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How does adding positive numbers turn negative?
Edit: after some quick googling apparently in this case "=" doesn't mean equal in the classical sense and means something else that people argue about to this day.
https://youtu.be/w-I6XTVZXww?si=dTIwd0oKtDAWt6nX
Spoiler alert: it really doesnt, but the -1/12 result for some weird reason still has some use in certain physics calculations for some reason
Not a one time calculator boy, so cant really explain further
This video has a more approachable explanation of why it's useful even though it's not purely accurate.
[https://www.youtube.com/watch?v=Z9S\_wUqLpv0](https://www.youtube.com/watch?v=Z9S_wUqLpv0)
Ok, I'm not a math guy, but how would that work?
I stopped after the S2 part.
How can you claim it is 2S2 when you are adding S2 and S2, but decide to shift how to add them together?
Let's pretend S2 isn't what they use but is instead S2 = 1 + 5 - 2 + 8. S2 = 12
I can't say that 2S2 would be
1 + 5 - 2 + 8
\+ 1 + 5 - 2 + 8
So is 2S2 = 1 + 6 + 3 + 6 + 8 = 24
Jesus fuck... how does this work?
EDIT: What if I have multiplication?
x = 5 + (8 * 3) = 29
2x would be:
5 + (8 * 3)
\+ 5 + (8 * 3)
5 + (13 * 24 * 3) = 941
or would it be 5 + (13 * 24) + 3 = 320
Either way it doesn't work with multiplication.
Ok, so this is just some trickery since it works with simple addition and subtraction since you're basically just adding and subtracting the same numbers but in a different order.
The proof relied on the fact that 1 - 1 + 1 - 1 + 1... = 0.5 was true, which it isn't. (Can't assign a value to an infinite series that doesn't converge)
Ramanujan made a logical mistake in his argument because he assumed two sets to be equal that weren't but the concept of that wasn't really invented yet and the kid was a genius either way.
>How does adding positive numbers turn negative?
It's a 'proof' that treats infinity as a real number. That's actually a violation of real numbers, and so it produces contradictory results.
In this case, I think it relies on things like the series 1 - 1 + 1 - 1 + 1 - ..... to equal 1/2, when it should be considered 'divergent' and not used in other calculations.
it doesnt, but its a bit of an anomoly that makes logical sense under particular definitions of a sum. and if you are into math it's very very fascinating.
there are a lot of you tube videos explaining it
https://www.youtube.com/results?search_query=The+Ramanujan+Summation
and the concept behind it does have real world uses.
Not exactly. Or, well, not universally. Without getting into it too much, if you have a series with both positive and negative terms, it can be what's known as either absolutely convergent, or conditionally convergent (assuming it's convergent at all). An absolutely convergent series is one that converges even if all of the terms were positive. A conditionally convergent series is one that diverges if all the terms were made positive.
For a conditionally convergent series, what you describe is correct. In fact, for a conditionally convergent series it is possible to rearrange the terms so that the series converges to any number that you want.
However for an absolutely convergent series, any rearrangement of terms will result in the same limit, and thus commutativity still applies
I love your explanation.
It's also a bad joke because in order for this to "work," they can't be "done"; they would have to literally be ordering beers forever.
The moment someone stops ordering a beer, there is a very positive, real number to deal with.
The joke could be salvaged:
In a bar, a pint of beer costs three dollars. The broke math department hatches a plan for how they can afford to drink all night.
The first mathematician asks a pint of beer
The second mathematician asks for two pints of beer
The third mathematician asks for three pints of beer
And so on.
The tenth mathematician stumbles up to the bar and slurs “look, we can come back tomorrow and keep doing this forever or we can quit now and you can just give us the quarter”
Just have each one order in half the time as the previous one.
edit: In case anyone is wondering, 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... = 2
so if the first person orders, the next person orders 1 minute later, the next 30 seconds later, the next 15 seconds later, etc. then they will have ordered infinite beers in 2 minutes.
Heey... Did u/[Sangorieur](https://www.reddit.com/user/Sangorieur/) post this question as u/[titickee](https://www.reddit.com/user/titickee/), to answer his own question and look smaht?
theres a famous thing in mathematics that states 1 + 2 + 3 + 4 + ...... up to infinity = -1/12, so if there are infinite mathematicians who pay for a pint more than the previous, then the sum of all payment is 3 × (-1/12) which is -1/4, so the bartender owes them a quarter
Can we not simply prove that -1/12 is bullshit by taking note of 3 basic facts, them being:
1. addition of positive numbers leading to another positive number that's bigger than both of the previous numbers
2. Only addition of positive numbers is happening
3. The pattern never breaks
How do math guys refute that?
It doesn't actually equal it in the conventional sense. However, there's a function called the Riemann Zeta function that is given by ζ(s) = sum from 1 to infinity (1/n^(s)). Its trivial to see ζ(-1) is the sum of natural numbers, but plugging it in we find ζ(-1) = -1/12 because of something called analytic continuation.
it’s literally never mentioned and this is a seriously niche joke. A normal person could never draw that conclusion, and in the non-mathematical world this joke makes absolutely no sense.
Edit: my issue isn’t that this joke is niche, that’s what this sub is for, it’s the dozen or so people pretending it’s more well know than it should be.
Not everyone is in stem or took calculus in high school.
This reminds me of my favorite joke:
What do you get when you cross a mosquito and Tenzing Norgay?
Nothing because you can’t cross a vector and a scaler.
Vectors and scalers are both used in math/physics. Scalers only have magnitude while vectors have magnitude and direction. You can’t cross multiply them ( don’t worry about it.). A mosquito is a vector (something that transmits) disease and tenzing Norgay was part of the first two men to scale mt Everest along with Edmund Hillary.
Mosquito = disease *vector*.
Tenzing Norgay = famous mountaineer, or "scaler". (Fish and lizards have scales, but "to scale" also means "to climb".)
"Vector" and "scal**a**r" are distinct types of data. Without getting into fine detail, they are essentially apples and oranges. They can't be used with each other.
[A more in-depth explanation of vectors and scalars here.](https://www.physicsclassroom.com/class/1DKin/Lesson-1/Scalars-and-Vectors)
It's funny, though I find homophone-based jokes less clever than ones that work as well when told aloud or in print. Probably that's just me.
The Zeta function itself cannot even take -1, exactly because it does not make sense. It just so happens that the analytic continuation of it yields -1/12 at -1. This also has implications in physics afaik.
“The value \(\zeta(-1) = -1/12\) shows up in physics in interesting ways. Think of it like finding hidden treasure in math that helps explain the Casimir effect—where empty space between objects has energy. It's like discovering that seemingly empty space has a secret force, which we see in quantum mechanics and has been proven in experiments. So, even though it sounds weird, it’s like a hidden key to understanding the quantum world.”
It's used a ton in string theory. A lot of string theory textbooks include that -1/12 equation in chapter 1 and are basically like "when you run into this infinite summation, use this value!"
But no, I don't know of a real world use 😂
That conclusion relies on using algebra in an environment where it's rules aren't really defined. It's like solving a problem by treating division by zero as being zero, then getting incorrect results.
If you add all the positive integers together then it just goes off to infinity and you don't get a real answer.
If you force math to give you an answer anyway then you get -1/12
It's usually not explained very well. If you add up all the numbers 1 + 2 + 3 + ..., it diverges (i.e., the sum gets bigger and bigger without approaching any specific finite number). However, if you assume (falsely) that it does approach a specific number and do the calculations to find said number, it turns out to be -1/12.
This is true but that doesn’t mean there aren’t other meanings of “=“ and methods to arrive at the -1/12. One of the million dollar math questions is actually to find all non trivial 0s on the goofy graph of the Riemann Zeta function, which is one way people get to -1/12
Some people would say that it's an incorrect application of math resulting in an invalid result.
Others would say that it's not incorrect, that math is just the consistent application of rules within a given context used for calculation and that this is just that, similar to how people called imaginary numbers invalid when they were first invented.
However, to directly answer your question:
When summing ALL positive integers, using the same logic you gave the result cannot in itself be a positive integer as that would have been included in the summation itself. So perhaps, in some specific contexts, the idea that it results in something other than a positive integer (say, a negative fraction...) isn't so insane.
Well technically that wouldn't be enough for a formal proof, as patterns that work up to X sometimes do break, even for very large X. That said, in your case it wouldn't be hard to make this into a proof by induction, but I'll leave that as an exercise for the reader.
Anyways, given such a proof, mathematicians will sometimes keep working on the system anyways. Normally working on a nonsense system only leads to more nonsense, but good mathematicians can eventually formalize some nonsense systems into things that have meaning, and sometimes those formal systems end up being useful. The most common examples are negative numbers and imaginary number. If you have 1 apple, you can't eat 2 apples and have negative one apple. Yet you are so accustom to negative numbers you likely don't even see them as weird. Imaginary numbers are even weirder and most still see them as weird, but they are surprisingly useful. There is even the imaginary number of imaginary numbers, the quaternions (it repeats infinitely but gets less useful each time).
Kinda like there are formal systems of math that consider numbers bigger than infinity. Weird, but sometimes useful for solving problems. For an example, consider that there are different sizes of infinity. Sometimes you can ask a question about a function that maps from one set to another and by showing the domain of a function is a smaller infinity than the range of the function it works as a proof that the function in question doesn't exist.
Sometimes math gives nonsense results that don't make sense. Those results can usually be ignored in most scenarios. For example, imaginary numbers or negative numbers out of square roots are technically correct but usually ignored.
This is a pretty similar result, where the -1/12 result can be usually ignored but is technically a possible answer.
No, there's plenty of theory in mathematics handling complex numbers. The complex numbers are necessary to define a set over which all roots of polynomials are defined. It's physicists and engineers who ignore complex numbers when they try to solve physical problems by using mathematics - unless those complex numbers actually prove useful (e.g., Landau damping, conformal mappings for aerodynamics, etc.)
In fact -1/12 is bullshit, it is a famous example that shows you can't manipulate infinite series using the same methods used for finite ones i.e. the associatovity of addition
It is not in fact true that the sum of the numbers from 1 to infinity is -1/12 -- the sum of all the numbers from 1 to infinity diverges (i.e., it has no sum), exactly as you'd expect.
But, suppose you you want to find a more general notion of "summing" that gives values to divergent series? (I'm not sure why you'd want to do that. Mathematicians have lots of time on their hands, I guess.) In that case, it turns out that the -1/12 thing pops out naturally, in a way that other numbers don't. So while "The sum of all positive integers is -1/12" isn't correct, it might be a bit more correct to say something like "The sum of all positive integers isn't anything, but if it *were* anything, it would be -1/12."
[Here's a useful explainer video](https://www.youtube.com/watch?v=YuIIjLr6vUA) that goes into a lot more depth but is nonetheless pretty accessible.
The why is that mathematicians are always looking for new systems of math even when we don't have a problem that fits the new system. There have been cases where it took decades for some seemingly nonsensical field of math to find a real world application. Sometimes it might never be useful, but those times are made up for by the times it is useful.
Legend has it that someone once had to do a math PhD on how water would behave on a completely submerged planet.
Bullshit functions came out that describes how waves would form and where every crest and trough would be once you took interference patterns into consideration.
Functions were lost in time, until some obstinate, Danish physicist decided that maybe electrons weren't particles, but instead behaved like probability functions.
All he needed to explain molecular structure turned out to be some bullshit math that described how water-like functions behaved on a completely submerged planet.
And hey presto, quantum mechanics became a thing.
Fuckin smart people posting links n shit.. I was ready for bed an hour ago, but here I am coming back to say thank you 40 minutes later... Didn't understand half of that video, but I do know more because of it.
Neat video, thank you for sharing.
There's a numberphile video about it.
Iirc, you do have to jump through some hoops. I think at one point they talk about the infinite series 1 - 1 + 1 - 1 + 1 - . . . to infinity. What's the sum? 1 or 0? They say one approach might be to call it 0.5 as the average between the two. Using 0.5 as the answer, you can do some tricky substitutions and get whacky results like finding that the sum of all the natural numbers is -1/12
I should note that saying that 0.5 is the answer isn't just derived from taking the average. If you say that infinite series of adding and subtracting 1s is A and look at adding A + A, you could do that by pairing the nth term of A with the n+1th term of the second A. So you get 1 + (1 - 1) + (1-1) + .... to infinity which it turns out gives you 1 + 0 + 0+ ... and so you've shown that 2A = 1, so A must be 0.5
it’s not incorrect, it’s interpretation is incorrect. The riemann zeta function gives the sum of 1/n^s correctly for all s where the series normally converges, the continuation can be interpreted as assigning values to the non-convergent series, but these values are not meaningful in terms of their series interpretation but are in some other areas of math.
People who don’t understand the point of the riemann zeta function then interpret it incorrectly and put it out into the world in the form of pop math, confusing people.
Yeah, the joke never says infinite mathematicians. Additionally, it would have to be an infinitely large bar for the infinite number of mathematicians and the bartender would somehow pour infinite numbers of beers before they could ask for the bill.
Well this seems to be the explanation that works best to explain the joke, but idk how adding positive numbers wouldn't just equal infinity 🤷♂️ then again, mathmaticans got too much free time
I assume you mean there's a famous trick in mathematics that appears to make 1+2+3+4+... sum to -1/12. If people actually believe that it's -1/12, then they haven't noticed the slight-of-hand going on.
It's obvious that this is the equivalent to doing a divide by zero and then believing you have an actual answer.
The trick here is that they're forcing a particular order of counting to come up with an answer. People don't notice the trick being performed, so it looks impossible.
In this video ( [https://www.youtube.com/watch?v=oaZKaV-oZ-g](https://www.youtube.com/watch?v=oaZKaV-oZ-g) ), they show that 1+2+3+... = -1/12 and then, six minutes into the video, they ALSO show that 1+2+3+... = -1/8
Using math like the one shown in this video, I can also show that 1+1+1+1+... = 0
Given the series S=1+2+3+4+...
If we calculate S-S, and shift the second series:
`S =1 + 2 + 3 + 4 + 5 ...`
`-S = - 1 - 2 - 3 - 4 ...`
Therefore
`S-S = (1) + (2-1) + (3-2) + (4-3) ...`
`S-S = 1 + 1 + 1 + 1 + 1 ...`
S-S = 0. And also: S-S = 1 + 1 + 1 + ...
Therefore 1+1+1+1... = 0
I usually pride myself on my understanding of math but how does one come to the conclusion of -1/12 instead of ... Just infinity? I'd like to understand.
In this case "equals" doesn't really mean equals. This site (https://www.3blue1brown.com/lessons/zeta) has a full explanation, here's a brief one based on one image from it.
https://preview.redd.it/1rkw12rqb19d1.png?width=1920&format=png&auto=webp&s=f582d58f65ee21444490ecace7545b34830c4b01
The right (orange) side of this graph is when that s term in the top left is positive. When s is positive that sum converges and equals means equals. The graph comes from summing infinite series of numbers, like 1 + 1/2 + 1/4 + 1/8 + ... = 2. The left half is blank and not defined, at least at first. Using some calculus we know that there is one, and only one, 'neat' way to fill in that left side which is what you see in blue. But that left side is no longer really the same function. The two sides are definitely linked, but not the same. On the left side, when s = -1, the blue line has an output of -1/12. If you put -1 back into the original function in the top left, you get 1+2+3+.... So the context where it is an infinite sum and the context where it equals -1/12 are completely different, even if it technically does both things.
It's basically a really complex version of the whole thing with what square roots should equal. On a rigidly technical level, sqrt(4) = 2 and does not equal -2. But there are some situations where it's useful to think about sqrt(4) equaling -2, so we came up with some reasoning for why we can do it that way.
The series is divergent, but certain summation techniques will assign it a finite sum. For example, see the Wikipedia article on [Ramanujan summation](https://en.wikipedia.org/wiki/Ramanujan_summation), which contains the example of 1 + 2 + 3 + 4 + .. = -1/12.
It took me so long to find a comment that actually addressed this.
Beers cost $3. They get back $.25. 3/12 is 25 cents. The negative sign means the bartender has to pay them.
Something like that? It's not fully clicking for me because that's like a 25 cent discount. Why's he so mad? You'd think he's giving them back more than they paid him.
And they ordered infinity beers. Does he have to give them infinity quarters? He already made infinity $$ times 3 off these guys
Deep math makes me honestly believe we haven't nailed the language of the universe, at all. I think we THINK we understand it, but the smarter aliens are laughing at our banana math.
I grasp it. I used to be an honor student. But I dropped taking advanced math once calculus and and further started to seem... Fishy to me. Don't get me wrong, I KNOW there are answers. And I know I don't know as much as physicists, not even close, but I did choose to say "fuck it" when it started feeling like we're just answering our own created problems, rather than answers that are likely right in front of us. But we're still not smart enough to see it.
In that case, I feel like the joke would work better if it stated that there were in fact in infinite number of mathematicians there, right? For all we know, there could be 12.
doesn't really make sense though, since it never says there are an infinite number of mathematicians in the bar. it says "for every single mathematician there" implying it's already a finite number
It does, though. Because you’re not kicking out the *last* guy, you’re kicking out someone in the middle which would break the f(n) = f(n - 1) + 1 chain.
Infinity is weird though. Like sure, infinite is infinite, but there's different infinities and some are smaller than others
Between 1 and 2, there's an infinite number of numbers, but they'll never be larger than 2, so even though they all add up to infinity, it's a smaller infinity than, for example, every positive integer
In this case this is what infinity looks like:
1 + 2 + 3 + 4 ...
Which if you do bad math is -1/12 and so yeah if you cut out the last one, well you'll never find the last one. But if you cut one out from the middle:
1 + 2 + 4 + 5 ...
That's no longer, by bad math, -1/12, so the bartender was successful
Infinity is crazy man
This joke only proves that the person who wrote it took assumptions from an equation they didn't understand.
A better version of the joke is:
An infinite number of mathematicians walks into a bar. The first one orders a pint of beer.
The second mathematician says, "I'll have half as much as he ordered," pointing at the first mathematician.
The third mathematician says, "I'll have half as much as him," pointing at the second mathematician.
The fourth mathematician says, "I'll have half as much..."
"Let me stop you right there," the bartender interrupts, and he pours the group two beers.
So essentially he takes care of everyone's requests because it's never ending? The first beer takes care of the first mathematicians request, and the second takes care of everyone's else's?
You retold the version of joke based on undergrad mathematics.
The version the joke that OP posted is based on [Ramanujan summation](https://en.wikipedia.org/wiki/Ramanujan_summation), which is a way to assign a numerical value to a divergent series. In this case the summation 1+2+3+4 .... is assigned numerical value of -1/12, which is why the bartender hands back a quarter.
In my favored telling the last line is:
The bartender says "You're all idiots" and pours two beers.
I just like the idea that he's *done* with this shit.
A lot of people are not explaining this well, explaining it incorrectly, or pointing to other sources which do the same.
There is a function in mathematics called the Riemann zeta function. It is an infinite sum of fractions where the denominator increases by 1 every step. Additionally, the denominator has an exponent which serves as the input to the function. For instance, inputting "2" as the exponent yields: 1/(1^2) + 1/(2^2) + 1/(3^2) + ... or 1/1 + 1/4 + 1/9 + ... and so on. HOWEVER, one can see that inputting "1" as the exponent results in: 1 + 1/2 + 1/3 + ... and so on; a famous infinite sum in mathematics (called the harmonic series) which is known to blow up to infinity. Thus, this form of the Riemann zeta function only makes sense for inputs greater than 1. Otherwise, it just equals infinity. Inputting "-1" to this function would clearly result in: 1 + 2 + 3 + ... = infinity.
You might notice I said "this form," which was intentional. It turns out, that the Riemann zeta function can also take *complex numbers* as exponents. I'm simplifying, but there are manipulations you can perform on the function in order to give it a different form. A form that actually makes sense when you input complex numbers where the real part can be less than 1. This form is called the "functional form" or the "analytical continuation" of the function as others have said.
When you input "-1" to the *functional form* of the Riemann zeta function, you get a result of -1/12. Keep in mind, this form is ENTIRELY DIFFERENT from the first form, i.e. the original infinite sum I mentioned.
People like to joke around or cause hubbub by saying "1 + 2 + 3 + ... = -1/12," which is an obvious absurdity. Really, people are just saying "if I put in a number that only makes sense for the SECOND FORM of the equation, use the format of the FIRST FORM, but keep the result from the SECOND FORM, I get a funny answer."
Which like...duh. The whole proposition makes no sense. It's like if you put a sentence through google translate into Mandarin, and then send that Mandarin sentence BACK through google translate into English. You're always gonna get something that's kinda far off from what you originally entered.
The joke in your post is just multiplying the result by three (since a pint costs $3), thus resulting in -1/12 * 3 = -1/4. So the bartender gives a quarter back. He says there will be trouble if he kicks someone out, because kicking someone out implies that the number of mathematicians in the bar is finite. Finite number of mathematicians = finite bill that needs to be paid (it will be very high)
You can add up all the natural numbers to get -1/12, but only if you do it in a specific order like the mathematical gangster Leonhard Euler did. The problem is that it's 'illegal', you can't just arbitrarily change the order of an infinite series because infinite addition isn't the same as regular addition; it's the limit of partial sums. Essentially, you look at the sums of more and more terms and see what they approach.
When you change the order, the trend or the limit you observe also changes.
But here's the weird part: in physics, there are several instances where similar methods are used to assign a constant to some divergent series, and these constants often end up predicting correct results. that's why some people think that there are hidden treasures in infinity by God.
https://preview.redd.it/0s2hlevi209d1.jpeg?width=1915&format=pjpg&auto=webp&s=e702d6e4726aceed23fef599092dd1b5423bf65d
alright, it's "fuckers".
This image was of me trying to piece together, btw.
https://preview.redd.it/8s01lx08419d1.png?width=708&format=png&auto=webp&s=b58825016af0024645dbe2cdc77daa3e18fed550
Peter’s math teachers left nut here. There is a famous summation in mathematics and physics that is very counterintuitive. It goes like this: the sum of all positive integers (1 + 2 + 3 +… to infinity) is equal to -1/12. So when a pint costs 3 dollars, and an infinite number of mathematicians order an ever increasing number of pints, the mathematicians are replicating this summation. The end result is they owe the bartender -1/12 the price of a single beer. That is to say, the bartender owes them 1/12th the cost of a 3 dollar beer, which is a quarter. The mathematicians are very smart and very drunk, the bartender is very upset, and I think I will get a pint myself now. Left nut out!
It's really awkward that they need the $3 to make the result a simple number of coins.
It's more a joke for people who are really tired of hearing about -1/12 rather than for people who actually use Ramanujan summation for anything. There was a time a few years ago where Numberphile on YouTube made a video about the -1/12 thing and the whole mathoblag was inundated by people asking about, misunderstanding it, arguing about it using their one semester of calculus, etc. I think you're supposed to empathize with the bartender's frustration at having to deal with these people more than anything else.
I feel like we're missing a lot of the joke here. How many men are there? Is it mentioned how many of them are mathematicians or the fact that none of them are.
Three mathematicians walk into a bar. Each orders a pint of beer. The bartender pours them three beers, which they pay for and leave a generous tip. Everyone behaves themselves, and no one leaves confused.
There is a function in mathematics called [Riemann ζ function](https://en.wikipedia.org/wiki/Riemann_zeta_function?wprov=sfla1) (that symbol is the greek letter zeta)
When s is a real number greater than 1 (or a complex number with real part greater than 1), ζ(s) is defined as the sum of 1/nˢ among n in the naturals (excluding n=0 obviously), but this definition as sum breaks down when the real part of s is ≤1
You can use [diabolical mathematical techniques ](https://en.wikipedia.org/wiki/Analytic_continuation?wprov=sfla1) to "smoothly" (in a mathematical sense) extend this function to all complex numbers except 1; using this extension, you can calculate that ζ(-1) is -1/12, while putting -1 in the original formula would give you 1+2+3+4...
Some years ago, the popular math channel [Numberphile](https://youtu.be/w-I6XTVZXww?si=oMlTTel9KF2xIPLJ) popularised a way of "rearranging" the terms of 1+2+3+4+... to get -1/12 as an answer, the problem is that they kinda "cheated" (I don't remember if they acknowledge the theorem below in the video and I don't care enough to watch it again).
There is this theorem, the [Riemann-Dini theorem](https://en.wikipedia.org/wiki/Riemann_series_theorem?wprov=sfla1), which states that if you have a sequence of real numbers aₙ for which its sum does not [absolutely converge](https://en.wikipedia.org/wiki/Absolute_convergence?wprov=sfla1) (as to say, summing the absolute values of each term does not get closer and closer to a real number), then you can find a rearrangement to get its sum to converge to any real number you want.
Obviously, |1|+|2|+|3|+... does not converge, which means that you can find a rearrangement to get any real number you want to get, be it 0, π, e, -1385, Rayo's number or -1/12.
Finally, the joke is that using the (incorrect) result from before, 3+6+9+12... = 3(1+2+3+4...) = 3(-1/12) = -1/4, so the bartender should not only be paid nothing, but he'd have to give a quarter of change to the infinite crowd of mathematicians.
The joke is the mathematicians used fake bs math to get out of a bill by pretending there is some rule where if you add 1+2+3+4 infinitely upward somehow it makes -1/12 and that times three is a -1/4 which still isnt a quarter because no one adds dollars as the whole they add cents as the whole. It would be a 0.0025$ or a quarter of a penny.
The bartender is Terence Howard, and the mathematicians are just trolling him because they know they can score free beer if they just let him feel smart for the night?
For some reason, the infinite sum of all positive integers is -1/12, multiplying by $3 per beer gives us a total cost of -1/4, so the bar tender pays them a quarter
A dumb joke that makes no sense.
There's a math equation regarding infinity that this is referencing.
But since there is a finite number of humans on earth, and even smaller finite number of mathematicians on earth, and an even smaller finite number of people that can fit in a bar, the joke is dumb and makes no sense.
The equation its referencing is dumb too because the equation only works because the mathematician that published it also redefined the equals sign for their proof.
The equation is... all positive integers from 1 to infinite = -(1/12) ie...
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 ~ = -(1/12)
They redefine the equals sign to not mean "is equal to" and instead mean "is associated with" which is a way of saying "is about".
They calculate it by combining 2 other "proofs"
1st is that subtracting and adding 1 and infinite number of times = 1/2
FORMULA X = 1-1+1-1+1-1+1 ~ (infinitely) = 1/2
This is because, with the same assumed meaning of the = sign...
1-1 = 0
0+1 = 1
Your equation will constantly flip between 0 and 1 as you progress down the equation infinitely. So the answer is "It's about 0.5" or "1/2"
Then you have another equation, subtracting and adding all integers from 1 to infinity.
FORMULA Y = 1-2+3-4+5-6+7 ~ = 1/4
They "solved" this one by converting it back in to the previous formula. You multiply the formula by 2 and convert all the subtractions to addition by turning your 1-2 in to a 1+-2, etc.
Then you can add the 2 copies of the equation together. Which will bring you right back to the same equation you had before which lets you then divide your answer of 1/2 in half to 1/4.
Then they subtract the Formula Y from...
FORMULA Z = 1+2+3+4+5+6+7~ (all positive integers added from 1 to infinity)
Which gives you an infinite addition of factors of 4.
Z-Y = 4+8+12+16+20+24~
Which can also be written as
Z-Y = 4(1+2+3+4+5+6~)
or as...
Z-Y = 4(Z)
And since we know what Y is...
Z-(1/4) = 4(Z)
We can reduce this down
-(1/4) = 3(Z)
And then if we divide both sides by 3
-(1/12) = Z
Or...
1+2+3+4+5+6+7+8+9+10+11~ = -(1/12)
But again, none of this is actually accurate. They're all estimations and the formulas only function with that redefined meaning of the equals symbol.
Also, the joke doesn't work because the bartender should have given 36 cents back, not a quarter. (12 cents per dollar. 3 dollars for the pint. 3x12)
This joke doesn't work. There is a finite number of mathematicians. You can be sure because they all finish ordering. The bartender should count the number of mathematicians and charge them ($3n)(n+1)/2. Also, where can I get a pint of beer for three dollars these days?
OP is a reposter or a bot. probably a bot.
https://www.reddit.com/r/PeterExplainsTheJoke/comments/16uj17w/my_dad_sent_me_this_and_i_dont_want_to_admit_i/
There is a certain way of manipulation the series 1 + 2 + 3 + 4 + ... , such that you get the resulting sum to be -1/12. . This was originally done by Ramanujan. Essentially you can algebraically manipulate the above series to get the desired value of -1/12. The pints the mathematicians asked for add up to -1/12, so they pay -1/4 of a dollar. I.e, the bartender owes them a quarter.
Of course you'd expect the sum to diverge. And it does, if you do the sum conventionally. But infinite series and sequences are tricky, and you cannot deal with them as if they were finite. An infinite series value is normally defined as the limit of its partial sums. And unless you series has certain properties, this limit is sensitive to the order you take your partial sums in; it is not the case that addition naturally implies commutativity, and the conditions that make commutativity true for finite series do not hold for infinite series.
More relevant to the series at hand, UNLESS your series converges you cannot do algebraic manipulations like multiply your series by some constant or add another series to it. A series like 4 + 8 + 12 + 16 + ... is not 4 times the series 1 + 2 + 3 + 4 because the latter doesn't even have a value in terms of a limit. Multiplication by 4 is not even defined for the divergent series. Therefore there is no relation between the series 1 + 2 + 3 + 4 ... and 4 + 8 + 12 + 16 + ... in the standard sense. Yet this is similar to what Ramanujan did and this is exactly how he got his answer of -1/12.
That said Ramanur than the limit of its partial sums, you can assign weird values to series. In the Ramanujan sense, the series 1 + 2 + 3 + 4 ... = -1/12. In the conventional sense the series diverges. Interestingly Ramanujan summation does actually make a comeback in physics. When studying systems with many degrees of freedom like a field or an ideal gas, you eventually end up having to compute what's known as a Zeta function, which is similar to this sum of all natural numbers. In order to assign a finite sensible value to these sums, you have to use Ramanujan summation. Mathematically we don't really know why you can do that yet.
I heard a similar one where an infinite number of mathematicians enter a bar. The first one asks for a beer. The second one asks for half a beer. The third: a quarter of beer. Fourth: eighth of a beer, and so on.
The bartender pours two beers and says, "Have at it."
Can someone explain why -1/12 is a part of this when it's not written in the joke?
Is the beginning of the joke missing? It doesn't say they are mathematicians til the end.
Also, what word is blacked out?
The joke only works if you're a math nerd and there are an infinite number of mathematicians. Did I miss the part where the joke says there are infinitely many mathematicians?
If I am getting this right, there's a formula where you go +1, -2, +3, -4, and so on. The weird thing this joke is trying to play off of comes in when you take an average of this equation approaching infinity. When you do that, you get the odd answer of -1/12. I don't know why exactly, I had a friend prove it to me once and it's just bizarre. All I know is it gets weird as you approach infinity.
This joke is attempting to reference this, but neglects the subtraction portion of the equation, so it's intended joke gets lost in the process.
There are people talking about 1 + 2 + 3 + 4 + ... = -1/12 but it's definitely not that, I think it's a joke about [the infinite hotel](https://youtu.be/OxGsU8oIWjY?si=NyYte7NtmT1RE876)
Its the fact that kicking one man out wouldn't change the bill, and there would still be the same amount of people ordering
This reminded me of a good joke:
An infinite number of mathematicians walk into a bar. The first says "I'll have a beer," the second says "I'll have half a beer," the third says "I'll have a quarter of a beer," and so on.
The bartender pours them two beers and says "You boys ought to know your limits."
It's a whole bunch of weird mathematical tricks where you start with "what's the sun of an infinite series of +1 and -1", the real answer is "does not converge", but some physicists have said "let's approximate it to be 1/2", and then from there you eventually get to -1/12 being the sum of all positive integers
Numberphile did a video on this, but they skip over a whole bunch of assumptions
Tl;Dr you play with math, the answer is -1/12, and 1/12 of $3 is a quarter, but it's negative so paying "-$0.25" is receiving a quarter
Make sure to check out the [pinned post on Loss](https://www.reddit.com/r/PeterExplainsTheJoke/comments/1472nhh/faq_loss/) to make sure this submission doesn't break the rule! *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/PeterExplainsTheJoke) if you have any questions or concerns.*
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How does adding positive numbers turn negative? Edit: after some quick googling apparently in this case "=" doesn't mean equal in the classical sense and means something else that people argue about to this day.
https://youtu.be/w-I6XTVZXww?si=dTIwd0oKtDAWt6nX Spoiler alert: it really doesnt, but the -1/12 result for some weird reason still has some use in certain physics calculations for some reason Not a one time calculator boy, so cant really explain further
This video has a more approachable explanation of why it's useful even though it's not purely accurate. [https://www.youtube.com/watch?v=Z9S\_wUqLpv0](https://www.youtube.com/watch?v=Z9S_wUqLpv0)
Makes sense. It isn't so much about math basic style it's about assumed probable math. Which comes up in physics
Ok, I'm not a math guy, but how would that work? I stopped after the S2 part. How can you claim it is 2S2 when you are adding S2 and S2, but decide to shift how to add them together? Let's pretend S2 isn't what they use but is instead S2 = 1 + 5 - 2 + 8. S2 = 12 I can't say that 2S2 would be 1 + 5 - 2 + 8 \+ 1 + 5 - 2 + 8 So is 2S2 = 1 + 6 + 3 + 6 + 8 = 24 Jesus fuck... how does this work? EDIT: What if I have multiplication? x = 5 + (8 * 3) = 29 2x would be: 5 + (8 * 3) \+ 5 + (8 * 3) 5 + (13 * 24 * 3) = 941 or would it be 5 + (13 * 24) + 3 = 320 Either way it doesn't work with multiplication. Ok, so this is just some trickery since it works with simple addition and subtraction since you're basically just adding and subtracting the same numbers but in a different order.
You can't shorten it to just the first numbers, the trick is that it is infinite.
It doesn't https://www.youtube.com/watch?v=YuIIjLr6vUA There was a badly communicated youtube video by numberphile which confused a lot of people.
From their vid, I don't get from S1 and S2, why you shift it down one. Why not shift it down 2 places and get whatever that would be?
That's precisely the issue why you cannot handle infinities the way they did.
Yeah, definitely not their finest hour.
Like they’re excited about a bad card trick.
While stealing your purse
Yes. It's fine from time to time to pull a trick. But for educational purposes, it's really bad.
The proof relied on the fact that 1 - 1 + 1 - 1 + 1... = 0.5 was true, which it isn't. (Can't assign a value to an infinite series that doesn't converge)
Ramanujan made a logical mistake in his argument because he assumed two sets to be equal that weren't but the concept of that wasn't really invented yet and the kid was a genius either way.
>How does adding positive numbers turn negative? It's a 'proof' that treats infinity as a real number. That's actually a violation of real numbers, and so it produces contradictory results. In this case, I think it relies on things like the series 1 - 1 + 1 - 1 + 1 - ..... to equal 1/2, when it should be considered 'divergent' and not used in other calculations.
it doesnt, but its a bit of an anomoly that makes logical sense under particular definitions of a sum. and if you are into math it's very very fascinating. there are a lot of you tube videos explaining it https://www.youtube.com/results?search_query=The+Ramanujan+Summation and the concept behind it does have real world uses.
Mind you the -1/12 thing only works if you add the numbers in an obtuse way.
IIRC series only works if you take them exactly as defined (commutativity doesn't apply). Is that legit?
Not exactly. Or, well, not universally. Without getting into it too much, if you have a series with both positive and negative terms, it can be what's known as either absolutely convergent, or conditionally convergent (assuming it's convergent at all). An absolutely convergent series is one that converges even if all of the terms were positive. A conditionally convergent series is one that diverges if all the terms were made positive. For a conditionally convergent series, what you describe is correct. In fact, for a conditionally convergent series it is possible to rearrange the terms so that the series converges to any number that you want. However for an absolutely convergent series, any rearrangement of terms will result in the same limit, and thus commutativity still applies
I love your explanation. It's also a bad joke because in order for this to "work," they can't be "done"; they would have to literally be ordering beers forever. The moment someone stops ordering a beer, there is a very positive, real number to deal with.
The joke could be salvaged: In a bar, a pint of beer costs three dollars. The broke math department hatches a plan for how they can afford to drink all night. The first mathematician asks a pint of beer The second mathematician asks for two pints of beer The third mathematician asks for three pints of beer And so on. The tenth mathematician stumbles up to the bar and slurs “look, we can come back tomorrow and keep doing this forever or we can quit now and you can just give us the quarter”
But why would he be giving them a quarter at all?
Because they’d owe him 3 * ramanujan’s infinite sum. Ramanujan’s infinite sum is -1/12, so -3/12 = -0.25.
Just have each one order in half the time as the previous one. edit: In case anyone is wondering, 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... = 2 so if the first person orders, the next person orders 1 minute later, the next 30 seconds later, the next 15 seconds later, etc. then they will have ordered infinite beers in 2 minutes.
And if they're too hammered to go home after the whole thing, there's a hotel a block away that happens to have enough rooms for them.
I see what you did there 🧐
But to sober up, they need infinite chocolate. Off to Tumblr!
Maybe the time to order, serve and drink decreases faster than the inverse of the number of beers. Then it finishes in finite time ...
Cool, that makes way less sense now.
i just learned about this "equation", and im flabbergasted it is taken seriously xD
Heey... Did u/[Sangorieur](https://www.reddit.com/user/Sangorieur/) post this question as u/[titickee](https://www.reddit.com/user/titickee/), to answer his own question and look smaht?
Thank you, Peter’s onetime human calculator!
Explain the punchline. If you keep coming back I’m going to kick one of you out.
theres a famous thing in mathematics that states 1 + 2 + 3 + 4 + ...... up to infinity = -1/12, so if there are infinite mathematicians who pay for a pint more than the previous, then the sum of all payment is 3 × (-1/12) which is -1/4, so the bartender owes them a quarter
= -1/12 Wait what
When infinity is involved and you try to use mathematics that only works on ordinary, non-finite numbers, you get weird results.
Can we not simply prove that -1/12 is bullshit by taking note of 3 basic facts, them being: 1. addition of positive numbers leading to another positive number that's bigger than both of the previous numbers 2. Only addition of positive numbers is happening 3. The pattern never breaks How do math guys refute that?
It doesn't actually equal it in the conventional sense. However, there's a function called the Riemann Zeta function that is given by ζ(s) = sum from 1 to infinity (1/n^(s)). Its trivial to see ζ(-1) is the sum of natural numbers, but plugging it in we find ζ(-1) = -1/12 because of something called analytic continuation.
it’s literally never mentioned and this is a seriously niche joke. A normal person could never draw that conclusion, and in the non-mathematical world this joke makes absolutely no sense. Edit: my issue isn’t that this joke is niche, that’s what this sub is for, it’s the dozen or so people pretending it’s more well know than it should be. Not everyone is in stem or took calculus in high school.
This reminds me of my favorite joke: What do you get when you cross a mosquito and Tenzing Norgay? Nothing because you can’t cross a vector and a scaler.
Peter, some of us need you again in the comments.
Vectors and scalers are both used in math/physics. Scalers only have magnitude while vectors have magnitude and direction. You can’t cross multiply them ( don’t worry about it.). A mosquito is a vector (something that transmits) disease and tenzing Norgay was part of the first two men to scale mt Everest along with Edmund Hillary.
Damn it’s like a niche joke onion for people smarter than I am in this comment thread
Small correction - they are scalars, not scalers, in math/physics (not that it affects the joke or the explanation)
Mosquito = disease *vector*. Tenzing Norgay = famous mountaineer, or "scaler". (Fish and lizards have scales, but "to scale" also means "to climb".) "Vector" and "scal**a**r" are distinct types of data. Without getting into fine detail, they are essentially apples and oranges. They can't be used with each other. [A more in-depth explanation of vectors and scalars here.](https://www.physicsclassroom.com/class/1DKin/Lesson-1/Scalars-and-Vectors) It's funny, though I find homophone-based jokes less clever than ones that work as well when told aloud or in print. Probably that's just me.
This is really funny
As a mountaineer, I <3 this joke, and am shocked I never heard it before.
I have no idea what you just said but I still giggled.
lol
I understood this joke because of "Intolerable Cruelty"
This reminds me of a funny joke from Kung Pow. What do you get when when you cross an owl with a bungee cord? My ass
I'm going to tell this to my physics professor today
Finally! A biology and random history fact joke! I get this!
Damn that's a solid geek joke. Got some history, biology and math up in there.
My grandfather would love this joke. Unironically.
You're going to be fucking livid when you hear about all the jokes they're telling in the other fields of academia. Many of them are much worse!
I'm just an engineer and I got the joke. That's the thing about jokes, not everyone needs to get them.
well yeah, that's the point of an injoke lol
Yeah, I think it’s a niche joke for mathematicians.
Interesting interesting, now lets see it in english.
There's a pattern that makes sense for counting numbers but when you plug in -1 you get a wacky result
The Zeta function itself cannot even take -1, exactly because it does not make sense. It just so happens that the analytic continuation of it yields -1/12 at -1. This also has implications in physics afaik.
What implications in physics does this have? I'm curious to know a real world use of this
“The value \(\zeta(-1) = -1/12\) shows up in physics in interesting ways. Think of it like finding hidden treasure in math that helps explain the Casimir effect—where empty space between objects has energy. It's like discovering that seemingly empty space has a secret force, which we see in quantum mechanics and has been proven in experiments. So, even though it sounds weird, it’s like a hidden key to understanding the quantum world.”
It's used a ton in string theory. A lot of string theory textbooks include that -1/12 equation in chapter 1 and are basically like "when you run into this infinite summation, use this value!" But no, I don't know of a real world use 😂
Tag me when you answer, it won't let me follow this
Also curious
That conclusion relies on using algebra in an environment where it's rules aren't really defined. It's like solving a problem by treating division by zero as being zero, then getting incorrect results.
If you add all the positive integers together then it just goes off to infinity and you don't get a real answer. If you force math to give you an answer anyway then you get -1/12
I gotchu! [Numberphile did a great video on it a while ago.](https://www.youtube.com/watch?v=w-I6XTVZXww)
where tf you get them symbols spaceman
Higher education
You won't trick me with your heretical hieroglyphics, wizard man, I know you're just trying to control my mind!
so do they pay y'all to make shit up or do you all still wish you picked computers instead
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You’re cereal is smarter then me. I’ve read this 3 times and it might as well be mandarin.
It's usually not explained very well. If you add up all the numbers 1 + 2 + 3 + ..., it diverges (i.e., the sum gets bigger and bigger without approaching any specific finite number). However, if you assume (falsely) that it does approach a specific number and do the calculations to find said number, it turns out to be -1/12.
That makes the most sense to me. Its like math saying, "Ask a bullshit question, get a bullshit answer"
Except it's actually a useful answer in the right context. Like how 𝑖 is nonsense in some contexts, but is useful in others.
Easy. Theoretical mathematicians simply do not consider reality. It’s kind of their thing.
This is true but that doesn’t mean there aren’t other meanings of “=“ and methods to arrive at the -1/12. One of the million dollar math questions is actually to find all non trivial 0s on the goofy graph of the Riemann Zeta function, which is one way people get to -1/12
Some people would say that it's an incorrect application of math resulting in an invalid result. Others would say that it's not incorrect, that math is just the consistent application of rules within a given context used for calculation and that this is just that, similar to how people called imaginary numbers invalid when they were first invented. However, to directly answer your question: When summing ALL positive integers, using the same logic you gave the result cannot in itself be a positive integer as that would have been included in the summation itself. So perhaps, in some specific contexts, the idea that it results in something other than a positive integer (say, a negative fraction...) isn't so insane.
Well technically that wouldn't be enough for a formal proof, as patterns that work up to X sometimes do break, even for very large X. That said, in your case it wouldn't be hard to make this into a proof by induction, but I'll leave that as an exercise for the reader. Anyways, given such a proof, mathematicians will sometimes keep working on the system anyways. Normally working on a nonsense system only leads to more nonsense, but good mathematicians can eventually formalize some nonsense systems into things that have meaning, and sometimes those formal systems end up being useful. The most common examples are negative numbers and imaginary number. If you have 1 apple, you can't eat 2 apples and have negative one apple. Yet you are so accustom to negative numbers you likely don't even see them as weird. Imaginary numbers are even weirder and most still see them as weird, but they are surprisingly useful. There is even the imaginary number of imaginary numbers, the quaternions (it repeats infinitely but gets less useful each time). Kinda like there are formal systems of math that consider numbers bigger than infinity. Weird, but sometimes useful for solving problems. For an example, consider that there are different sizes of infinity. Sometimes you can ask a question about a function that maps from one set to another and by showing the domain of a function is a smaller infinity than the range of the function it works as a proof that the function in question doesn't exist.
Sometimes math gives nonsense results that don't make sense. Those results can usually be ignored in most scenarios. For example, imaginary numbers or negative numbers out of square roots are technically correct but usually ignored. This is a pretty similar result, where the -1/12 result can be usually ignored but is technically a possible answer.
No, there's plenty of theory in mathematics handling complex numbers. The complex numbers are necessary to define a set over which all roots of polynomials are defined. It's physicists and engineers who ignore complex numbers when they try to solve physical problems by using mathematics - unless those complex numbers actually prove useful (e.g., Landau damping, conformal mappings for aerodynamics, etc.)
imaginary and negative numbers usually represent the presence of oscillations within whatever system you’re working with
In fact -1/12 is bullshit, it is a famous example that shows you can't manipulate infinite series using the same methods used for finite ones i.e. the associatovity of addition
Wouldn't "non-finite" be infinite?
Yes. They probably meant to say "finite"
It is not in fact true that the sum of the numbers from 1 to infinity is -1/12 -- the sum of all the numbers from 1 to infinity diverges (i.e., it has no sum), exactly as you'd expect. But, suppose you you want to find a more general notion of "summing" that gives values to divergent series? (I'm not sure why you'd want to do that. Mathematicians have lots of time on their hands, I guess.) In that case, it turns out that the -1/12 thing pops out naturally, in a way that other numbers don't. So while "The sum of all positive integers is -1/12" isn't correct, it might be a bit more correct to say something like "The sum of all positive integers isn't anything, but if it *were* anything, it would be -1/12." [Here's a useful explainer video](https://www.youtube.com/watch?v=YuIIjLr6vUA) that goes into a lot more depth but is nonetheless pretty accessible.
The why is that mathematicians are always looking for new systems of math even when we don't have a problem that fits the new system. There have been cases where it took decades for some seemingly nonsensical field of math to find a real world application. Sometimes it might never be useful, but those times are made up for by the times it is useful.
Legend has it that someone once had to do a math PhD on how water would behave on a completely submerged planet. Bullshit functions came out that describes how waves would form and where every crest and trough would be once you took interference patterns into consideration. Functions were lost in time, until some obstinate, Danish physicist decided that maybe electrons weren't particles, but instead behaved like probability functions. All he needed to explain molecular structure turned out to be some bullshit math that described how water-like functions behaved on a completely submerged planet. And hey presto, quantum mechanics became a thing.
Fuckin smart people posting links n shit.. I was ready for bed an hour ago, but here I am coming back to say thank you 40 minutes later... Didn't understand half of that video, but I do know more because of it. Neat video, thank you for sharing.
Oh, sorry they didnt reduce the fraction. Its should be -.5/6 duh I may have failed course 2...
There's a numberphile video about it. Iirc, you do have to jump through some hoops. I think at one point they talk about the infinite series 1 - 1 + 1 - 1 + 1 - . . . to infinity. What's the sum? 1 or 0? They say one approach might be to call it 0.5 as the average between the two. Using 0.5 as the answer, you can do some tricky substitutions and get whacky results like finding that the sum of all the natural numbers is -1/12 I should note that saying that 0.5 is the answer isn't just derived from taking the average. If you say that infinite series of adding and subtracting 1s is A and look at adding A + A, you could do that by pairing the nth term of A with the n+1th term of the second A. So you get 1 + (1 - 1) + (1-1) + .... to infinity which it turns out gives you 1 + 0 + 0+ ... and so you've shown that 2A = 1, so A must be 0.5
Integer overflow error. Simulation confirmed.
the guy who invented this made an incorrect assumption leading to that result, but it was still a brilliant and novel enough idea that it got famous.
it’s not incorrect, it’s interpretation is incorrect. The riemann zeta function gives the sum of 1/n^s correctly for all s where the series normally converges, the continuation can be interpreted as assigning values to the non-convergent series, but these values are not meaningful in terms of their series interpretation but are in some other areas of math. People who don’t understand the point of the riemann zeta function then interpret it incorrectly and put it out into the world in the form of pop math, confusing people.
S is not converging.
(it doesn't)
The joke really needs to mention that there's infinite mathematicians. That's a key missing fact
Yeah, the joke never says infinite mathematicians. Additionally, it would have to be an infinitely large bar for the infinite number of mathematicians and the bartender would somehow pour infinite numbers of beers before they could ask for the bill.
And infinity -1 is still infinity so kicking one of them out would change nothing.
https://i.redd.it/au3tubc9b09d1.gif
And i would assume the “kicking one of you out” line means it’s not infinity all of a sudden they owe a lot of money for a lot of beer
Well this seems to be the explanation that works best to explain the joke, but idk how adding positive numbers wouldn't just equal infinity 🤷♂️ then again, mathmaticans got too much free time
Yeah I think the math doesn’t work out that way but I think that’s where the joke is pointing
I assume you mean there's a famous trick in mathematics that appears to make 1+2+3+4+... sum to -1/12. If people actually believe that it's -1/12, then they haven't noticed the slight-of-hand going on. It's obvious that this is the equivalent to doing a divide by zero and then believing you have an actual answer. The trick here is that they're forcing a particular order of counting to come up with an answer. People don't notice the trick being performed, so it looks impossible. In this video ( [https://www.youtube.com/watch?v=oaZKaV-oZ-g](https://www.youtube.com/watch?v=oaZKaV-oZ-g) ), they show that 1+2+3+... = -1/12 and then, six minutes into the video, they ALSO show that 1+2+3+... = -1/8 Using math like the one shown in this video, I can also show that 1+1+1+1+... = 0 Given the series S=1+2+3+4+... If we calculate S-S, and shift the second series: `S =1 + 2 + 3 + 4 + 5 ...` `-S = - 1 - 2 - 3 - 4 ...` Therefore `S-S = (1) + (2-1) + (3-2) + (4-3) ...` `S-S = 1 + 1 + 1 + 1 + 1 ...` S-S = 0. And also: S-S = 1 + 1 + 1 + ... Therefore 1+1+1+1... = 0
I usually pride myself on my understanding of math but how does one come to the conclusion of -1/12 instead of ... Just infinity? I'd like to understand.
In this case "equals" doesn't really mean equals. This site (https://www.3blue1brown.com/lessons/zeta) has a full explanation, here's a brief one based on one image from it. https://preview.redd.it/1rkw12rqb19d1.png?width=1920&format=png&auto=webp&s=f582d58f65ee21444490ecace7545b34830c4b01 The right (orange) side of this graph is when that s term in the top left is positive. When s is positive that sum converges and equals means equals. The graph comes from summing infinite series of numbers, like 1 + 1/2 + 1/4 + 1/8 + ... = 2. The left half is blank and not defined, at least at first. Using some calculus we know that there is one, and only one, 'neat' way to fill in that left side which is what you see in blue. But that left side is no longer really the same function. The two sides are definitely linked, but not the same. On the left side, when s = -1, the blue line has an output of -1/12. If you put -1 back into the original function in the top left, you get 1+2+3+.... So the context where it is an infinite sum and the context where it equals -1/12 are completely different, even if it technically does both things. It's basically a really complex version of the whole thing with what square roots should equal. On a rigidly technical level, sqrt(4) = 2 and does not equal -2. But there are some situations where it's useful to think about sqrt(4) equaling -2, so we came up with some reasoning for why we can do it that way.
The series is divergent, but certain summation techniques will assign it a finite sum. For example, see the Wikipedia article on [Ramanujan summation](https://en.wikipedia.org/wiki/Ramanujan_summation), which contains the example of 1 + 2 + 3 + 4 + .. = -1/12.
It took me so long to find a comment that actually addressed this. Beers cost $3. They get back $.25. 3/12 is 25 cents. The negative sign means the bartender has to pay them. Something like that? It's not fully clicking for me because that's like a 25 cent discount. Why's he so mad? You'd think he's giving them back more than they paid him. And they ordered infinity beers. Does he have to give them infinity quarters? He already made infinity $$ times 3 off these guys
Deep math makes me honestly believe we haven't nailed the language of the universe, at all. I think we THINK we understand it, but the smarter aliens are laughing at our banana math. I grasp it. I used to be an honor student. But I dropped taking advanced math once calculus and and further started to seem... Fishy to me. Don't get me wrong, I KNOW there are answers. And I know I don't know as much as physicists, not even close, but I did choose to say "fuck it" when it started feeling like we're just answering our own created problems, rather than answers that are likely right in front of us. But we're still not smart enough to see it.
Me too dude… me too…. I don’t think either of us are going to get an explanation that actually makes sense. Sometimes the math ain’t mathing…
Watch this for a layman explanation https://www.youtube.com/watch?v=w-I6XTVZXww
In that case, I feel like the joke would work better if it stated that there were in fact in infinite number of mathematicians there, right? For all we know, there could be 12.
So the kicking one of them out? Is it that, if they kick one of them out, that is one less than infinity and they all have to pay for their beer?
doesn't really make sense though, since it never says there are an infinite number of mathematicians in the bar. it says "for every single mathematician there" implying it's already a finite number
OP cut the joke short, which is why it starts "in this bar".
ah fair enough, but kicking one out of an infinite number out, wouldn't make it a finite number either, so it still doesn't make sense
It does, though. Because you’re not kicking out the *last* guy, you’re kicking out someone in the middle which would break the f(n) = f(n - 1) + 1 chain.
you're right, I was too focused on the finite/infinite part of it
That assumes that kicking one out reduces the number of people. But its infinite mathematicians. Imagine ♾️ getting defeated by -1… smh
Infinity is weird though. Like sure, infinite is infinite, but there's different infinities and some are smaller than others Between 1 and 2, there's an infinite number of numbers, but they'll never be larger than 2, so even though they all add up to infinity, it's a smaller infinity than, for example, every positive integer In this case this is what infinity looks like: 1 + 2 + 3 + 4 ... Which if you do bad math is -1/12 and so yeah if you cut out the last one, well you'll never find the last one. But if you cut one out from the middle: 1 + 2 + 4 + 5 ... That's no longer, by bad math, -1/12, so the bartender was successful Infinity is crazy man
This joke only proves that the person who wrote it took assumptions from an equation they didn't understand. A better version of the joke is: An infinite number of mathematicians walks into a bar. The first one orders a pint of beer. The second mathematician says, "I'll have half as much as he ordered," pointing at the first mathematician. The third mathematician says, "I'll have half as much as him," pointing at the second mathematician. The fourth mathematician says, "I'll have half as much..." "Let me stop you right there," the bartender interrupts, and he pours the group two beers.
So essentially he takes care of everyone's requests because it's never ending? The first beer takes care of the first mathematicians request, and the second takes care of everyone's else's?
yeah, the series converges to two
The punch is "you need to know your limits!" and puts down two beers.
Ok damn that's actually so good
Oh tee hee infinite reduction!
Exponents :3
You retold the version of joke based on undergrad mathematics. The version the joke that OP posted is based on [Ramanujan summation](https://en.wikipedia.org/wiki/Ramanujan_summation), which is a way to assign a numerical value to a divergent series. In this case the summation 1+2+3+4 .... is assigned numerical value of -1/12, which is why the bartender hands back a quarter.
the real joke is always in the comments
In my favored telling the last line is: The bartender says "You're all idiots" and pours two beers. I just like the idea that he's *done* with this shit.
Well that was reductive.
Bartender knew thier limit.
Separate glasses, please.
Finally, a joke no one can be all smarmy about "ANYone should get this it's OBvious 🙄🙄🙄"
I feel like OP’s dad might be like that
AnYoNe ShOuLd GeT tHiS! iT’s So ObViOuS 😂🤣😂🤣😂🤣
A lot of people are not explaining this well, explaining it incorrectly, or pointing to other sources which do the same. There is a function in mathematics called the Riemann zeta function. It is an infinite sum of fractions where the denominator increases by 1 every step. Additionally, the denominator has an exponent which serves as the input to the function. For instance, inputting "2" as the exponent yields: 1/(1^2) + 1/(2^2) + 1/(3^2) + ... or 1/1 + 1/4 + 1/9 + ... and so on. HOWEVER, one can see that inputting "1" as the exponent results in: 1 + 1/2 + 1/3 + ... and so on; a famous infinite sum in mathematics (called the harmonic series) which is known to blow up to infinity. Thus, this form of the Riemann zeta function only makes sense for inputs greater than 1. Otherwise, it just equals infinity. Inputting "-1" to this function would clearly result in: 1 + 2 + 3 + ... = infinity. You might notice I said "this form," which was intentional. It turns out, that the Riemann zeta function can also take *complex numbers* as exponents. I'm simplifying, but there are manipulations you can perform on the function in order to give it a different form. A form that actually makes sense when you input complex numbers where the real part can be less than 1. This form is called the "functional form" or the "analytical continuation" of the function as others have said. When you input "-1" to the *functional form* of the Riemann zeta function, you get a result of -1/12. Keep in mind, this form is ENTIRELY DIFFERENT from the first form, i.e. the original infinite sum I mentioned. People like to joke around or cause hubbub by saying "1 + 2 + 3 + ... = -1/12," which is an obvious absurdity. Really, people are just saying "if I put in a number that only makes sense for the SECOND FORM of the equation, use the format of the FIRST FORM, but keep the result from the SECOND FORM, I get a funny answer." Which like...duh. The whole proposition makes no sense. It's like if you put a sentence through google translate into Mandarin, and then send that Mandarin sentence BACK through google translate into English. You're always gonna get something that's kinda far off from what you originally entered. The joke in your post is just multiplying the result by three (since a pint costs $3), thus resulting in -1/12 * 3 = -1/4. So the bartender gives a quarter back. He says there will be trouble if he kicks someone out, because kicking someone out implies that the number of mathematicians in the bar is finite. Finite number of mathematicians = finite bill that needs to be paid (it will be very high)
Thank you! Glad to see a proper explanation here. 3blue1brown has a GREAT video about the Riemann Zeta Function that explains this idea very well.
I love math but not that much, but thanks for the explaination ( I am the top comment )
This is the best explanation, and should be the top comment
You can add up all the natural numbers to get -1/12, but only if you do it in a specific order like the mathematical gangster Leonhard Euler did. The problem is that it's 'illegal', you can't just arbitrarily change the order of an infinite series because infinite addition isn't the same as regular addition; it's the limit of partial sums. Essentially, you look at the sums of more and more terms and see what they approach. When you change the order, the trend or the limit you observe also changes. But here's the weird part: in physics, there are several instances where similar methods are used to assign a constant to some divergent series, and these constants often end up predicting correct results. that's why some people think that there are hidden treasures in infinity by God. https://preview.redd.it/0s2hlevi209d1.jpeg?width=1915&format=pjpg&auto=webp&s=e702d6e4726aceed23fef599092dd1b5423bf65d
I have never been more confused on a Peter Explain The Joke post what the fuck
I think the redacted word is "fuckheads". Hope this helps!
uhhh... https://preview.redd.it/mmc8ypzro09d1.png?width=708&format=png&auto=webp&s=d1fff21264cc23d67cc199ede205c948b44024e7
"fuckers" would fit, right?
alright, it's "fuckers". This image was of me trying to piece together, btw. https://preview.redd.it/8s01lx08419d1.png?width=708&format=png&auto=webp&s=b58825016af0024645dbe2cdc77daa3e18fed550
I thought it was a bundle of sticks
Thank you, Peter!
thank you. censorship like this bothers me a lot more than it really should. so fucking annoying
Have you heard the one about the constipated mathematician ? He worked it out with a pencil .......
Peter’s math teachers left nut here. There is a famous summation in mathematics and physics that is very counterintuitive. It goes like this: the sum of all positive integers (1 + 2 + 3 +… to infinity) is equal to -1/12. So when a pint costs 3 dollars, and an infinite number of mathematicians order an ever increasing number of pints, the mathematicians are replicating this summation. The end result is they owe the bartender -1/12 the price of a single beer. That is to say, the bartender owes them 1/12th the cost of a 3 dollar beer, which is a quarter. The mathematicians are very smart and very drunk, the bartender is very upset, and I think I will get a pint myself now. Left nut out!
Math is ridiculous
https://preview.redd.it/1qybo6baa09d1.jpeg?width=640&format=pjpg&auto=webp&s=09671687c19336b6b5416427bf437fcfb7cd6c33
This is such a poorly written joke. Even the explanation given feels like a stretch
It's really awkward that they need the $3 to make the result a simple number of coins. It's more a joke for people who are really tired of hearing about -1/12 rather than for people who actually use Ramanujan summation for anything. There was a time a few years ago where Numberphile on YouTube made a video about the -1/12 thing and the whole mathoblag was inundated by people asking about, misunderstanding it, arguing about it using their one semester of calculus, etc. I think you're supposed to empathize with the bartender's frustration at having to deal with these people more than anything else.
You should punch your dad.
I feel like we're missing a lot of the joke here. How many men are there? Is it mentioned how many of them are mathematicians or the fact that none of them are.
Three mathematicians walk into a bar. Each orders a pint of beer. The bartender pours them three beers, which they pay for and leave a generous tip. Everyone behaves themselves, and no one leaves confused.
Reading these comments makes me feel like a dumb dumb
At least you’re gaining some self awareness
There is a function in mathematics called [Riemann ζ function](https://en.wikipedia.org/wiki/Riemann_zeta_function?wprov=sfla1) (that symbol is the greek letter zeta) When s is a real number greater than 1 (or a complex number with real part greater than 1), ζ(s) is defined as the sum of 1/nˢ among n in the naturals (excluding n=0 obviously), but this definition as sum breaks down when the real part of s is ≤1 You can use [diabolical mathematical techniques ](https://en.wikipedia.org/wiki/Analytic_continuation?wprov=sfla1) to "smoothly" (in a mathematical sense) extend this function to all complex numbers except 1; using this extension, you can calculate that ζ(-1) is -1/12, while putting -1 in the original formula would give you 1+2+3+4... Some years ago, the popular math channel [Numberphile](https://youtu.be/w-I6XTVZXww?si=oMlTTel9KF2xIPLJ) popularised a way of "rearranging" the terms of 1+2+3+4+... to get -1/12 as an answer, the problem is that they kinda "cheated" (I don't remember if they acknowledge the theorem below in the video and I don't care enough to watch it again). There is this theorem, the [Riemann-Dini theorem](https://en.wikipedia.org/wiki/Riemann_series_theorem?wprov=sfla1), which states that if you have a sequence of real numbers aₙ for which its sum does not [absolutely converge](https://en.wikipedia.org/wiki/Absolute_convergence?wprov=sfla1) (as to say, summing the absolute values of each term does not get closer and closer to a real number), then you can find a rearrangement to get its sum to converge to any real number you want. Obviously, |1|+|2|+|3|+... does not converge, which means that you can find a rearrangement to get any real number you want to get, be it 0, π, e, -1385, Rayo's number or -1/12. Finally, the joke is that using the (incorrect) result from before, 3+6+9+12... = 3(1+2+3+4...) = 3(-1/12) = -1/4, so the bartender should not only be paid nothing, but he'd have to give a quarter of change to the infinite crowd of mathematicians.
The joke is the mathematicians used fake bs math to get out of a bill by pretending there is some rule where if you add 1+2+3+4 infinitely upward somehow it makes -1/12 and that times three is a -1/4 which still isnt a quarter because no one adds dollars as the whole they add cents as the whole. It would be a 0.0025$ or a quarter of a penny.
Electronics is one of the use cases where imaginary numbers are definitely not imaginary.
I can't solve it without the missing word.
Or the opening sentence that's missing.
The bartender is Terence Howard, and the mathematicians are just trolling him because they know they can score free beer if they just let him feel smart for the night?
For some reason, the infinite sum of all positive integers is -1/12, multiplying by $3 per beer gives us a total cost of -1/4, so the bar tender pays them a quarter
A dumb joke that makes no sense. There's a math equation regarding infinity that this is referencing. But since there is a finite number of humans on earth, and even smaller finite number of mathematicians on earth, and an even smaller finite number of people that can fit in a bar, the joke is dumb and makes no sense. The equation its referencing is dumb too because the equation only works because the mathematician that published it also redefined the equals sign for their proof. The equation is... all positive integers from 1 to infinite = -(1/12) ie... 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 ~ = -(1/12) They redefine the equals sign to not mean "is equal to" and instead mean "is associated with" which is a way of saying "is about". They calculate it by combining 2 other "proofs" 1st is that subtracting and adding 1 and infinite number of times = 1/2 FORMULA X = 1-1+1-1+1-1+1 ~ (infinitely) = 1/2 This is because, with the same assumed meaning of the = sign... 1-1 = 0 0+1 = 1 Your equation will constantly flip between 0 and 1 as you progress down the equation infinitely. So the answer is "It's about 0.5" or "1/2" Then you have another equation, subtracting and adding all integers from 1 to infinity. FORMULA Y = 1-2+3-4+5-6+7 ~ = 1/4 They "solved" this one by converting it back in to the previous formula. You multiply the formula by 2 and convert all the subtractions to addition by turning your 1-2 in to a 1+-2, etc. Then you can add the 2 copies of the equation together. Which will bring you right back to the same equation you had before which lets you then divide your answer of 1/2 in half to 1/4. Then they subtract the Formula Y from... FORMULA Z = 1+2+3+4+5+6+7~ (all positive integers added from 1 to infinity) Which gives you an infinite addition of factors of 4. Z-Y = 4+8+12+16+20+24~ Which can also be written as Z-Y = 4(1+2+3+4+5+6~) or as... Z-Y = 4(Z) And since we know what Y is... Z-(1/4) = 4(Z) We can reduce this down -(1/4) = 3(Z) And then if we divide both sides by 3 -(1/12) = Z Or... 1+2+3+4+5+6+7+8+9+10+11~ = -(1/12) But again, none of this is actually accurate. They're all estimations and the formulas only function with that redefined meaning of the equals symbol. Also, the joke doesn't work because the bartender should have given 36 cents back, not a quarter. (12 cents per dollar. 3 dollars for the pint. 3x12)
This joke doesn't work. There is a finite number of mathematicians. You can be sure because they all finish ordering. The bartender should count the number of mathematicians and charge them ($3n)(n+1)/2. Also, where can I get a pint of beer for three dollars these days?
Eat shit for the censor.
OP is a reposter or a bot. probably a bot. https://www.reddit.com/r/PeterExplainsTheJoke/comments/16uj17w/my_dad_sent_me_this_and_i_dont_want_to_admit_i/
There is a certain way of manipulation the series 1 + 2 + 3 + 4 + ... , such that you get the resulting sum to be -1/12. . This was originally done by Ramanujan. Essentially you can algebraically manipulate the above series to get the desired value of -1/12. The pints the mathematicians asked for add up to -1/12, so they pay -1/4 of a dollar. I.e, the bartender owes them a quarter. Of course you'd expect the sum to diverge. And it does, if you do the sum conventionally. But infinite series and sequences are tricky, and you cannot deal with them as if they were finite. An infinite series value is normally defined as the limit of its partial sums. And unless you series has certain properties, this limit is sensitive to the order you take your partial sums in; it is not the case that addition naturally implies commutativity, and the conditions that make commutativity true for finite series do not hold for infinite series. More relevant to the series at hand, UNLESS your series converges you cannot do algebraic manipulations like multiply your series by some constant or add another series to it. A series like 4 + 8 + 12 + 16 + ... is not 4 times the series 1 + 2 + 3 + 4 because the latter doesn't even have a value in terms of a limit. Multiplication by 4 is not even defined for the divergent series. Therefore there is no relation between the series 1 + 2 + 3 + 4 ... and 4 + 8 + 12 + 16 + ... in the standard sense. Yet this is similar to what Ramanujan did and this is exactly how he got his answer of -1/12. That said Ramanur than the limit of its partial sums, you can assign weird values to series. In the Ramanujan sense, the series 1 + 2 + 3 + 4 ... = -1/12. In the conventional sense the series diverges. Interestingly Ramanujan summation does actually make a comeback in physics. When studying systems with many degrees of freedom like a field or an ideal gas, you eventually end up having to compute what's known as a Zeta function, which is similar to this sum of all natural numbers. In order to assign a finite sensible value to these sums, you have to use Ramanujan summation. Mathematically we don't really know why you can do that yet.
I heard a similar one where an infinite number of mathematicians enter a bar. The first one asks for a beer. The second one asks for half a beer. The third: a quarter of beer. Fourth: eighth of a beer, and so on. The bartender pours two beers and says, "Have at it."
Can someone explain why -1/12 is a part of this when it's not written in the joke? Is the beginning of the joke missing? It doesn't say they are mathematicians til the end. Also, what word is blacked out?
Appears to be "fuckers"
The joke only works if you're a math nerd and there are an infinite number of mathematicians. Did I miss the part where the joke says there are infinitely many mathematicians?
Came here for an explanation and you all only confused me further
Only r/theydidthemath can get us out of misery.
Don't worry if you don't get it. It's not funny.
Yeah, but how would Terrence Howard explain this?
There's a mathematical reference in there, just do not have the brain power to fish it out.
If you're worried that it doesn't make sense because there aren't an infinite number of people there, you are correct.
Your dad's a very special type of need isn't he
May it be the depreciation of the dollar while you drink?
If I am getting this right, there's a formula where you go +1, -2, +3, -4, and so on. The weird thing this joke is trying to play off of comes in when you take an average of this equation approaching infinity. When you do that, you get the odd answer of -1/12. I don't know why exactly, I had a friend prove it to me once and it's just bizarre. All I know is it gets weird as you approach infinity. This joke is attempting to reference this, but neglects the subtraction portion of the equation, so it's intended joke gets lost in the process.
There are people talking about 1 + 2 + 3 + 4 + ... = -1/12 but it's definitely not that, I think it's a joke about [the infinite hotel](https://youtu.be/OxGsU8oIWjY?si=NyYte7NtmT1RE876) Its the fact that kicking one man out wouldn't change the bill, and there would still be the same amount of people ordering
This reminded me of a good joke: An infinite number of mathematicians walk into a bar. The first says "I'll have a beer," the second says "I'll have half a beer," the third says "I'll have a quarter of a beer," and so on. The bartender pours them two beers and says "You boys ought to know your limits."
It's a whole bunch of weird mathematical tricks where you start with "what's the sun of an infinite series of +1 and -1", the real answer is "does not converge", but some physicists have said "let's approximate it to be 1/2", and then from there you eventually get to -1/12 being the sum of all positive integers Numberphile did a video on this, but they skip over a whole bunch of assumptions Tl;Dr you play with math, the answer is -1/12, and 1/12 of $3 is a quarter, but it's negative so paying "-$0.25" is receiving a quarter
This is the worst joke I've ever heard
Sometimes you don’t get the joke. Sometimes it’s just a bad joke.