Homer Simpson vs Pierre de Fermat - Numberphile
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- เผยแพร่เมื่อ 30 ก.ย. 2024
- Simpsons Book: amzn.to/1fKe4Yo -- Main Fermat Theorem video: • Fermat's Last Theorem ... -- Water Ballons: • Science of Water Ballo...
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Author Simon Singh on Fermat's Last Theorem in popular culture, especially The Simpsons.
Also mentioning Al Jean and David X Cohen.
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When will we see a video on pancake flipping?
^
3master o
WarpRulez YOU SHOULD KNOW THE ANSWER TO THAT BEING FROM THE FUTURE
a near miss of the order of 10^30.
i wish i could do that in my physics exams!
I'm surprised you haven't had a numberphile about e yet. It's a fascinating number that I'm sure you could delve quite deeply into. Euler's Identity would be another excellent (and related) topic.
"The writing staff held three Ph. D.s, seven master's degrees, and cumulatively had more than 50 years at Harvard University. Series writer Patric M. Verrone stated, "we were easily the most overeducated cartoon writers in history". (talking about Futurama which also featured the work of David X. Cohen)
I'm wondering : am I the only one who's bad at math but enjoys numberphile ?
I believe James Grime has done a video similar to this but with Futurama, on his own channel singingbanana.
Maybe a link to that one as well Brady?
What ever happen to the good old day? You know, 1+1=2.
What, the thing that took several hundred pages of Principia Mathematica to prove? Yeah, I hanker after those times, they were so much simpler.
Wait... I do Maths at Warwick. Are you telling me I may end up working on The Simpsons? :D
hm. 3987^12+4365^12 is about 1.2 Million Trillion Trillion Trillion bigger than 4472^12. how is that a "near miss"?
Damn right! My pocket calculators all say the same. Cool.
So taking Pythagorean's theorem and applying it to geometries greater than 2D fails? Is that the essence of this theorem?
Can you do a video on the great genius of Leonard Euler ,?
6:43 It would be second in broadcast order, first in porduction order.
Is that the Squeaky Voiced Teen behind the camera?
I wish that mathematics wasn't taught so dully and uninterestingly in our culture. math is an art and we should be emphasizing the importance of math more than anything
Math isn't an art. That's what makes it so great.
Well, the best way to do it is to do away with the more utilitarian mindset behind education, after all technically most stuff we get taught can be considered to be "useless" and it's not just us liberal arts majors who can be looked down upon as knowing "useless" stuff.
What is useless info anyways? I think how you answer the question can tell about your mentality behind this question, if your meaning of life is making money then only some business majors and most engineering careers are useful studying.
Perhaps because of these two answers?
The one side is very strict and says: "shouldn't treat it as an art at all", lets keep the classes dull.
and the other goes of on an extreme tangent, preferring to attempt to answer broad/philosophical questions, rather than tackle it practically.
I'm not sure it IS about the "importance", but simply, appealing to students. Everything CAN be important, but if it isn't being taught in a way that people will (want to) apply it, it's still not useful.
Personally from highschool, I remember endless equations of things like: solve (x+4)(x-12)=0
While, now, I realize I'd love to solve stuff like that, back then I just couldnt get the hang of it, by ONLY having the dry, stuffy, equation.
What's the purpose? What is this solving, in real life? Can I get a handle on it that takes it OUT of the theoretical and gives me some insight, rather than just having to crunch numbers again and again.
Perhaps ironically, when I see people like Matt Parker, I get excited about it, and want to learn. All it takes, for me, is to have it presented in a fun way that makes me want to come back for more.
Maybe it's the teachers? Most I've had didn't make the lessons very fun or engaging. Some did. The books didn't really help, they had SOME humor and real-life experiences in it, but they were the lame kind. "Alice and Bernard walked up to their friend Charles". Clearly just to describe points A,B,C. More pedantic than appealing.
how is math an art
Says you
th-cam.com/video/ReOQ300AcSU/w-d-xo.html
+Zero Ryoko It's a^n+b^n=c^n for positive a, b, and c. 0 doesn't count because it isn't positive (it's neither positive nor negative).
j
I had my own near miss solution with a^3 + b^3 = c^3 where a=242, b=720, and c=729. So close, yet so far away
starreactor Again, only because of the odd-even properties ;)
Haha you were 1 away from being right with that near miss solution (729^3 - (242^3 + 720^3) = 1)
+Bengt Bengt 1^3 + 1^3 = 1^3 also near-miss tho XD
Pius Pambudi actually not because x, y and z must be different numbers
I've never seen the stipulation that they need to be. It is easily provable that they cannot be - in a^n+b^n=c^n (a, b, c, n all integer; a, b, c >=1; n>2) c obviously needs to be larger than both a and b, since otherwise you would add something positive to a number and it would stay the same. But also a and b have to be different, because if a=b, then a^n+b^n=a^n+a^n=2*a^n=c^n. Taking the n-th root, we's get (n-th root of 2)*a=c, but since both a and c must be integers but the n-th root of 2 isn't even rational, this simply is not possible.
1:23 there is also an attempt at breaking topology at the bottom
Sachin Sahay Nice catch!
Sachin Sahay too bad it wasn’t REAL.
thats Poincaré's conjecture, isn't it?
Homerlogy.
Simon might just have the most beautiful handwriting of all the Numberphile guests
egalomon Hes a writer. It makes sense.
"Doing a troll"
I love you Brady.
+Badatstuff I thought he said "being" a troll, haha
The Drüid lol
He definitely said "Being a troll."
1782^12+1841^12=1922^12
It actually equals to 1921,999999955...^12 ._.
VEEEEERY close
Yup, not bad.
8730^12 + 7974^12 ≈ 8944^12 is closer, though.
(8944.00000001412-8944)/8944 ≈ 1.58e-12
(1921.999999955-1922)/1922 ≈ -2.34e-11
or better: 48767^4 + 24576^4 ≈ 49535^4 or e.g. 89,970^3+8,999^3 ≈ 90,000^3 and 90,000^3+9001^3 ≈ 90,030^3
My attempt 0000^12+0000^12 =0000^12.... Fricken math.. no idea what I'm doing but that equation checks out as far as I'm concerned.
@Sandra Braithwaite Sure. That was for fun.
you think he wrote a book about the Simpsons, met the writers (of both shows) and did nothing about Futurama!
Stay tuned for more (or buy his book!)
Another example would be Rowan Atkinson who studied engineering at university.
+Slim Charles Indeed, and his long-time side-kick Ben Miller - who studied physics.
Is that how he put on shorts without taking off is trousers?
Yes. It's a topological problem.
This whole phenomenon of serious mathematics being referenced in light entertainment reminds me of Charles Dodgson's mathematical references in "Alice in Wonderland", although mathematics plays a much more central role in his book than it does in the Simpsons.
Actually, here's a good idea for Numberphile, assuming they haven't already done it: Do an episode on maths in "Alice in Wonderland" (and "Through the Looking Glass")!
Just came back here to visit another Parker Square solution to Fermat's last theorem.
I literally only read the comments to see if someone referenced Parker for that almost-solution for Fermat's theorem.
The real solution is 3987^12 + 4365^12 = 4472^11 X 4472.00000008
No, not quite, it has to be to the 12th each, what you’ve done is reduce it and then add a decimal.
It doesn't really fit the problem.
@@acewmd.Well what he is saying is that if he did put it in the form of x¹², then the decimal part would be smaller and more precise, so he's just compressing it.
The reason these are being dropped into the episodes is not because mathematicians-turned-into-comedy-witers want to make a nod at their alternate occupation. It is because they are very effective comedy writers. They write comedy for ALL intellectual levels.
That's the beauty of the series and the probable reason it has survived as long as it has. Trailer Park Joe laughs at the bodily function jokes, Office Jack reads the humor in popular culture spoofs and Science Peter gets a kick out of why would a 10 year-old have a Kasparov lunch box.
Case in point: The "faux solution" to Fermat's Last Theorem is a very effective bit of comedy (...even if buried almost as an Easter-egg...) because, under the show's logic and being Homer who he "is", had he - by some divine intervention - really turned into a researcher, Dr. Simpson being convinced he reached the actual theorem solution via a false proposition would be the kind of elevated blunder, leading to all sort of problems, he most certainly would be involved in.
To be fair, you have to have a very high IQ to understand the Simpsons. The humour is extremely subtle, and without a solid grasp of mathematics most of the jokes will go over a typical viewer’s head. There’s also Bart’s nihilistic outlook, which is deftly woven into his characterisation- his personal philosophy draws heavily from Narodnaya Volya literature, for instance. The fans understand this stuff; they have the intellectual capacity to truly appreciate the depths of these jokes, to realise that they’re not just funny- they say something deep about LIFE. As a consequence people who dislike the Simpsons truly ARE idiots- of course they wouldn’t appreciate, for instance, the humour in Homer’s existential catchphrase “D’oh,” which itself is a cryptic reference to Turgenev’s Russian epic Fathers and Sons. I’m smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as Al Jean’s genius wit unfolds itself on their television screens. What fools.. how I pity them. 😂
And yes, by the way, i DO have a Simpsons tattoo. And no, you cannot see it. It’s for the ladies’ eyes only- and even then they have to demonstrate that they’re within 5 IQ points of my own (preferably lower) beforehand. Nothin personnel kid 😎
There are two kinds of people.
Anybody care what this guy thinks?
NO!
To be fair, it could be for both of those reasons, as they are not mutually exclusive.
It's Anatoly Karpov on the lunchbox, not Garry Kasparov.
If you want the brown paper from this video there is a link in the vid description
(it is just another way to help support our videos - but the best thing you can do is just watch us and share with friends!!!)
I have another problem with no solution; how do you get a USB to fit properly on the first try?
+Arun Singhal you can, but It's hard to explain on text xD
+Arun Singhal
the answer lies in elliptic curves
+Arun Singhal I have the solution...but the whole data that can fit on the Internet is too little to fit it inside
the side with the USB symbol will always be the top side.
also i know this is late but it is worth mentioning
[GD] Unearth not if it's sideways
did anyone notice that the first equation that Homer writes is also a very close approximation of mass of Higgs Boson ? and that episode aired way before we proved the existence of higgs boson
@Xenon Creed it was predicted by Higgs 🤦♂️ the guy the particle is named after.
@@woobilicious. 🤣
Just want to say how thankful I am that he wrote that book. It got me back my long lost and burning passion for maths, and lifted me out of a long and horrible depression. It reminded me that life can be exciting, and actually worth living.
Yeah that's the spirit. Dont let others control your life. You know I had gone through the same circumstance.
I only came because TH-cam recommended it and because I read Homer Simpson....
They work in comedy because not every mathematician can tolerate the life of abject poverty that they would find themselves in if they stayed in academia. I'm also a Math PhD, I work in IT.
It's off by about 10^33 :-)
exscape less than one part per billion then
futurama has many more math jokes in it and David X Cohen comments on every single episode on the DVDs. RIP Futurama :(
futurama is an even better example
"When you can't get a job in mathematics, you find a job in arts"
Phew.
He underestimates modern phone calculators.
True. Most even those simple ones (including mine) use 52bits of precision. 204290^3 + 146996^3 = 227033^3 does the trick, though.
Man that is a really clever reference. Props to the Simpsons writers.
Amazing video, I love this Simpsons, Math, and Science.
"This is a solution."
"A solution? That's problematic!"
I love mathematicians :')
One of the reasons you see stuff like the 'Karpov' joke in The Simpsons is that they are willing let a joke be missed by most viewers. Most TV shows are controlled to the tiniest detail and a reference to something so arcane would be seen as a weakness that needs to be sent around the writers' room again.
The Simpsons *used* to be novel in that they would put tons of mini-gags into the show that wouldn't be noticed at all by 99% of those watching. These days everyone does it of course.
I saw Simon give a talk in Leeds the other day. I asked him to sign my boob and he said no.
He's a classy guy!
Is this the episode where Homer makes the Lazy Man Reclining Toilet Chair?
yep, then accidentally leaves it in the Thomas Edison museum, and Edison gets credited for it.
Edison invented it, Homer just stole the idea
we've done a video on that!
rd r r
hardy harr harr, get it?
thanks!
the Pythagorean theorem, anyone?
***** Men it says for n>2, and is allways proven when x+y>z.
I just remember "In This House We Obey The Laws of Thermodynamics" hahaha funny
The answer is X to the power of Cellsior.
Saw this joke on the Simpsons yesterday :
√-1 2^3 sum of (Sigma) Pi
And it was delicious
What does it mean ??
D Gurung i ate some pie...and it was delicious
Haha! Thanks
+D Gurung √-1 = imaginary number, denoted by letter 'i' = I
2^3 = 8 = eight = ate
sum = some
of = of
Pi = pie
...
And it was delicious
I assume the words "sum" and "of" are not supposed to be there because that's what the sigma is for. :)
I ate some pie
D Gurung i 8 some pi aka I ate some Pie
sorry
It's impossible you say? We'll see about that
For me somehow this professor reminds me of the mathematician in the Jurassic Park original movie
Fermat's Last Theorem applies for n = 0 (trivially) and n < -2 as well. You can find general solutions for n = -1 and n = -2 near the bottom of Wikipedia's article for Fermat's Last Theorem.
Funny fact: x^3 + y^3 does not equal z^3, BUT w^3 + x^3 + y^3 DOES equal z^3!!
3^3 + 4^3 + 5^3 = 6^3
27 + 64 + 125 = 216
The theorem just skips the easy one. 3^2+4^2= 5^2 => 9 + 16 = 25 => 25=25
The theorem has to has n>2 just to skip this one.
Also the other easy one x^0 + y^0 = Z^0
Sam Crosswell, Nope, 1+1 is not equal to 1. You're probably thinking of 0^n+0^n=0^n.
"If you were really smart, you wouldn't need a calculator to know there was something wrong" is way, way more true than most people think. I mean, sure, you probably need a calculator to know what's right when you get to complicated stuff, but usually if an error creeps in it explodes enough that you can just go "Wait, that can't be right..."
Hey Bert!, where's Ernie?
If you were really smart, you wouldn't need to be a mathematician to know that Simpsons isn't providing a "solution" to Fermat's Last Theorem, rather he was trying to DISPROVE Fermat's Last Theorem. It seems NPR and Singh have trouble with basic semantic logic.
you think he didn't!?
Or: Mathematicians are unemployed
1:18
The reason why the equation doesn't work:
3987 is a multiple of 3, so 3987^12 is a multiple of 3
Also, 4365 is a multiple of 3, so 4365^12 is a multiple of 3
Therefore: 3987^12+4365^12 is a multiple of 3
However, 4472 has a remainder of 2 when divided by 3 . . . so 4472^12 has a remainder of 2^12=4096 (or remainder 1) when divided by 3.
Since a number clearly cannot have a remainder of *both 0 and 1* when divided by 3, the two sides of the equation are unequal.
n>2
Yes
To this day, one the funniest scenes in the Simpsons is when Bart is searching for Milhouse in the tree house: he moves his gaze from corner to corner, and he finds him in the sixth corner of a four-corner house 😆😄😂
Because of the narrower focus of the show, there are more opportunities for the creative team to play on Futurama, and you see more math references there. The most notable is probably the novel and rigorous proof about the mathematics of body swapping in "The Prisoner of Benda".
Homer also has the fine-structure constant and Planck mass on the board.
It's actually the mass of the Higgs boson (which explains the H^0), and from what I remember is actually pretty close to the actual mass measured when it was discovered many years after this episode aired.
thanks
Karpov was great in the seventies (world champion great), and he is still great today. Consistent over time, perhaps the greatest chess player ever.
You guys should definitely do a video on the futurama theorem
are those significant dates?
1782,1841,1922
1782 could be bernoulli?
It's weird, i plugged in the equation to my calculator's verify function (3987^12+4365^12=4472^12) and it turns out to be false. Accuracy mabye?
oh wait never mind, it's a near miss
shellsamurai Not even near
My calculator said it was perfectly accurate. I use a scientific calculator - CASIO fx-82AU PLUS. We just disproved a massive proof that took years to form.
MultiOmps sorry my CASIO fx-86DE PLUS, CASIO ClassPad II fx(CP-400) and HP Prime all stated it was off by about 1.2121*10^33
MultiOmps it looks fine with 4 digits but when you go out to something like 7 or 9 digits then its wrong in one of the digits. That's a near-miss.
Interesting little thing with Homer's first sum... if you count all the numbers until you get a single, it goes to 9 + 9 = 9. Then, counting them together will give you 9.
Personally, I like to call the number nine an infinite number, because anything that gets counted to a single amount and ends at nine will stay nine (1+8; 2+7; 3+6; etc.) Thus 9 is ninefinite :D
/sillyness
i just noticed i own a book by him already lol
If they pay that much attention to details in series, then who "dropped" 911 in the episodes before 911 happened? I just want to know who, that's all.
Yeah, there is validation to this guy's theory on why David X Cohen drops math based stuff in The Simpsons and even Futurama, he leaves it as little teasers to other math nerds in the world, of course there are others on the team but it was mostly Cohen explaining all of this on DVD audio commentary, there is other stuff he drops in like fake alien languages that they come up with and it leaves a secret message or something that is mostly in the futurama universe though.
Maybe another reason so many mathematicians have found their way to the writing staff of the Simpsons might be that they can make more money and have more fun then they could being a professional mathematician.
Please do a video on Futurama!
Using a high accuracy calculator for the first example in this video I calculated a difference of 1.21188681x10E33 between the summation on the left side of the equals symbol and the number on the right side of the equals symbol. This is a near miss and further confirms Femat’s last theorem. The equation that I am referring to is 3897^12+4365^12=4472^12 from the example in this video. When you rearrange this equation to 3897^12+4365^12-4472^12 you get 1.21188681x10^33.
When you add 3987^12+4365^12 with a high precision calculator you will get 447200000000705929073821352941449^12 which not a whole number.
In the first example I used a DM32 calculator and found a difference of 1.21189*10E33 between the numbers on both sides of the equation. The sum on the left side of the equation is 6.39766564969861261…*10E43 while 6.3976653848672580686235…*E43 is the number on the right side of the equation. When you subtract the sum on the left side of the equation from the number on the right side of the equation with a high accuracy calculator you get the difference mentioned above. This is a near miss which is further proof of Fermat’s equation.
On homer cubed there is also the equation of N=NP
Proof of Fermat's Last Theorem for Village Idiots
(works for the case of n=2 as well)
To show: c^n a^n + b^n for all natural numbers, a,b,c,n, n >1
c = a + b
c^n = (a + b)^n = [a^n + b^n] + f(a,b,n) Binomial Expansion
c^n = [a^n + b^n] iff f(a,b,n) = 0
f(a,b,n) 0
c^n [a^n + b^n] QED
(Wiles' proof) used modular functions defined on the upper half of the complex plane.
c = a + ib
c* - a - ib
cc* = a^2 + b^2 #^2
But #^2 = [cc*] +[2ab] = [a^2 + b^2] + [2ab] so complex numbers are irrelevant.
Note: there are no positive numbers: - c = a-b, b>a iff b-c = a, a + 0 = a, a-a=0, a+a =2a
Every number is prime relative to its own base: n = n(n/n), n + n = 2n (Goldbach)
1^2 1 (Russell's Paradox)
In particular the group operation of multiplication requires the existence of both elements as a precondition, meaning there is no such multiplication as a group operation)
(Clifford Algebras are much ado about nothing)
Remember, you read it here first)
The equation in the first example should be 3987^12 + 4365^12 = (4472.0000000070592907382135292414494094^12). This is not a whole number.
Try x^24 + y^24, x^48 + y^48, and x^96 + y^96 for even closer near misses to Femat’s last theorem. You have to have a calculator that shows up to 100 digits after the decimal point.
Great video. Thanks for sharing that. I have just bought Simon Singh's book and cannot wait to read it!
Hmmmm pancakes
Yep. Died this year (for the second time). RIP best show on television.
you can check this with exactness in the Python programming language with the function:
def homer(a, b, c, n):
return a**n + b**n == c**n
by calling:
homer(3987, 4365,4472,12)
the exact calculation is effectively instant, and exact.
I can highly recommend "Trick or Treatment" by Simon Singh and Edzard Ernst. Not much math trough.
3+9+8+7=27
2+7=9
4+3+6+5=18
1+8=9
Since both numbers are divisible by nine, running either of them through the nth power should give us a number divisible by 9. Adding those products together should give us a number divisible by nine. However:
4+4+9+8=17
1+7=8
It doesn't factor into 9 and it doesn't factor into 3. No manner of powers will change that. Therefore it isn't a solution.
Here a more exact answer (4472.0000000070592907382135292414494094,0) for the first example.
I typed it into desmos and I got the result a^12+b^12= 4472.00000001^12
So it was off by .00000001 VERY close but not breaking any theorem.
I also checked 1782^12+1841^12=1921.9999996^12
.9999996 DOES NOT = 1
So it's wrong to make it 1922
I like Simon Singh. He's well spoken and has a very cool presentation style. More please!
Brady!!!!!
He mentions Pancake Flipping in mathematics, what is that? Can you make a video on that?? maybe with James Grime? Thank you so much!
I'm Anthony, from Pasadena, CA, USA by the way :D
A calculator can't get a near miss because the integers in question when raised to the power of 12 will only return integer values and only add or subtract integer values so how is decimal precision an issue?!
Strange....this video is basically describing my life right now. I'm 18 years old doing A2 Level Maths, Further Maths and Physics. I love all the maths but I quite regret taking physics. However, my life ambition now is to become a computer animator.
I find this video freaky, it's describing me o.O
x^n+y^n=z^n
n>2
what if 2=(1+1)-(1+1)
there fore 1^1+1^1=2^1
since that two equals zero, this works, but i am breaking math here, that is what I like to do :)
The one in "Treehouse of Horror VI" can easily be disproven just by looking at it: any odd number raised to a positive integer power is odd (since the product of any two odd numbers is odd), and any even number raised to a positive integer power is even, so 1782^12 + 1841^12 = 1922^12 becomes "even plus odd equals even," which is impossible.