Exactly and may be "growing in my garden" means he needed sheets and sheets to lay out on the ground for evaluating the expanding formula, lots of papers all with written numbers, sums and digits on them for calculation and approval. Such a genius brain, too bad his garden was just big enough to evaluate Zeta of 3.
You could not have been closer in 87 trials: 87 / 71 - 1.20205 = 0.02330 87 / 72 - 1.20205 = 0.00628 87 / 73 - 1.20205 = -0.01026 To get no error: 1 / (1.202056903 / 87) = 72.3759 expected number of primes.
When he said "They grow in my garden" I thought he was going to go on to say that he found that the formula modelled the growth of mushrooms or leaves on a branch or something like that...
You know it's a good Numberphile video when you already know the maths behind it and you are still both entertained and enlightened. I mean, you kinda know it's a good Numberphile video when you get the notification, but still.
That's fabulous. I actually burst out laughing when he ran that fraction through the calculator and pulled Apery's Constant out of the hat. My eldest daughter thinks I'm loony. Well done!
As an engineering student I found this channel amazing, I have seen every video on this channel and every single one of them teached me something. Loving Numberphile ❤️
In case anyone needed further explanation: 69 is a sexual move (double oral), 4/20 is a pothead's favorite day and 4:20 their favorite time, and "over 9000" is a Dragon Ball Z reference (hence 9001).
I know. I was merely pointing out how well the experiment went for such a small sample size! Just one set of numbers going the other way would have made things worse. If it was me I wouldn't tempt fate by increasing my sample size - job done with just 87!
I don't think so it's like Euler's number the thing if you get interest every second from the bank ... for example if you use 25 samples 25% close 50 samples 37.5 % closer, 75 samples 40% closer ...
I think the point is to show why Apery wasn't taken seriously by his colleagues and why it was so surprising in general that he solved the problem, when people like Euler could not. I don't sense any jealousy here at all.
Dry sarcasm by Apery when he was asked from where he got the formula as it was in disbelief on the part of the audience that seemingly couldn't imagine Apery succeeded where Euler failed.
@@at7388 I know all of what you said and much more. Specifically I appreciate the magnitude of Euler's intelligence so that If Euler did not solve it after concentrating for a week, then it might be difficult for ordinary mathematicians to do it in years of work.
This is some of the first use of Monte Carlo i've seen in Numberphile which I think has been a real missed opportunity for the channel as MC is such an interesting topic. I think it could make an interesting video to talk about how we can approximate other constants like pi and e or solve integrals etc. using random numbers.
*gets notification* Oh boy a new Numberphile video, gonna solve that 'unsolvable problem' with my extraordinary intelligence... *watches video* Yea, I definitely understand some of these words...
Big applause ! Love this kind of videos, where something relatively simple but not known is explain, like how calculate zeta function of integers with twitter. Love it !
If you pause the video at 4:45 you can read some part of the demonstration (in French). The 6th point starts with "si on a de la chance.." means "if we are lucky" which is kinda funny in such a paper
"not a great mathematician but just good" goes on to solve something the brilliant Euler himself couldnt solve ...ha, im sorry but that should *instantly* place you in the great category, even if you failed all other things
indeed , that was an inappropriate and disrespectful remark and in fact to this day many mathematicians have tried and failed to generalize apery's proof although his proof got them closer to it , which indicates his impact.
I interpreted that statement as a reflection of Apery's reputation as a mathematician at the time before his proof and constant. A kind of historical narrative if you will, but yeah, it is not pretty.
As a layman, I appreciate the way you warn me that you're about to cite some historical mathematical gobbledegook I've never heard of by prefacing it with the words "Of course"
"OK. how...? why?" his excitement is my favourite part of this video. Like a child that really wants to show something he or she learned at school. this kind of enthusiasm for maths is what needs to be introduced to children and students imo.
0:36 I had to pause myself, to think that: ”Oh, yeah! QED also means: ”Quantum Electrodynamics”.”; because I automatically think of: ”Quod Erat Demonstrandum” 😅.
-be born 150-200 years ago -make a convergent series with a bunch of low digit numbers -call the constant after yourself -??? -get remembered at great mathematician -be immortal in the memory of people
NIST: "so where did you get these huge elliptic curve numbers, P and Q, from?" NSA: "they grow in our garden" NIST: "perfectly acceptable answer, standard approved !!!" Alice: " wtf ? " Bob: " fml :( " Bruce: " ffs !!! "
Actually, 1.208333 is as accurate as it can be with that sample size. 87/73 = 1.1917808(irr), so 1.20206 sits right between those two values, meaning this was actually exactly perfect. Amazing.
Note that the letter pi in the latter part of the video is an upper-case pi (means product). The pi at the beginning is lower-case (the constant pi). Both of them are discussed in the context of Euler though...
On a completely different note, I did find a simpler way of representing the ceiling function with an infinite sum of the sign function (or my version which is x/|x|) and moving it around, it might simplify the collatz conjecture or something
Just ran a little simulation in Mathematica. Turns out asking if three numbers are coprime in Mathematica (CoprimeQ[a,b,c]) is NOT the same as asking if the greatest common divisor of the three is 1 (GCD[a,b,c]==1). In the first case, it checks each pair of numbers to see if they are coprime and returns true only if ALL pairs are coprime. In the second, it simply finds the greatest divisor common to all three. So, CoprimeQ[2, 4, 9] --> False, but GCD[2, 4, 9] ==1. To approximate Apéry's Constant, you have to use GCD.
By using the arithmetic series 1/(1-r) = 1+r+r^2+... with r=1/p^3 and a simple combinatory argument, using the fundamental theorem of arithmetic it is not hard to see that Apéry's constant equals the product over all primes p of (p^3)/(p^3-1). So Apéry's constant is the limit of n to infinity of the ratio a/b where a = prod{i=1 to n} (p[i]^3) and b = prod{i=1 to n} (p[i]^3-1), p[i]= the i-th prime number and a and b are coprime and get arbitrary large. But the sheer fact that we need arbitrary large numbers a and b to express the representation a/b for A is not yet any proof that A itself is irrational. After all 99999999... /100000000... = 1. Didn't expect to solve it, just nice stuff to play with!
Man, you messed up the joke. It goes "What is that? Are you armed?"
"No, I am legged"
Really??! Then he butchered it hard..!;)
@@mienzillaz unlikely that he would have been speaking English
@@rad858 that was about joke, that story can't be true..:)
That makes no sense in French though. Not in German either.
That certainly isn't a leg of humor
Euler seems to have been involved with every dam constant in his days.
I wonder what Euler would do if he had access to MATLAB.
he died, so he can't be a constant
Robb V. Constantly involved
@Pedro Marinho: If Euler had access to MATLAB, we would be enjoying the Star Trek Transporter by now...
Wouldn't that make right almost half of the time? ;)
And the Gestapo shot Apery on sight because although he wasn’t armed he was legged.
I heard his mate was so upset about the shooting he got legless to drown his sorrows
This is alleggedly what happened that night
Exactly and may be "growing in my garden" means he needed sheets and sheets to lay out on the ground for evaluating the expanding formula, lots of papers all with written numbers, sums and digits on them for calculation and approval. Such a genius brain, too bad his garden was just big enough to evaluate Zeta of 3.
More like LEGEND.
My garden is too small to include the proof
Heliocentric otro argentino viendo numberphile?
Nicolás Torchia tres
quinto por aca
Heliocentric I have a fantastic little proof, but there isn't enough room in my garden to write it down
"I'm gonna do a pro-Fermat move"
"Apéry's quite an interesting character, he's French" yes... very interesting...
+
×
/
^
666th comment.
You missed the most important part...
WHY DO THEY GROW IN HIS GARDEN???
I wanna know too!
Now proofs don't grow on trees do they?
i think i might've finally cracked this one.
Not enough time in the video, or space in the margins of the description to include the explanation!
You could not have been closer in 87 trials:
87 / 71 - 1.20205 = 0.02330
87 / 72 - 1.20205 = 0.00628
87 / 73 - 1.20205 = -0.01026
To get no error: 1 / (1.202056903 / 87) = 72.3759 expected number of primes.
epic
Thank you for doing this. Amazing. 😂
Not only that, but it could not have been closer with 72 co-primes.
86/72 - 1.20205 = -0.00760,
87/72 - 1.20205 = 0.00628
88/72 - 1.20205 = 0.02017
1/(constant/87) can be simplified to 87/constant, because (1*87)/(constant/87*87)=87/constant
This is pretty fantastic
6:03 - Matt Parker's reply always the best :)
Oh, Matt...
IIARROWS such a parker square
69
420 blaze it
last one is over 9000
XD
There has to exist some number base where the numbers would have fit. Might have had to use emoji.
I'm a birdplane
Literally got the closest possible result with that sample size. Well done!
When he said "They grow in my garden" I thought he was going to go on to say that he found that the formula modelled the growth of mushrooms or leaves on a branch or something like that...
Me too!
Why would he tell the truth? He was not talking to Gestapo.
You know it's a good Numberphile video when you already know the maths behind it and you are still both entertained and enlightened.
I mean, you kinda know it's a good Numberphile video when you get the notification, but still.
That's fabulous. I actually burst out laughing when he ran that fraction through the calculator and pulled Apery's Constant out of the hat. My eldest daughter thinks I'm loony. Well done!
As an engineering student I found this channel amazing, I have seen every video on this channel and every single one of them teached me something. Loving Numberphile ❤️
One of my favorite numberphiles. Tells good story with plot, personalities and suspense. Fun.
69,420 and 9001 what a meme..
why?
In case anyone needed further explanation: 69 is a sexual move (double oral), 4/20 is a pothead's favorite day and 4:20 their favorite time, and "over 9000" is a Dragon Ball Z reference (hence 9001).
shouldnt we consider cloning euler if we can get dna from his remains
Who says maths is boring?
Columbine happened on 4/20 too
With a sample size of 87 you can't actually get any closer to the actual constant than this, can you?
I think he might mean if he counted more of tweets, thus increasing the sample size?
I know. I was merely pointing out how well the experiment went for such a small sample size! Just one set of numbers going the other way would have made things worse. If it was me I wouldn't tempt fate by increasing my sample size - job done with just 87!
Tom Blakeson I agree
i know right...
I don't think so it's like Euler's number the thing if you get interest every second from the bank ... for example if you use 25 samples 25% close 50 samples 37.5 % closer, 75 samples 40% closer ...
10:09 : "makes sense?" Complete silence from Brady XD
This mathematical relations are so astonishingly beautiful. It's like watching the source code of the universe being shown to me.
At 2:47
Gestapo: "Is that your firearm?"
Apéry: "No, i'ts my friend's _leg_!"
Gestapo: "Oh"
Given how often Padilla claims that Apery was "good but not great" I get a strong vibe that he is just lowkey jelly he didn't get to solve it.
I think the point is to show why Apery wasn't taken seriously by his colleagues and why it was so surprising in general that he solved the problem, when people like Euler could not.
I don't sense any jealousy here at all.
Cobalt Hey, get back to the PUBG series
this is the last place i would expect to see other nlss fans
Nice name
Not great as in, he solved only one major mathematical problem of his time instead of dozens like Euler or Gauss.
Well wait, hold on. What did he mean by "they grow in my garden"? It was never explained in the video!
Dry sarcasm by Apery when he was asked from where he got the formula as it was in disbelief on the part of the audience that seemingly couldn't imagine Apery succeeded where Euler failed.
@@at7388 I know all of what you said and much more. Specifically I appreciate the magnitude of Euler's intelligence so that If Euler did not solve it after concentrating for a week, then it might be difficult for ordinary mathematicians to do it in years of work.
@@nahidhkurdi6740 i was thinking maybe he does math outside in his garden.
This is some of the first use of Monte Carlo i've seen in Numberphile which I think has been a real missed opportunity for the channel as MC is such an interesting topic. I think it could make an interesting video to talk about how we can approximate other constants like pi and e or solve integrals etc. using random numbers.
the buffons matches video uses a monte carlo method to calculate pi
0:52 Of course!
1:43 Of course!!
1:56 Of course!!!
2:01 Right.
2:10 Of course!!!
2:12 Of course!!!!
Of coarse!
If we divide the total number of interjections by the number of "of course" occurrences we get 6/5 = 1.200. Great Apery's constant approximation!
*gets notification*
Oh boy a new Numberphile video, gonna solve that 'unsolvable problem' with my extraordinary intelligence...
*watches video*
Yea, I definitely understand some of these words...
Ibrahim Fadhil Senjaya LOL
Big applause !
Love this kind of videos, where something relatively simple but not known is explain, like how calculate zeta function of integers with twitter.
Love it !
FINALLY! I've been wondering for 3 months what you wanted these for
Quantum electrodynamics sounds quite intimidating.
7:00 respect the dedication
Wow, I'm impressed... Tony does a video related to the Riemann zeta function without mentioning a certain negative rational number.
"We recognize that, of course, as the riemann zeta function"
Me, stuffing another handful of cheetos i my mouth: "Yeah, of course"
8:00 quite a ... Parker Square
Brotcrunsher 😂😂😂
That's what Matt tends to say too..."not bad"
(first digit comes out and is correct)
Matt : Not bad , look at that
How is doing exactly what he set out to do a Parker square?
I can imagine Matt's voice: LOOOOK AT THAAAT!!
If you pause the video at 4:45 you can read some part of the demonstration (in French). The 6th point starts with "si on a de la chance.." means "if we are lucky" which is kinda funny in such a paper
"not a great mathematician but just good"
goes on to solve something the brilliant Euler himself couldnt solve
...ha, im sorry but that should *instantly* place you in the great category, even if you failed all other things
indeed , that was an inappropriate and disrespectful remark and in fact to this day many mathematicians have tried and failed to generalize apery's proof although his proof got them closer to it , which indicates his impact.
I believe he was referring to him prior to having solved this
Yup, kinda disrespectful from Tony Padilla....
Consistency over luck I recon
I interpreted that statement as a reflection of Apery's reputation as a mathematician at the time before his proof and constant. A kind of historical narrative if you will, but yeah, it is not pretty.
As a layman, I appreciate the way you warn me that you're about to cite some historical mathematical gobbledegook I've never heard of by prefacing it with the words "Of course"
0:37 "It's a *crazy* number."
Twitter... Crazy... Yep, it fits
PlayTheMind lol so true
true
Didn't think I'd see you here PlayTheMind haha
Playthemind ,when is your next video ? :D
6:02 Matt Parker: "I tried..."
The numbers could almost fit. You could say it was a bit of a
Parker square! hahaha im funny validate me
I've already seen it. Brady uploaded the live stream of the editing. Great editing Brady!
"That's why it worked.... Make sense?"
Amazing! Maybe it made sense to Euler, but not to me.
Every Tony video I watch, I wonder why he's not a mathematician. He seems to be very passionate about mathematics and numbers!
(6:03): This is the moment in this video that earned my thumbs-up!
10:09 Uhmm yea... sure..
When I try to explain maths to my sister
Watch Mathologer's video on the Riemann Zeta Function! It helped me understand the coprime part
You don't need to understand what the Riemann Zeta function is, the crux of this video is just some basic statistics.
"OK. how...? why?" his excitement is my favourite part of this video. Like a child that really wants to show something he or she learned at school. this kind of enthusiasm for maths is what needs to be introduced to children and students imo.
His estimate is actually the closest he could have got with only 87 random triads of numbers! Makes it even more impressive!
Very clever and a great way to demonstrate how it generalizes to the real world. Thanks!
0:36 I had to pause myself, to think that: ”Oh, yeah! QED also means: ”Quantum Electrodynamics”.”; because I automatically think of: ”Quod Erat Demonstrandum” 😅.
8:07 really mind blown. Explanation is even better.
So far, the best Numberphile video to me.
The probabilistic interpretation of the inverse zeta function at integer values was really clever! Never thought of it that way.
-be born 150-200 years ago
-make a convergent series with a bunch of low digit numbers
-call the constant after yourself
-???
-get remembered at great mathematician
-be immortal in the memory of people
-profit
Underpants!
Actually, others named it after him.
i always read Oiler in my head when someone mentions Euler and think they're some sort of specialized bike mechanic who goes around oiling things
I used to pronounce Euler like "Ferris Bueller"
@@elietheprof5678 I still pronounce it like that, and just to really rile up the mathematicians, I also pronounce Euclid as "Oiclid".
Fascinating! I like Padilla very much
Wonderful :-)
You here...
Cool
Tony is back!
Fascinating. Though, Matt Parker have done this for his Pi day video for ζ(2) to estimate π.
NIST: "so where did you get these huge elliptic curve numbers, P and Q, from?"
NSA: "they grow in our garden"
NIST: "perfectly acceptable answer, standard approved !!!"
Alice: " wtf ? "
Bob: " fml :( "
Bruce: " ffs !!! "
I love you. Please continue.
We missed you Professor
I'm no mathematician but that was amazing.
amazing stuff for non mathematicians. Great divulgation, thanks!
Wow man. This video made my day.
It really bugs me that he doesn't write 1/1^s
He did, you just don't see it =)
@Furrane yes, it's like the invisible motorcycle meme.
1/1^s equals 1 for all complex numbers, so 1:38 is correct afaik
I like this type of video keep it up
An open ended question of integers usually results in a logarithmic distribution.
Im sorry but "not a great mathematician" and "figured something out that Euler struggled with and gave up on" are both mutually exclusive.
i love Tony! more of him please
These are priceless gems for the grand archives. Brady keep 'em hot like this.
Breathtaking
Actually, 1.208333 is as accurate as it can be with that sample size. 87/73 = 1.1917808(irr), so 1.20206 sits right between those two values, meaning this was actually exactly perfect. Amazing.
That roundabout demonstration using Twitter was super cool.
Gotta love the one they kept on the screen longest was 69, 420, 9001 XD
Great video
10:05 MINDBLOWN
Note that the letter pi in the latter part of the video is an upper-case pi (means product). The pi at the beginning is lower-case (the constant pi). Both of them are discussed in the context of Euler though...
"69, 420, 9001"
What a spicy meme
6:03 - what a Parker square of a reply
Absolutely wonderful, thanks.
I like how Google reads my mind recommending videos. I have a math clock, and just saw the 1 on the clock (which in my case is apery's constant).
This was so beautiful!
This was beautiful math!
THIS is why I watch Numberphile
He's like so happy in the end :)
When Padilla writes the word prime I can't stop seeing the word prune.
"Is that a gun?"
"No it's a leg"
This is essentialy what Matt Parker did on pi day. But it's nice to see how this generalizes to other values of the zeta function
>Solves problem Euler couldn't
>gets called "not a great mathematician"
He wasn't considered great before, but this one definitely put him on the map!
"the chance that any random number is dividable by p, is 1/p", i learned something :O
This guy is amazing!
This guy has so much doing his work
On a completely different note, I did find a simpler way of representing the ceiling function with an infinite sum of the sign function (or my version which is x/|x|) and moving it around, it might simplify the collatz conjecture or something
When I saw Tony and ζ in the same video I got so on edge waiting for that -1/12 to appear out of nowhere.
That's an amazing result!
Great, impressive!
Fascinating!
I like his happy little face at 10:09.
"Is that an arm you've got concealed there?" "No it's a leg"
Great stuff.
Somebody needs to photoshop Euler dabbing.
Just ran a little simulation in Mathematica. Turns out asking if three numbers are coprime in Mathematica (CoprimeQ[a,b,c]) is NOT the same as asking if the greatest common divisor of the three is 1 (GCD[a,b,c]==1). In the first case, it checks each pair of numbers to see if they are coprime and returns true only if ALL pairs are coprime. In the second, it simply finds the greatest divisor common to all three. So, CoprimeQ[2, 4, 9] --> False, but GCD[2, 4, 9] ==1. To approximate Apéry's Constant, you have to use GCD.
By using the arithmetic series 1/(1-r) = 1+r+r^2+... with r=1/p^3 and a simple combinatory argument, using the fundamental theorem of arithmetic it is not hard to see that Apéry's constant equals the product over all primes p of (p^3)/(p^3-1).
So Apéry's constant is the limit of n to infinity of the ratio a/b where
a = prod{i=1 to n} (p[i]^3) and
b = prod{i=1 to n} (p[i]^3-1),
p[i]= the i-th prime number
and a and b are coprime and get arbitrary large.
But the sheer fact that we need arbitrary large numbers a and b to express the representation a/b for A is not yet any proof that A itself is irrational. After all 99999999... /100000000... = 1.
Didn't expect to solve it, just nice stuff to play with!
Woah that's amazing!
Tony is the type of guy that grows on ya