыл бұрын

Jason -e^(pi•i)

You killed my party trick

@christianrasmussen1

4 жыл бұрын

It'll be fine. You can still be an illusionist.

@bhavikshankar3235

4 жыл бұрын

Your part trick is still alive see from 41:15

@RedRad1990

4 жыл бұрын

Matt Parker's card trick, my friend :)

@cdavis7693

4 жыл бұрын

What kind of parties have you been going to?

@kristoferkoessel4354

3 жыл бұрын

Do 1=2 proof

I keep coming back to this video every so often, and each time I am utterly amazed at how intuitive Burkard makes these complex topics. I appreciate that he is so careful with his terminology, and of course his graphics are awesome. It was so cool to have Burkard run down exactly the problems in the Numberphile calculation and how to "fix" them...when he did the transition from the Numberphile S-S_2 to zeta-eta I was blown away; in an instant, he transformed a simple, familiar, but false expression into a deep, rigorous, and true statement, highlighting the "simplicity" and "familiarity" behind things as complicated as power series in the complex plane. Literally one of the best math videos ever made.

I've always had a fascination w/ Euler's infinite summing. I've never been able to reconcile the shifting of the equations to apply basic algebra to rewrite the initial equation (as done in your video) to something more useful w/ other equations when it comes to right before infinity and infinity (The former behaving finitely and the latter not). A sum of integers that approach infinity would seemingly approach infinity faster if each is e.g. squared than if not. So, my basic understanding of HOW every equation that yields infinity just doesn't seem like it's equal to another equation that equals infinity, yet gets there faster. Will you kindly provide some resources that will help understand how this works?

Confused 1+2+3+…=-1/12 comments originating from that infamous 2014 Numberphile video keep flooding the comment sections of my and other math KZreadrs videos. And so I think it’s time to have another serious go at setting the record straight. In this video I’ll do just that by having a really close look at the bizarre calculation at the center of the Numberphile video and then stating 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. Lots of nice 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, some more of Euler’s mathemagical tricks, etc. 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.

@volvoxfraktalion5225

6 жыл бұрын

Thanks for that. I'm not realy mathematicly educated, but i enjoy watching your videos and thank you for clearing that myth out which i myself believed

@dantom5232

6 жыл бұрын

Mathologer what happened to the plain black shirt at start 😁

@Nmmoinn

6 жыл бұрын

Sorry to be a dick but 41.44 minutes /= 41 minutes 44 seconds

@frederickm9823

6 жыл бұрын

Didn't you mean a "series go" :)

@alejandrolopeztobon1643

6 жыл бұрын

Thanks for your video. I regularly watch both numberphile and your videos and love them both. Not being a mathematician but being in science I really appreciate them. Likewise I know that in science arrogance spurs easily and often egos simple don't match even where facts have the reason. I was a bit surprised by the aggressive nature of your video, I just hope you pointed out their mistake directly to numberphile guys before doing this video. I reckon that may have been the case and they didn't took it well and that led to the tone of this video.

"Kids in primary school should be able to follow it!" He should meet my coworkers...

@A_Box

3 жыл бұрын

what is your line of work tho?

@jessers1712

3 жыл бұрын

@@A_Box Physicist, sadly ;'(

@kotarojujo6365

3 жыл бұрын

Jesse Kucharek he should meet me.

@DrCorndog1

3 жыл бұрын

Emphasis on "should."

@segmentsAndCurves

2 жыл бұрын

@@jessers1712 Remember to blink twice.

THANK YOU! The -1/12 meme has gone way too far.

@madlad4206

4 ай бұрын

It's not a meme, it's used widely in physics and maths

@Doeff8

3 ай бұрын

Nonsense comment. It's a perfectly valid evaluation of this series. Mathologer is an annoying pedantist.

@yiutungwong315

Ай бұрын

41:20

So much attention to detail in a long video. Great work

Numberphile: 1+2+3...=-1/12 Mathologer: Impressive, every word in that sentence was wrong.

@danildmitriev5884

6 жыл бұрын

Ohhhhhh yesssss, Star Wars references ^_^

@deadaccount4221

6 жыл бұрын

Mr Banana808 What is wrong with you

@NinjaoftheEnd

6 жыл бұрын

Mr Banana808 Are you an actual banana?

@jesuslovespee

6 жыл бұрын

Francesco Santi his pharmaceutical clock has dilated.

@Jotakumon

6 жыл бұрын

So clearly what you wrote is all non-sense, but damn was it funny to read anyway. My favourite ones: "All scientists think light speed is c in the vacuum, they all wrong." Gee, I wonder what the light speed in vacuum is then... and what letter should we use to represent that value? "Iss is fake, AC systems cannot work in vacuum space" No, Iss is fake because there is no sound in space, so their alarm clocks wouldn't function properly. Get your facts straight. "If heat can radiate into space, [...], the whole universe will be at the same temperature, thermal equilibrium." *long stare* ... sure ... it's called heat death...

Everybody gangsta till there’s math KZreadr drama.

One thing I'm struggling with, which I'm sure I could fix it in my head if given enough time, but I don't! so asking away here. When we take eta from zeta, we seem to just dispose of the zeros. BUT, as this is a divergent series where we are using supersumming as part of these identities, why do we not have to keep the zeros? Thanks in advance to anyone who can offer a lovely answer to this question!

I’m learning data structures and algorithms and came to this video after a teacher told me to check out numberphile’s -1/12 video. So glad I pulled that thread and landed here where you made it all make “sense”. I would have laid awake in bed for far too long trying to wrap my head the bogus numberphile solution.

1+2+3+...=-1/12 is a Parker sum.

@C1Ansy

6 жыл бұрын

Ben McDaniel And that is?

@minerscale

6 жыл бұрын

A funny joke: kzread.info/dash/bejne/k4OIwcSAXdm9qco.html

@benmcdaniel

6 жыл бұрын

When something in math isn't quite right, you name it after Matt Parker: kzread.info/dash/bejne/k4OIwcSAXdm9qco.html

@C1Ansy

6 жыл бұрын

Ben McDaniel Ah, that guy. I recognize him. Thanks a lot.

@Tymon0000

6 жыл бұрын

I LOLed :D

Oh god, mathematical hell is gotta be like 10 times worse than regular hell.

@Mathologer

6 жыл бұрын

-1/12 time worse :)

@skhumbuzocele1330

6 жыл бұрын

😂😂😂😂😂😂😂

@metacylinder

6 жыл бұрын

All you do is math problems there...chilling

@TheLK641

6 жыл бұрын

I would have said pi time worse.

@ilpinto4925

6 жыл бұрын

it is the analytical extension of regular hell

The -1/12 thing always seemed more like a party trick than a genuine maths solution.

Nice to see someone do this. I randomly stumbled across someone still in university (I think an engineering program) bringing up these sums, I think as fun puzzles. I quickly put up proofs of their divergence, I might be a chemist but I was taught well enough to test a series for convergence before running off with it in my math classes (that and the sum of all natural numbers is obviously divergent). I was vaguely aware of non-standard summations such as cesaro sums and brought up that those series can be assigned summation values, but struggled to explain the nuance of the difference between being able to assign a value and the sum being that value. If only I could go back in time and have actually studied mathematics instead of science.

Reminds me of the first time i learned about the dirac delta function in physics. I was basically told "there's some complicated math that proves this is correct but it works and that's all we really care about."

@keineangabe8993

2 жыл бұрын

Well in the case of the Dirac delta, they are at least not giving wrong arguments why it works, do they? Btw: the foundations of distribution theory are really nice imo, worth checking out.

@schizoframia4874

2 жыл бұрын

Not satisfying at all

@davidr1138

Жыл бұрын

I remember loving Laplace Transformation until I found the Dirac Delta function felt like a brick wall.

@thewatchman_returns

Жыл бұрын

Physicists being physicists

@PC_Simo

Жыл бұрын

@@keineangabe8993 And at least they don’t try to change the definitions; e.g., try to pass off Ramanujan-summation as standard summation 😅.

I was watching 8 mile ending rap battles and this came up Not disappointed this is a very mathematical diss track

@XavierDesroches

5 жыл бұрын

Did you end up finishing 8 miles, or was that too much of a diss-track-tion? Alright, I'll go hide...

@Caribbeanmax

5 жыл бұрын

@@XavierDesroches

@realdragon

5 жыл бұрын

This is math war, very brutal war

@crabsynth3480

5 жыл бұрын

Screw nitwit 8 mile crap... this is real rhyme and reason not just random rhyming words by a dumb rapper looking for a pissing contest.

@natevanderw

4 жыл бұрын

Crab Synth whoosh

The way I always explained the "nonsensical" result of -1/12 coming from the Zeta function was this: The original zeta function is defined as the given sum, for only Re(z)>1. The analytically continued Zeta Function takes those same values for Re(z)>1, but is _not_ defined by the sum over its whole domain. I don't know if we know the closed form of the extended Zeta, but that form would relate -1 to -1/12 - and have nothing to do with the 1+2+3... Sum.

The Numberphile video in question seems to violate the principle, "Make it as simple as you can, but no simpler." Simplicity is a noble goal, and I laud those who try to make complex ideas understandable to a wider audience, but simplicity has boundaries beyond which it becomes simplistic or simply wrong.

I can't believe I am just now finding this video. The -1/12 thing has been confounding me for years. Well explained, thank you.

@rygerety8384

2 жыл бұрын

Same here, never made sense to me why all of the POSITIVE, INTEGERS sum to a NEGATIVE, FRACTION. Always seemed completely backwards, and +infinity makes far more sense

@veronicaacevedo4314

Жыл бұрын

Same here!

@lanchanoinguyen2914

Жыл бұрын

@@rygerety8384 (1-1+1-1...)=1 or 0 now 2(1-1+1-1...)=2 or 0 so it is undefined.It could be 0 or another number because it is an infinite structure of conditions.You can say an infinite number is not a number.We calculate base on renormalized numbers. Infinity is not real in real life maybe,because if the world is real so it must be a limited structure of numbers,an well defined number that represents for physics laws. Zeno had said,time or motion is not real and you can't prove he wrong,no mathematics or physics solution can prove the cause and effect work in such a infinite manner.

@ittipongchaisayun878

Жыл бұрын

same here

@l.w.paradis2108

Жыл бұрын

That Numberphile video was nothing short of vicious. I literally hate them for doing that.

The fallacy of the first series reminds me of the analysis of the human race that concludes the average human has one boob and one ball.

@jedinxf7

3 жыл бұрын

lol

@thelickpolice1210

3 жыл бұрын

Underrated comment, that's actually funny as hell, I was thinking of an analogy and this is a perfect one!

@jedinxf7

3 жыл бұрын

that's really just a bimodal distribution situation, not sure if it's quite applicable to the fallacy at work here. but it's funny as hell

@karlkiili1572

3 жыл бұрын

PFFFFFTTTT dang!

@russell2952

3 жыл бұрын

The average human has 9.x fingers and 9.y toes. Averages never claim to represent a single one of the values that went into calculating them. Another good example are population BMIs (body mass indexes) being applied to individuals. It's almost always wrong.

Does he respond to the "little puzzle" at 22:08? He says if we add infinitely many zeroes (and shows the new sum) the super sum is no longer 1/2 - but I worked it out, it IS still 1/2. Did they use an incorrect question to demonstrate their point? Perhaps if they added a 0 after every +1 but not any of the -1 terms, then he would be correct (and it would still be infinitely many zeroes).

@JohnDoe-ti2np

2 жыл бұрын

Good catch! You're quite right. He probably meant to do what you suggested; that would lead to a supersum of 2/3.

@telaferrum

Жыл бұрын

I got the same result. I'm glad I came across your comment. I trying to figure out whether I was missing something but this is the first comment I found actually trying the puzzle.

@jorgenharmse4752

9 ай бұрын

I forget which sum he wrote, but you can make it come to anything between 0 and 1 if you put the zeros in the right places. (Each zero causes a repetition of the previous partial sum, and that changes the average.) I think you can even make it not super summable.

@BenDRobinson

5 ай бұрын

Yay! I had to scroll a long way to find someone who answered this. I quickly concluded exactly the same thing, so I think that is a genuine mistake in the video.

@BenDRobinson

5 ай бұрын

@@JohnDoe-ti2npindeed - perhaps her just mucked up when doing the graphic

Prof. Pulster you are amazing. I learned alot from you. Thanks. 🌹

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

@srimaryati337

4 жыл бұрын

Blananas2 wow a new religion have been born is Math Religion.

@srimaryati337

4 жыл бұрын

Blananas2 wow a new religion have been born is Math Religion.

@hypehuman

4 жыл бұрын

Mathematical Hell = Being doomed to make wrong predictions about the world

@jkellyk7920

4 жыл бұрын

You are tortured with people using 3 for pi and x for sin(x)

@pavanato

4 жыл бұрын

OMG 314 LIKES

In (slight) defense of Numberphile, they did follow up with a much more informative discussion with Prof Edward Frenkel. Some aknowledgement of the flaws in that video that Mathologer is complaining about; the first thing we hear is Frenkel saying with some dismay "Oh... it's /you/ who made that video." He chuckles and shakes his head. Then what follows is some explanation of assignment rather than summing. They are very explicit: "[-1/12] is certainly not the result of summation of these numbers [1+2+3....]. It is something else, but what is it?" kzread.info/dash/bejne/YoOV3MRwebrgkqQ.html

@Mathologer

6 жыл бұрын

Yes, I actually like that video with Edward Frenkel, he is a very good mathematician and really knows what he is talking about :)

@ragnkja

6 жыл бұрын

Lesson learned: Don't ask a physicist to explain number theory.

@TomJacobW

6 жыл бұрын

Nillie I still think they were meming hard and were just joking in that video. ^^

@ExpIohd

6 жыл бұрын

There is also the 'extra footage' video on Numberphile 2 which goes into greater depth of the math on the original- kzread.info/dash/bejne/d2GYm8-gn5usd84.html

@AzCcc

6 жыл бұрын

In this video (Frenkel's @ 10:19), Brady asks "My understanding of Math is it's very rigid and rigorous and it's never arbitrary, how can you throw away the dirt and keep the gold?". This question is the reason why I hated the 1+2+3...= -1/12 from the very first moment. Because that kind of destroys my view of Math (as the only concrete, unambiguous and objectively true tool we have). Mathologer if you're going to make a discussion video about this subject, PLEASE address this question.

I think this brilliant video shows how "math popularization" and "intuition" both have enormous limits. If you get below a certain rigour level, you're bound to make mistakes or say confusing or even totally false thing. Numberphile is a charming and even informative channel, but their format has some downside. When you get into stuff like power series and the zeta function you HAVE to dive into more "formal" math (that is the only math around!).

@marshallsweatherhiking1820

2 жыл бұрын

I think the original video was click-bait. It worked pretty well for that. It never made any sense to write down a bunch of infinite series without giving a solid definition of what you mean by the “sum”. Also, in introductory real analysis you at at least prove as a theorem something that states the conditions under which series can be added term by term. Non-convergent series are not included. The business of assigning numbers to non-convergent series is theoretically interesting, especially when you move out to the complex plane, but its not standard summation anymore.

@l.w.paradis2108

2 жыл бұрын

@@marshallsweatherhiking1820 thank uou

@alvarogoenaga3965

2 жыл бұрын

@@marshallsweatherhiking1820 . This -1/12 business is a more sophisticated trick than the 1=2 " proof"we know from our high school days.

@samueldeandrade8535

8 ай бұрын

... not really.

The thing about maths is that mathematians always care about and give the general case whereas physicists in physics always cares about and give the special case And yes Richard Feynman said something like this

26:14 - "now let's play a game." Me: sweet I love games *Shows a graph* Me: is this some kind of German game that I'm not structured/organized enough to understand?

@irongolem5539

3 жыл бұрын

To some people (like me) gragh (maths) is a game

@nolann2382

3 жыл бұрын

@@irongolem5539 and you're losing

@markopolic9964

2 жыл бұрын

@@nolann2382 You are always losing a game of graphs

Yooooo Mathologer throwing the shade at Numberphile... This calls for a math off!!!

@mheermance

6 жыл бұрын

I think they would prefer a maths off.

@playscirox2129

6 жыл бұрын

Geez that would be a close call, depending who from Numberphile would fight Mathologer.

@awsomebot1

6 жыл бұрын

I've heard "math duels" were the main income source of mathematicians from few centuries ago.

@alexanderf8451

6 жыл бұрын

*sharpens division symbols*

@IllumTheMessage

6 жыл бұрын

Now if we can get the Vatican in on this fight we'll have the scene set for some epic Math Drama!

Hi Mathologer, the last part of how the shaded part equals -1/12 is amazing and as you said no coincidence. Is there some PhD you know that connects the analytic continuation of zeta function with the shaded parts in the negative area of quadratics or polynomials? I am not a mathematician so my question might not be all that coherent. But I hope there is something you can investigate this in a PhD dissertation or even general idea of the complex plan area's connection with the negative part of polynomials or the are of the negative component of symmetrical functions such as quadratics. What do you think Mathologer?

@Mathologer

2 жыл бұрын

Actually this connection is not that hard to explain if you are familiar with some more advanced mathematical tools than the ones I allow myself to use in these videos :)

@kosttavmalhotra5899

5 ай бұрын

@@Mathologer please tell the connection i am gone compleley mad before finding this, but unable to any hint

I just found the number numberphile video yesterday and now KZread recommended this video to me. Thanks for doing this!

Mathematics equivalent of a diss video

@jasonbucy

6 жыл бұрын

haha yes! Mathologer is basically Eminem

@88michaelandersen

6 жыл бұрын

Mathematicians reuse the same symbols with different meanings all of the time. It is much easier to say, here is this idea I am working with, and here is a nice symbol for it, than to come up with a brand new symbol for everything. Numberphile's problem was not putting a disclaimer up saying "Here is the standard meaning for this notation, and here is another idea that uses the same notation, but isn't the same thing." They should have made the distinction clear, instead of not mentioning it.

@___xyz___

6 жыл бұрын

Obviously it's not always a great honour to be corrected in science. Some of the most renowned scientists of all time, including Newton, Kelvin, Edison were all challenged after having reached fame; their ideas about the universe and the contents of papers they had published were corrected, but they refused to accept and acknowledge these discoveries, many of which were ignored for a century before finally resurfacing providing solutions in other sciences. A great deal of this was the fact that basically all people are stubborn and will give in to power and fortune. You can think of it as great scientists being corrupted, or there being little to no difference in science emotionally from other endeavours. If you can acknowledge that you were indeed mistaken in your assumptions, then standing corrected may be a personal honour. But that actually has very little to do with being wrong. Most researchers for instance do not care about being right or wrong at all: providing an argument in the publishing of a discovery is just a formality. Being recognised for posing the right question and having the idea that sparked the study is a much greater honour. And when then someone comes afterwards and points out a mistake in a study you were the mind behind, you are quite simply flattered. Feeling honoured for being dissed in science is the worst pseudo spiritual zen bullshit myth I have to live with. It's just a mindset overrepresented by Hollywood movies.

@hellfrost333

6 жыл бұрын

Math isn't a rational subject: It's a system "we" created based off axioms which are accepted as true. (When a Contradiction occurs in Math- we either correct for the contradiction or avoid doing what caused error) Eugene Wigner wrote a really famous paper called: "The unreasonable effectiveness of mathematics in the natural sciences." *If there is an infinite amount of numbers between 1 & 2 (How do you get to Two?) *If it's Zero degrees outside and the weather man says it's going be twice as cold tomorrow as it is today. (What's the temperature going to be tomorrow? [ 2 x 0 = ? ] ~Not Zero you need to switch the formula. 1+1=3 When a Man and a Women enter a Dark-room- Nine-months later you have Three people... 'Math is litterally the Definition of *close enough;* The Great Pyramid of Giza is the most accurately aligned structure on earth- and it's still off 3/6 a degree True-North. (Rolls eyes) Don't get me wrong- Math is extremely important: Without Math we'd suck at 4th dimensional physics. But there's really only one number and that number is: *EVERYTHING*

@TrickyTrickyFox

5 жыл бұрын

Math is an observational tool, and while yes, we agreed to 1 = one object, 2 = two objects and so on to be the case, it doesn't change the fact that there was two objects in the first place. For your points: 1. Eugene Wigner, while being a wonderful physicist bringing light and joy to people arround the globe by some of his greater projects (sarcasm, obvs), absolutely did that. And he also has several others - "Maths being shit in economics", "Maths being shit in everything" and so on (obvious hyperboly is obvious). Reading through those articles (thank you for bringing it up in the first place, was an interesting read) - I came to a conclusion, that either: A - he is not aware, why does physics need some of the cooler stuff and how mathematics and physics are connected or B - he was just a hater for the sakes of it (especially when it comes to economics one, since Eugene seems to be fairly low knowledgable in the field). 2. By defining the step of your infinity in the first place. The one you mentioned is an uncountable (1;2) infinity 3. Extendanding an example to the concept - is a logical failure on your behalf (or wherever you took the quote from). One guy saying, that it will be twice as cold tommorow, when it is 0 today - isn't really the best example of human brain functioning in the first place 4. That is not really how babies work. If you want to be tehnical - throw in all of the variables (the baby doesn't appear out of nowhere, it has energy consumption throughout the whole process). Otherwise, I will extend your example on two rocks being left alone in the dark room for 9 months - and after that a third rock would magically appear 5. Great Pyramid of Giza - is "close enough" in your statement, not the other way around 6. You wouldn't be able to write your comment in the first place without math. Or watch the video for that matter. Or use KZread. Assuming you'd have Internet to open KZread. And an internet connection in the first place - to your PC, of course, if it'd exist 7. Hey look, I used numbers to make my comment easy to read. When were you born tho? Answer me in everythings please ^^ And also, if 0 degrees outside - you are a flat earther!

I remember explaining how 1+2+3+... diverges in the comment section and people responded that I'm wrong since I'm not a university professor. So thank you very much for this video! Math is about truth, not educational authority.

@Noah-fn5jq

6 жыл бұрын

But... they are! en.wikipedia.org/wiki/Indiana_Pi_Bill (end sarcasm) That was a sad day

@vacuumdiagrams652

6 жыл бұрын

"I remember explaining how 1+2+3+... diverges in the comment section " It does diverge. Everybody agrees that it diverges. The question of what it "equals" is conceptually separate and requires agreeing beforehand on what the word "equal" means. It's not at all true that the only possible meaning of "equal" for an infinite series is that of the limit of the partial sums. That is a choice, one which makes sense in many circumstances, but sometimes you may want a different one.

@fblio7146

6 жыл бұрын

Vacuum Diagrams yes but then one has to make it very clear what equal means in a certain context, especially when the large amount of viewers might not be math students

@ShinAk1raSama

6 жыл бұрын

I'm pretty sure Appealing to Authority is a logical fallacy. So, I wonder why people use it...

@vacuumdiagrams652

6 жыл бұрын

"yes but then one has to make it very clear what equal means in a certain context" Indeed, but this applies to _convergent_ sums just in the same way. When I say that 2 + 2 = 4, I mean something quite different than when I say that 1 + 1/2 + 1/4 + 1/8 + ... = 2. The former is the result of a single addition, while the latter is a statement about convergence and limits. It's a nonstandard use of the equal sign, just like the use in 1 + 2 + 3 + 4 + ... = -1/12 is nonstandard.

S(infinity) only exists when the modulus of the common ratio of elements in a set is between 0 and 1. The set of {1, -1, 1, -1,...} has a common ratio of (-1) between elements of the set and thus has no sum to infinity

This is such a brilliant video. I am so happy I watched it. Initially I wanted to watch it in two sittings but I could not take my eye off it.

I think Mathologer deserves no criticism for this video. I like the Numberphile guys, but in that video, they presented a very misleading argument for the "sum" of these divergent series. The first rule in any, ANY argument regarding series is: "you can make some algebraic manipulations with series ONLY IF they converge". Notice the "IF". This is very important, because, with divergent series, you'll end up with nonsensical results applying algebraic manipulation. Let us check a stupid example. Let us suppose that I don't know if the following two series are convergent or divergent. S1 = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6... S2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6... Now, let us take, S1-S2, which, computating term by term, we get: S1 - S2 = (1/2 + 1/2) + (1/4+1/4) + (1/6+1/6) + ... = 1 + 1/2 + 1/3 + ... = S1 So, S1-S2 = S1, and thus, clearly, S2 = 0. Right?. WRONG. S2, as Leibniz discovered, converges to ln(2). The argument is invalid because S1 is a divergent series. So, my algebraic manipulation is invalid. The Numberphile guys should have made that very clear in the video, saying "these algebraic rules are only valid if the series are convergent. But, we'll be playful, and let's see what strange shennanigans happen if we ignore the convergence criteria". With that disclaimer, everything would be completely fine, but they failed to do so, so they deserve criticism in that regard.

@SparelWood

4 жыл бұрын

And they further state their math is valid because it "shows up in physics." Thats the part that irritated me.

@elasiduo108

4 жыл бұрын

@@SparelWood I think the Numberphile guys were trying to be informative regarding these "strange sums" which appear in advanced mathematics. But, of course, without any disclaimer, these identities are just nonsense. For example, we all know that "S1 = 1+1+1+1... = infinity". In fact, that is the main definition we use to explain people what infinity is!. But, let us again ignore any rules regarding convergence. S1 = 1+1+1+1+1+1+... S2 = 1-1+1-1+1-1+1-... S1 + S2 = 2+2+2+2+2+... = 2*S1 S1 = S2 So, given that we "know" that S2 = (1/2), then, S1 = (1/2). And thus, "infinity = (1/2)". So, even it is true that some process in physics in which the partial sum of a value can be considered "averaged" occurs in reality, but that is NOT an argument for justifying this kind of nonsense.

@MrTiti

3 жыл бұрын

@@elasiduo108 ....... " because it shows up in physics" ...... LMAO.

@Wyverald

3 жыл бұрын

what a beautiful comment, and great counterexample. well said!

@jstodd4398

2 жыл бұрын

This is the best counterexample ive seen

“On my home planet, this symbol stands for S U P E R S U M”

Explained really really clearly to someone with a limited math background, nice job

This video also explains why certain applications in theoretical physics might assume the sum of the positive integers converges. I suspect it might be a consequence of following the statistical approach to calculate the average of values over a set of objects. We do this is in thermodynamics all the time. Great video 👍

Z -> Q loses single representation, Q -> R loses countability of the set, R -> C loses the order of numbers, C -> H loses commutativity of multiplication, H -> O loses associativity of multiplication. EDIT: s/looses/loses/g

@Mathologer

6 жыл бұрын

Cool :)

@swerasnym

6 жыл бұрын

Must admit i had to look up octonions, but had enough knowledge to do the rest!

@GSandSDS

6 жыл бұрын

Why stopping there? We also have the Sedenions. ;) O -> S looses alternativety of multiplication.

@Stefan1of3

6 жыл бұрын

What do we loose going from Reals to Surreals? (Honest question. Those exist.)

@DanielBeecham

6 жыл бұрын

Heyo, cool!

Mathematical équivalent of a diss track

This video gave me hope that maybe, just maybe, maths isn't as crazy difficult as I thought it was

@saptarshidebroy7075

Жыл бұрын

nothing is crazy difficult if you practice enough

@Kfruistik

11 ай бұрын

@@saptarshidebroy7075 and "crazy difficult" things require much more practise. Some people wouldn't be able to comprehend it

Bookmarks: Starts at 2:50, gives explanation of Numberphile’s logic. 5:30 “These three identities are false.” 10:28 Properties of convergent infinite series. 13:22 “Does this prove that M is 1? No.” The series must be convergent (not just assumed to be) in the first place to do this kind of calculation. 16:10 Super Sum properties 19:03 if ANY of these new series converge, the super sum of the original series converges to that. 20:54 RECAP 24:08 Super Sum is more like a super average than a summy sum. 24:45 RIEMANN-ZETA FUNCTION 26:10 “Rough and ready intro” to Analytic Continuation. 30:22 Combining two extension ideas. 33:55 How Numberphile used Riemann Zeta trick. 36:28 the punchline 38:45 wrapping up 40:53 -1/12

@PC_Simo

Жыл бұрын

Thank you for devoting the effort to put up all these bookmarks, it must have been quite a bit of work 🙏🏻🙇🏼‍♂️.

@king_noah_2692

Жыл бұрын

@@PC_Simo I did it just for you

@PC_Simo

Жыл бұрын

@@king_noah_2692 Thank you 😌👍🏻.

**stares at the length of the video** **stares at the fully loaded coffee machine** **unpants** **presses play**

@DanJan09

6 жыл бұрын

unpants? ok, you do you ;P

@AndreiNeacsu

6 жыл бұрын

Panting = breathing quickly. unpanting = not breathing quickly. So, "he unpants" could be interpreted as "he calms down and no longer pants". www.dictionary.com/browse/panting

@DamianReloaded

6 жыл бұрын

Nah I just fap while I drink coffee and think about math. XD

@VeteranVandal

6 жыл бұрын

This is hardcore math.

@JLConawayII

6 жыл бұрын

Do you actually think anybody on the internet is wearing pants?

TOP 10 ANIME FIGHTS OF ALL TIME

@1stPCFerret

6 жыл бұрын

Anime?

@MrPointness

6 жыл бұрын

The strongest attack in his arsenal: Serious Series: Infinite Sum!!

@glowingdawn9179

6 жыл бұрын

respect

@hernandojosedeavilapereira511

6 жыл бұрын

jajajajajaaj

@solarisone1082

5 жыл бұрын

Vegetto vs Buuhan: Mathematics Edition.

for supersums, what if we need an infinite amount of averaging but after that actually converge to a finite number? (would that be even possible?) does that sequence then still have a supersum? thx!

OK so I've been trying hard to understand this concept . Now my level of maths understanding is low , I'll admit but working on the formula mathologer gave using simple graphs and set substitutions I've tried to understand the subject matter . Visually graphically and substitution wise assessing the raw data of the sets step by step my first real problem occurs with the assumption 0,4,0,8 0, is the same as 4a . If you asses the sets graphically you can see the sets S minus S2 step by step creates a line that varies around the S average line in the same way set S2 varies around the 0 line as should be . The set 4S when plotted does not equal the sets S minus S2 the highest possible value for which is 2S and the low points always 0 . So if S - S2 doesn't equal 4S then the calculation falls down . Unless anyone can describe why this should be .

There was a video made by Numberphile called, "Why -1/12 is a gold nugget", where the professor, Edward Frankel, made it clear on what the identity "1+2+3+...=-1/12" really meant.

@Mathologer

6 жыл бұрын

Yes, a very nice video :)

@MDelorean

6 жыл бұрын

Would be fair to mention that video as well. Otherwise the term 'misled' could be partially true for your video. It's clear math videos like to be 0 or 1 :) Great video, my issue is just a small footnote.

@Mathologer

6 жыл бұрын

I link to it and lost of other relevant thing in the description. There is only so much you can say in a video :)

@MDelorean

6 жыл бұрын

Yes, that's also the case with Numberphile of course, but their videos are shorter so they cut (too many) corners. I just like the 'gold nugget' metaphor and wanted your opinion. Maybe you have another (better) metaphor. But like I said before, it's only a footnote in an otherwise very well made video, the effort really shows!

@setha3287

4 жыл бұрын

Isn't that the video that compared the infinity-ness of the series as a bunch of dirt that can be swept away, leaving a gold nugget behind. I found that almost as troubling as the first. It was like an explanation why it's true without explaining how it's true.

"If you've made it this far you know..." I stopped knowing at the 10 minute mark

@constantly-confused5736

4 жыл бұрын

Well, I found it releatively easy to follow along.... then again... I have a math degree ;P

@jamest3828

4 жыл бұрын

@@constantly-confused5736 I'm 14 and I understood it

@alexandrubragari1537

4 жыл бұрын

Me too and i actually like the video and seen until the end and i just completed high school and some shit calculus and algebra from computer science.. Many time i wish i choosed math or phisics instead of cs

@hassanakhtar7874

4 жыл бұрын

@@alexandrubragari1537 rip bro

@1992WLK

4 жыл бұрын

I stopped at the 10 minute mark too. Cause it felt he was done explaining the wrongness. "What else is there? An extra 30 minutes! What the hell... I don't remember signing up for this."

I recently came across a formula that supposedly gives the results to zeta functions analytic continuation. One problem I am having with it however is one term, s! ! If s = a + bi how do you find the factorial to that???

Once again I appreciated this amazing result "-1/12". I wonder how it can be related to the well-known Gauss formula (c ^ 2 + c) / 2 for the sum of numbers in the sequence from 1 to c?

@japanada11

2 жыл бұрын

There is actually a connection! Though it's a bit weird and I don't honestly understand how it works. Start with regular infinite sums. If you plot the sequence of partial sums, it converges to a horizontal line L. Represent this by a constant function f(x)=L. Then L is equal to the average value of f(x) over any interval: 1/(b-a) times the integral from a to b of f(x)dx. This suggests a new, continuous way of averaging the partial sums (compared to the "supersum" mentioned in the video using a discrete average of the partial sums). Now consider the series 1-1+1-1+... It doesn't converge to anything, but you can represent the partial sums 1,0,1,0,... using a wave; for example f(x)=cos^2(pi x/2). If you take the average of this function over any interval of integer length, you get 1/2. The integral in this case cancels out the oscillations, revealing the "gold nugget" middle value 1/2 that the partial sums are bouncing around and trying to reach. Now in the case 1+2+3+..., the partial sums can be represented by f(x) = (x^2+x)/2. So what if we do the same thing? The integral from -1 to 0 of f(x)dx is... -1/12. Again, I don't know a good explanation for why this works, how it generalizes, or why the interval [-1,0] is the right one to use (I would guess it has something to do with -1 and 0 being the roots of f(x) - maybe this roughly corresponds to integrating from "trough to trough" on the previous wave example). But I do know that it's not just a coincidence - there is a real, legitimate connection there that people actually use. Would love to someday figure out how exactly this works.

Excellent video. Unlike some, I don't think you were being harsh. When millions have viewed flawed information, a clear refutation can be seen as a public service.

@Mathologer

6 жыл бұрын

That's the way I look at it :)

@CGoody564

6 жыл бұрын

Agreed. Can't fix a problem if you won't admit there is one.

@screwhalunderhill885

6 жыл бұрын

Thanks a lot for your effort. I saw that numberphile video years ago when I began my studies and it confused me a lot because we've all been told you cannot do anything with divergent series. This video finally cleared things up for me.

@johnblah1234

6 жыл бұрын

kzread.info/dash/bejne/YoOV3MRwebrgkqQ.html

@macronencer

6 жыл бұрын

John Deacon - that is a nicely-worded response, but it is, after all, written from the point of view of a physicist. I understand the points he makes, and he's quite right about the usefulness of analytic continuation - but that isn't the point. The point is that the audience of the video may have been given the impression that such things can be stated without context, as being strictly true. To me, it is clear that summing the natural numbers cannot possibly result in -1/12, UNLESS you state clearly that your context is one of analytic continuation. This is a subtlety unlikely to be understood by a general audience, and the complaint was that this was not made clear. I think this was a fair complaint. I differ from you about the style of Mathologer's video too - I don't think it was unpleasant. But of course, that is subjective and therefore not open to debate.

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

@innamordo

5 жыл бұрын

couldn't agree more about the pot shots coming from the Henchman

@Dondala

5 жыл бұрын

your right, thats not smart, but I understand his point. It is like when Sheldon tries to trap his rage about schrödingers cat.

@MrYourDry

5 жыл бұрын

Couldn't agree more, he should've been dissing with all his heart.

@inyobill

4 жыл бұрын

This is the Mathologer's video, he doesn't have a problem with it, and the videographer actually does contribute.

@tommyvasec5216

4 жыл бұрын

He is contributing, representing you the ignorant public.

God bless finally, I was sick and tired of hearing people try to tell me that adding infinitely positive numbers equals a negative number.

subbed! I love your content

In an earlier Numberphile video, Dr James Grime described S_1 as PSEUDO-convergent, which I think is the most accurate description, since it doesn't *really* converge to 1/2.

@cameronholt4407

6 жыл бұрын

Gimme a link fam I wanna see Grime :)

@ragnkja

6 жыл бұрын

Here's the relevant video: kzread.info/dash/bejne/gnepwaSHfqybqJc.html And here are a couple of other videos he's made on his own channel about infinite sums: kzread.info/dash/bejne/aZp70cuno5rXY9Y.html kzread.info/dash/bejne/lquNsrGiXavMl5s.html

@cameronholt4407

6 жыл бұрын

Thanks!

@samus88

6 жыл бұрын

Then the infinite sum doesn't *really* converge to -1/12... because it just doesn't converge at all. It goes to infinity.

@cameronholt4407

6 жыл бұрын

willprogresivo I agree I'm just here for the maths drama ;)

To all commenters. I'm sorry that this comment is so long and ask you to be patient. The debate in the comment section whether Mathologer is rude/too late/ignoring other Numberphile videos on the subject is making me smile, so I'll put my two cents, too :) Numberphile made a video about a subject which is completely counter-intuitive. So it went viral, to the point that my father, who is 50+ years old electrical engineer, completely unconcerned with mathematics other than that helps to do his job in reality and barely speaking English, and even some medical doctor I went to (knowing that I studied physics), both claimed to me that the sum of all positive numbers is -1/12 ... That doctor even stated that nowadays mathematics is incomprehensible :) That's exactly the point which drives people like Mathologer out of their minds - claiming such counter-intuitive statements without proper disclaimers (I'm not even saying proper context, like Zeta function and analytical continuation). One guy in comments says (I'm paraphrasing) "All natural numbers can be written as a sum of 1s. So, 1+2+3+4+...=1+(1+1)+(1+1+1)+...=1+1+1+1+1... You say that 1+2+3+4=-1/12 and 1+1+1+1=-1/2. So now -1/12=-1/2 ??? " I guess that some people, uninvolved in mathematics, thought to themselves after seeing that video "And these people get paid for that ?" Numberphile should have added only one minute, saying that: "equals sign in these equations should be understood as "is assigned to", not "is equal to" " and "these calculations are not intended as a proof, they merely show what answer is to be expected from more rigorous methods". That's it. Everyone (almost) would be happy. Instead, all we heard was "astounding", "amazing" and "correct". Someone says (I'm paraphrasing) "How dares Mathologer cite Numberphile out of context? Numberphile did two other videos on the subject, which (more or less) address the issues with the first video. Mathologer ignores that. " Mathologer is perfectly aware of this. He even links one of them ("Why -1/12 is a gold nugget") in his description. The reason is simple: view count. The first two Numberphile videos on that subject, which completely miss to point out the crucial distinction between "is equal to" and "is assigned to" have been viewed 7.7 M times combined as of 2018 July. The one which discuses the subject properly ("Why -1/12 is a gold nugget") has been viewed only 1.6 M times. The difference is those confused people inundating comment sections. Another person says (I'm para...) " The goal of Numberphile channel is to make mathematics interesting to wider audience. Don't expect rigour there. Anyone who is wiling to get deeper understanding should follow the links and research themselves." Well, this youtuber forgot that he is commenting in ... KZread :) Content providers in KZread, especially those who want to appeal to "wider audience", should keep in mind "least action principle" - most people these days will spend the least effort to get information. Those who will research seriously, I assume, are those who already find mathematics interesting + small minority newly engaged. Most people, I guess, come there just to see "what interesting video did Numberphile upload today ?" I even suspect that many people rejected the video as nonsense, not wanting to have anything to do with divergent sums anymore, barring further research. All in all, I don't think that Mathologer is rude or incorect, I think he is right on the money (except that cameraman. He should have kept his jokes off-record.)

@adamzeggai5506

5 жыл бұрын

lol

@seacaptain72

5 жыл бұрын

This is the most precise explanation I've read in this whole comment war. Well done.

@Hexanitrobenzene

5 жыл бұрын

seacaptain72 Thank you.

@badlydrawnturtle8484

5 жыл бұрын

1. You fail to actually address the rudeness. There is a clear tone of condescension throughout the video, not just from the cameraman. Who is factually correct is irrelevant to whether Mathologer was rude, which he was, by standard observation of tonality and wording. Your comment rather comes off as ‘I think he's right, therefore he wasn't rude’, which is a nonsense argument. 2. Your argument is essentially that this video is to address misconceptions of people who viewed the Numberphile video and misunderstood it. Meanwhile, this video actually directly tells Numberphile they are wrong, repeatedly. For what? Not being able to control what their viewers say and do? No. You don't get to blame Numberphile for that. Your suggestions for what they should have said may have affected things… but you fail to provide a reason why they would know those suggestions would be necessary BEFORE THE VIDEO WAS MADE AND PUBLISHED. Funny; those suggestions are followed in the other videos that both you and Mathologer handwave away… almost like it doesn't matter what Numberphile does or doesn't do, they're just wrong because of what people watching them do. Either your understanding of this video's purpose is incorrect, or both your and Mathologer's understanding of responsibility is crude.

@Hexanitrobenzene

5 жыл бұрын

Badly Drawn Turtle Hm, on a second thought I guess I gave Mathologer a pass to being condescending, because he is right. Ok, I can somewhat concede this point. However, that first Numberphile video was just doomed to be interpreted incorectly. I believe this was because he was asking physicists to explain it. Physicists are less concerned with nuances in mathematics, and more concerned with applications, which in this case was knowing what number can be assigned to this sum. When Numberphile came to mathematician, namely Edward Frenkel, who has seen the video, Edward immediately understood that the solution was not explaining rigour, details, zeta function and all that, but an abstract meaning of that hapless equals sign. In fact, an advanced physics textbook is shown in an original video, and there is an arrow instead of equals sign. They did not explain that crucial detail which would have made a lot of people happier.

Can you confirm the answer to the puzzle at 22:19 ? The sequence of partial sums is 1, 1, 0, 0, 1, 1, 0, 0, .... The average of these terms converges to 1/2. So the result has not changed with the addition of infinite 0's Am I missing something?

@vincenzo527

2 жыл бұрын

It seems like they made a mistake in stating the supersum of that particular addition of 0s would be different. However, if you add infinitely many zeros is other ways, you can obtain a different supersum. For example 1 + 0 - 1 + 0 + 0 + 1 + 0 - 1 + 0 + 0 + 1 + 0 -... will have a different sum

@seanmacfoy5326

2 жыл бұрын

@@vincenzo527 Really interesting. It seems like you can manufacture any rational m/n, where m < n by judiciously inserting 0s. If you want m in the numerator, add (m-1) 0s after every 1. If you want n in the denominator, add as many 0s as necessary after every -1 so that every period of the sequence partial averages contains n terms (n - m - 1). You'll yield (n-1) sub-sequences that converge to m/n and one partial sequence with all terms m/n.

@BenDRobinson

5 ай бұрын

I reckon he accidentally put the wrong thing in the graphic. As it appears, I'm 100% sure you're right that the answer is still 1/2.

the fact that octonion multiplication is not even associative is just mind blowing. I love math

the answer is 42

@tsresc

5 жыл бұрын

That's the answer for everything+nothing. 42=(-1/12)+X. So the value of nothing is 503/12. Yeah, I discovered the value of nothing. I'm starboy mathematician. Yay! Bingo! Allons-y! Eureka! Ola! Yo! THICC!

@samt1705

5 жыл бұрын

What was the question though? 😃

@the_luna_lily6234

5 жыл бұрын

Sam T everything 42 is the answer to life

@aidankhan6194

5 жыл бұрын

@@samt1705 it's a reference to hitchhiker's guide to the galaxy. There's actually people who try to prove this.

@samt1705

5 жыл бұрын

@@aidankhan6194 just what I expected it to be.. Thanks!

Teacher: “What’s 1+2+3... forever?” Me: “Infinity” Teacher: “Wrong. It’s -1/12” Me: *_”DID I STUTTER.”_*

@grantorino2325

3 жыл бұрын

MY AUNT: But, the way that I calculated it, you owe me money for my purchasing all of this. *Everyone stares at us.* ME: Please excuse my dear Aunt Sally.

@rohangeorge712

2 жыл бұрын

you may me 10000000000000000000000000000000000000000000000000000000000000000 dolllars. i tell u to keep giving me money and i will pay u back. soon enough i keep getting money from u infinitely and i say it can be represented by 1 + 2 + 3..... and he is like yea whtver give me back my money. and i say nope, i owe u -1/12 of a dollar, which means u owe me 1/12 of a dollar GG (ps: ty for all the money hehe

@PlatonicPluto

2 жыл бұрын

@@grantorino2325 :O

@roseCatcher_

Жыл бұрын

This video proves you wrong too.

@NTNscrub

Жыл бұрын

@@roseCatcher_How so?

Never doubt someone who explains math in a german accent.

@grantorino2325

7 ай бұрын

Indeed! Just keep him safely away from his stupid sister, DeeDee. 👱🏻‍♀️

If you insert an infinite 0 into the series and calculate the super sum, you can get an average that converges to 0 if the amount of zeros is sufficiently greater than the amount of positive/ negative values of that series, which could converge to a different value.

@jorgenharmse4752

9 ай бұрын

Starting with 1-1+1-1 ..., inserting zeros in the right places can make the super sum come to anything between 0 and 1 (inclusive), since you effectively choose how much the two possible partial sums are repeated. I think you can even arrange to have no super sum by inserting increasingly large blocks of zeros.

@BenDRobinson

5 ай бұрын

I'm scrolling through the comments to see if anyone answered the puzzles he set, because I had a quick think about the one he asked about the super sum of 1+0-1+0+1+0-1... he said the super-sum is not = 1/2, but I'm quite sure that it is. Mind you, he didn't exactly say that the inserted 0s are every second element of the new version of the series, but said "if we insert infinitely many 0s, _like_this_", and the fact that he posed the question as though there was a fixed answer suggests that we can assume that pattern continues.

@BenDRobinson

5 ай бұрын

@@jorgenharmse4752 I think you're right on both counts. (Which is pertinent to my other comment.) I doubted your second conjecture at first, but it does make sense. If you keep adding enough 0s while the partial sum is on 1, you can drag the cumulative average up as close as you want to 1, and then likewise down arbitrarily close to 0 again while the partial sum is on 0. Then again, maybe the fact that you get to keep iterating the averaging step an unlimited number of times defeats that strategy. I suspect that for any finite n you could put in enough zeros for the first n iterations not to converge, but you might not be able to ensure it forever with a fixed choice of inserted zeros.

@jorgenharmse4752

5 ай бұрын

@@BenDRobinson I agree that my conjecture is not obvious. I said 'I think' because I was too lazy to try to write a proof at the time, but here it is. The original sequence of partial sums is just 1,0,1,0,1,0,1,0,... . Padding the summands with zeros gives us blocks with no change, e.g. 1,1,0,1,1,0,1,1,0,..., for which the long-run average is 2/3. Once you have a convergent sequence, repeated averaging just gives you more sequences that converge to the same limit. Can we make the blocks grow fast enough to avoid convergence entirely? Consider an eventually-constant sequence a_1,a_2,...,a_m,c,c,c,c,c,... of real numbers. However large m may be and however big the absolute values of a_1,...a_m, the limit of the averages is c, and any amount of additional averaging gives us the same limit. Averaging slows the convergence, but for any k we can pick n such that for every average up to k-th order the (m+n) position has a number that differs from c by at most 1/k. Now consider any sequence that starts with a_1,a_2,...,a_m and n occurrences of c (in that order). Anything after the (m+n) position has no effect on the repeated averages up to that position, so the (m+n) positions for all averages up to k-th order still have numbers that differ from c by at most 1/k. Now consider a sequence with n_0 occurrences of 1, n_1 occurrences of 0, n_2 occurrences of 1, ..., n_2k occurrences of 1, n_{2k+1} occurrences of 0, ... (in that order), where n_0=1 and n_k is determined recursively so that all averages up to k-th order have in the (n_0+n_1+...+n_k) position numbers that are within 1/k of the constant in that block. For every k, the k-th order average has inferior limit equal to 0 and superior limit equal to 1, so it doesn't converge.

Of course the - 1/12 meme will be the first video of the year

@LaTortuePGM

6 жыл бұрын

yeah. of F*CKIN' course.

@LaTortuePGM

6 жыл бұрын

oh no, not mohamed adibou.

@guy_th18

6 жыл бұрын

is it a meme? where?

@steliostoulis1875

6 жыл бұрын

Guy in KZread. Facebook and among mathematicians

@kel000001

6 жыл бұрын

At least if one of us owe a numberphille fan an infinite amount of money they’s pay us 1/12 bucks back

Thank you for explaining analytic continuation in an actually good way. I've seen so many math KZreadrs talk about it and every time it boils down to "the most natural extension of a specific function," which, I imagine, would leave many questions in the audience's head. I can see myself understand this when I didn't already know what analytic continuation or any kind of analysis deals with. Really shows why derivatives shape a function which is not traditionally defined. Great job!

@General12th

6 жыл бұрын

3blue1brown defines it pretty well. It's most natural because the derivative is constant and it preserves angles.

@jbiasutti

6 жыл бұрын

The exact definition of the analytic continuation is that the value and derivative of the function is the same as the data given at all point.

Unlike the previous times I watched this video, I managed to understand convergent vs divergent series, and basically understood everything up to the Zeta function. Now I'm watching just trying to understand xD

When the numberphile guys said "so this series alternates between 1 and 0, so the sum must be 0.5" I was like, "what, no, it doesn't work like that", but since I only have 'high school' maths and they're professors, I went along with it. I am feeling relieved and validated now that youtube has recommend me this. I'll be honest, started to struggle to follow around the zeta/eta part, but at least thanks to the first half of this vid I can rest assured the 0.5 thing was indeed nonsense

@tomsvoboda2309

2 жыл бұрын

One can do all kinds of stuff with the Grandi's series, for example I can make it equal to 1 by writing 1-1+1-1+... = 1 - (1-1) - (1-1) - .. = 1 + 0 + 0 + .. = 1 and I can take it even further and make it equal to any number X by writing 1-1+1-1+... = (1-1) + (1-1) + .. = 0 + 0 + ... = (X-X) + (X-X) + ... = X - (X-X) - (X-X) = X - 0 - 0 -.. = X This series is actually the most profound counter example for unjustified arithmetic operations with infinite series. It's one of the first things a math major learns in the theory of infinite series. It's incredible how dishonest that Numberphile video was in that regard.

@LifeInZadar

Жыл бұрын

This reminds me of the story the little engine that could. Gotta have some faith in yourself. Be a fucking Zaibatsu.

He switched his t-shirt while he was talking, thats what I call a mathemagician (5:31)

@RationallySkeptical

4 жыл бұрын

Know where most magicians are born? Magichigan.

@pranavlimaye

3 жыл бұрын

@@RationallySkeptical *M A G I C H E L L E O B A M A*

@BlastinRope

3 жыл бұрын

M A G A (?)

@the.invincible.9542

3 жыл бұрын

He's wearing four different T-shirts in the video.

@seanwickham8905

3 жыл бұрын

@@RationallySkeptical Unibomber?

I get scared everytime he laughs :(

@inyobill

5 жыл бұрын

Funny, I find his laugh charming. Different strokes, and all that.

@Spathephoros

5 жыл бұрын

Hilarious

@teukkaboy

5 жыл бұрын

@@Spathephoros Seems like to some people it was

@chrisprilloisebola

5 жыл бұрын

lol

@dannygjk

5 жыл бұрын

Don't worry, (unless he is holding a big knife).

Can the second identity, where the partial sums alternate between increasing positive and negative values, equal to unsigned infinity, as in the real projective line

Interesting. How one can justify the need to shift one bottom term to the right ?? (quote 4:08 video time) It seems to me to do so is somehow *tricky*

People taking this video as offensive have little respect for mathematics. In the mathematical community proofs must be truths not follower fights in terms of what channel i like better. The way is presented may get some angry but the proof seems to be correctly developed

@oenrn

6 жыл бұрын

Welcome to the snowflake generation. Where the truth doesn't matter anymore, only if you "hurt people's feelings" (TM)

@TheVergile

6 жыл бұрын

the problem is not his proof, but something no serious scientist would do: quoting parts of someone else work without considering the other half of their work. Numberphile themselves added two more videos to their introductory video which went viral. In these videos (esp. "why -1/12 is a gold nugget") they explain in more detail how -1/12 actually differs from a convergent sum and why it is still meaningful. What Mythologer does here is quoting and attacking (yes attacking. The headline of this video and the way it is presented is sensationalist and honestly a bit disappointing, since it is in general good content) part of someones work, ignoring other parts completely. Especially if the part of work you quote is a video made to introduce non math-PhD people on the internet to interesting and "mindblowing" concepts in mathmatics.

@WitchidWitchid

6 жыл бұрын

But it's not the right answer. The correct answer is that the infinite series 1+2+3+4+... is divergent. It does not converge to -1/12. This is what Mathologer has pointed out. If an infinite series diverges it diverges. Stating "it diverges" is stating the correct answer.

@WitchidWitchid

6 жыл бұрын

In a mathematical context it's not an attack nor is it sensationalist.It's only an attack if one is defending a channel or brand.

@WitchidWitchid

6 жыл бұрын

I am not basing my conclusion on intiuition but rather on regular summation. If we derive an expression for the partial sums of 1+2+3+4+... (i.e. Sn=n(n+1)/2 ) we find that the partial sums get increasingly larger as n->infinity thus the series is divergent with respect to regular summation and is a valid and correct answer. If we use zeta function regularization (i.e Reimann Zeta function) / Reimann summation we can assign values to otherwise divergent summations. Applying such techniques we can indeed correctly answer 1+2+3+4+... + = -1/12. Such results have value and meaning in Physics and I stand corrected in my assertion that it is the wrong answer. n the contect of regular summation however we find ever increasing partial sums and we conclude the series s divergent which in this latter context is correct although not particularly useful if you're a Physicist. :) Nonetheless 1+2+3+4+5+6+... is divergent is correct with respect to it's regular sum which is proven when we look at the limit of the expression for partial sums S = n(n+1)/2 as n-> infinity which is clearly divergent therefor 1+2+3+4+5+6+... is divergent. Q.E.D.

"Do not use it, or you will burn in mathematical hell!"

@OHYS

6 жыл бұрын

StarlightVisual 200th like

@Japan_C2

6 жыл бұрын

it is used in string theory

@NICK-uy3nl

6 жыл бұрын

Major Homer - The string theory is a bunch of nosense

@Japan_C2

6 жыл бұрын

NICK .....so says someone who can't spell

Analytic continuation is completely determined, _provided_ some conditions are met. The new domain must be specified, it must be a connected open set, and an extension must exist. For example, the logarithm cannot be complex-analytically continued to the complex plane, even after you throw out the obvious singularity at 0. You need a branch cut from 0 to complex (unsigned) infinity, and the values depend on how you choose the branch cut.

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