
English: 
If you were really smart
you wouldn't need a calculator
to know there was something wrong...
"Fermat's Last Theorem & Homer Simpson"
Numberphile
Films by Brady Haran
There was a short story called
The Devil and Simon Flagg,
where Simon Flagg makes a deal
with the devil
and part of the deal is
that he can keep his soul
if the devil can prove
Fermat's Last Theorem.
Of Course, the devil can't prove
Fermat's Last Theorem.
Fermat's Last Theorem crops up
in Star Trek
x^n+y^n=z^n.
It crops up in Dr Who - 
The eleventh doctor
in order to prove himself
rewrites Fermat's original proof.
It pops up in Bedazzled,
the film with Liz Hurley,
where she plays the devil as well.
So there's quite a
devilish link to Fermat.
It pops up in Arcadia
played by Tom Stoppard.
So, it's very much a bit of math
that people can use
in novels and films and plays,
because it's sort of has
a bit of glamour around it,
and people have perhaps vaguely heard of it.
Recently I spotted it in an episode
of The Simpsons.

Serbian: 
Ako si baš bistar
ne treba ti digitron
da bi znao da ovde nešto ne valja.
 
Ima jedna kratka priča, koja se zove "Đavo i Sajmon Fleg"
u njoj Sajmon Fleg pravi ugovor sa đavolom
i deo tog ugovora je da može zadržati svoju dušu
ako đavo uspe da dokaže Fermaovu poslednju teoremu.
I naravno, đavo ne može da dokaže poslednju Fermaovu teoremu.
Fermaova teorema se pojavljuje nakratko i u Zvezdanim stazama!
x^n+y^n=z^n.
Pojavljuje se u Doktor Hu-u. Jedanaesti doktor
kako bi se dokazao, pokazuje Fermaov originalni dokaz.
Pojavljuje se u filmu "Začaran", u kojem glumi Liz Harli
gde ona igra đavola.
Eto, često povezivanje đavola sa Fermaom.
Pojavljuje se i Arkadi-i, u kojoj glumi Tom Stopard.
Očigledno je to nešto što ljudi mogu da koriste
u romanima, filmovima i predstavama,
jer je ima neku pompu oko sebe,
a ljudi su već verovatno načuli nešto o tome.
Nedavno sam video teoremu u jednoj epizodi Simpsonovih.

Serbian: 
To je epizoda "Čarobnjak zelenih teresa",
u kojoj Homer Simpson želi da postane pronalazač,
ima neku školsku tablu,
vidimo ga kako piskara nešto po njoj,
i jedna od jednačina koju je Homer Simpson napisao na tabli
izgleda kao rešenje Fermaove poslednje teoereme.
To je neki četvorocifreni broj na 12ti stepen
plus neki četvorocifreni broj na 12ti stepen,
jednako neki treći četvorocifreni broj na 12ti stepen.
E sad, Fermaova teorema kaže da tako nešto ne može da postoji.
Dakle, Homer pokazuje da su Ferma i Endrju Vajls u krivu!
Ako imate digitron na telefonu i ukucate ove brojeve,
i proverite Homerovo rešenje, koje ne bi smelo da postoji
i ispada da je to potpuno tačno rešenje.
(Brejdi) Čekaj malo, pa to je ozbiljan problem...
Da, da, to je veliki problem. Rešenje tog problema je ...
to je takozvani "mali promašaj"
što znači da, ako koristite digitron na telefonu

English: 
There's an episode called
"The Wizard of Evergreen Terrace",
where Homer Simpson wants
to become an inventor,
and he has a blackboard.
We see him scribbling things
on the blackboard.
And one of the equations
Homer Simpson writes on the blackboard
is an apparent solution
to Fermat's Last Theorem.
It's some 4-digit number to the 12'th power
plus a 4 digit number to the 12'th power
equals a 4-dight number to the 12'th power.
Now, Fermat's Last Theorem says
that should not exist.
So, Homer is defying
Fermat and Andrew Wiles.
Now, if you have an old phone calculator
and you type in the digits,
and you check Homer's solution,
which should not exist,
it turns out it's a perfect
valid solution.
BRADY HARAN: Hang on a second,
this is a problem...
SIMON SINGH: [laughs] This is a big problem.
Um, the solution to the problem is...
It's called a near miss solution,
which means that
if you've got a phone calculator

English: 
with only 10 decimal places
you won't see the problem.
But if you go to 15 or 20
decimal places
you'll see that the equation
doesn't quite balance.
It's very very close
but not quite there.
His solution is
3,987^12+4,365^12=4,472^12
Try that at your phone calculator
it will kind of make sense.
It's not the only near miss
in The Simpsons.
There's another one in an episode called
"Homer Cubed"
which is part of the
"Treehouse of Horror VI" episode of The Simpsons.
And when I saw the second one
I remember thinking:
There's somebody on The Simpsons
who clearly likes math.
And the culprit is a chap called
David X. Cohen.
David X. Cohen did physics at Harvard.
I did physics as well,
and physicists like math,

Serbian: 
sa samo 10 decimala, nećete moći da vidite problem
Ali ako imate 15 ili 20 decimala
videćete da jednakost baš i ne važi
Vrlo je blizu, ali nije potpuno tačno.
Njegovo rešenje je:
3,987^12 + 4,365^12 = 4,472^12
Probajte ovo na telefonu
i ispašće dobro.
I to nije jedini mali promašaj u Simpsonovima.
Postoji još jedno u epizodi "Homer na kub"
koja je deo epizode "Horor kuća na drvetu VI"
I kada sam video taj drugi, sećam se da sam pomislio
postoji neko u ekipi Simpsonovih ko mnogo voli matematiku.
I posmunjao sam na lika koji se zove Dejvid Iks. Kojen.
Dejvid Kojen je studirao fiziku na Harvardu.
I ja sam studirao fiziku, a fizičari vole matematiku

Serbian: 
tako da to objašnjava Dejvidovu opsednutost matematikom.
On je i masterirarao na informatici
čak je i objavio neke naučne radove iz matematike.
Postoji čitava oblast matematike pod nazivom "okretanje palačinki"
ali to je potpuno druga priča.
Ali Dejvid Kojen je ozbiljan matematičar.
koji se ubacio u Simpsonove.
Pa je svako malo u Simpsonovima, on ubcivao neke mrvice matematike.
Kada Dejvid Kojen ubaci ova lažna rešenja Fermaove poslednje teoreme,
on suptilno ukazuje na svoju prošlost i svoju ljubav prema matematici.
A posebno je čudno što on nije jedini matematičar koji radi na Simpsonovima.
Tu je i Al Džin koji je završio matematiku na Harvardu.
Tu je i Ken Kiler, koji je doktorirao na primenjenoj matematici.
Tu je i Majk Ris,
koji je bio u prepisci sa velikim matematičare Martinom Gardnerom,
velikim amaterskim matematičarem Martinom Gardnerom,
kada je bio klinac.
Dakle, ima puno matematičara na Simpsonovima,

English: 
so that kind of explains
David's obsession with mathematics.
He then did a Master's degree in
Computer Science,
and then went on and published research
papers in mathematics.
In fact, there is a whole area
of mathematics known as "pancake flipping",
which is a whole other story.
But David X. Cohen is
a serious mathematician
who finds his way into The Simpsons.
And so every so often in The Simpsons
he would drop in little bits of mathematics.
When David X. Cohen drops in these
false solutions to Fermat's Last Theorem,
he is kind of nodding back to his past
and his love of mathematics.
And the really weird thing is he's
not the only mathematician on The Simpsons.
There is Al Jean
who did mathematics at Harvard.
There's a guy called Ken Keeler,
who has a Ph.D. in Applied Math.
There's a guy called Mike Reiss,
who is corresponding with
the great mathematician Martin Gardner,
the great recreational mathematician
Martin Gardner,
when he was a young kid.
So there are a lot of mathematicians
on The Simpsons,

English: 
and they all drop in bits of math
in The Simpsons.
BRADY HARAN: What should we
read into the fact
that all these mathematicians
are on The Simpsons writing stuff?
SIMON SINGH: It's tricky. I spoke to them,
I met them last year.
And I said to them: "Why have you all
ended up as being comedy writers?"
And they gave me various theories.
One theory that many of them share
is that mathematicians love logic,
and therefore they love breaking logic
and playing with logic,
and they love the illogical,
and a lot of humor is based on that.
One explanation that Al Jean gave me
as to why they work
in animation, in particular,
is that animation is all about control.
What you storyboard, what you script
appears on screen.
In mathematics what you write down
on paper is what happens.
We can contrast that with
a real action sitcom,
where you don't have control.

Serbian: 
i svi ubacuju ove matematičke sitnice u Simpsonove.
(Brejdi) Šta treba da zaključimo iz činjenice
da su svi ovi matematičari u ekipi koja pravi Simpsonove?
Nejasno je, razgovarao sam s njima prošle godine
i pitao sam ih: "Kako to da ste svi završili kao pisci komične serije?"
I oni su mi ponudili različite teorije.
Jedna teorija, oko koje se većina slaže,
je da matematičari vole logiku,
i stoga vole i da krše logiku i igraju se s njom
oni vole ne-logično, a veliki deo humora je je zasnovan na tome.
Objašnjenje koje mi je Al Džin dao
zašto se oni bave, konkretno, animacijama
to je zato što se animacija direktno tiče kontrole.
Šta napišeš ka priču, šta režiraš - to će se pojaviti na ekranu.
U matematici, šta napišeš na papiru - to je ono što se dešava.
Možemo to uporediti sa pravim sitkomom,
gde nemate potpunu kontrolu.

English: 
You know, the actors put in their ideas,
scripts will change, scenes will change,
everything is up for grabs.
And science is a bit like that as well.
When you do a science experiment
things change,
things go wrong,
test tubes break, etc.
So there does seem to be
a very strong link
between mathematicians and comedy,
and mathematicians who write comedy,
who then work in animation.
When we took our near misses,
we're looking at..., kind of proportionally,
is at a near miss.
So, we're looking at 4-digit numbers
to the 12'th power.
So we're looking at 48-digit numbers.
And so if they're out
by millions of millions,
that's only a tiny amount,
because we're looking at
such massive digits.
And, so, on most calculators
you won't see the error.
If you were really smart,
you wouldn't need a calculator
to know there was something wrong
in one of these.
If you look at the second one,
now this one is obviously wrong.
Now, the reason it's obviously wrong is
because this is an even number,
that's an odd number,
that's an even number.

Serbian: 
Glumci ubacuju svoje ideje
scenario se menja, sve je otvoreno za intervencije...
I nauka je nalik tome, takođe.
Kada pravite eksperimente, stvari se menjaju,
nešto ispadne, nešto se pokvari, itd...
Pa izgleda da postoji jaka veza
između matematike i komedije
i posebno matematičara koji pišu komedije koje su animirane.
Kada posmatramo ova "za malo netačna rešenja"
mi zapravo gledamo... na osnovu proporcionalnosti šta je "mali promašaj"
Ovde gledamo četvorocifrene borjeve na 12ti stepen.
Dakle, to je 48ocifreni broj...
Ako se tu radi o milionima miliona...
onda je ovo samo mala razlika
i pošto sada gledamo na te jako udaljene cifre,
na većini digitrona nećete videti grešku
Ali ako ste baš pametni, neće vam ni biti potreban digitron
kako biste znali da nešto ne valja u nekim od ovih rešenja.
Kada pogledate ovo drugo, očigledno je pogrešno.
Razlog zašto je to očigledno je u tome što je ovo prvo paran broj,
ovo drugo je neparan, a ovo opet paran.

Serbian: 
Paran broj na 12ti stepen je takođe paran broj.
Neparan broj na 12ti stepen mora da bude opet neparan broj.
A paran broj plus neparan broj je neparan broj.
Zato to novo ne može biti jednako ovome.
(Brejdi) Govorio si o ovim malim promašajima,
ili ova dva mala promašaja koja su ubačena
da li on odaje poštovanje nečemu?
Ili samo troluje? Da li je on trol?
(Sajmon) Pa ne, to je kao
kad volite nešto,
a ja mislim da Dejvid Kojen voli komediju,
i pored toga voli matematiku,
prirodno je da želite da to nekako spojite.
Ali ne spajate ih na silu.
Matematika u Simpsonovima nikad ne ometa glavnu priču.
Ali ako se ukaže prilika da se ubaci nešto što volite ...
Baš u pravoj epizodi Simpsonovih
jedno dete ima posudu za ručak sa slikom Anatolija Karpova na njoj.
Ja se sećam Anatolija Karpova kao sjajnog šahistu iz ranih 70tih,
pretpostavljam da neko od scenarista Simpsonovih takođe voli šah,
i navijač je Anatolija Karpova.

English: 
An even number to the 12'th power
must still be an even number.
An odd number to the 12'th power
must be an odd number.
An even number plus an odd number
is an odd number.
So that cannot equal that.
BRADY HARAN: You were talking about
this near miss,
or these two near misses that
were put in,
Is he paying tribute to something here?
Or is he trolling?
Is he being a troll?
SIMON SINGH: No, it's very much...
When you love something,
and I thing David X. Cohen
loves comedy,
he loves comedy writing
and he loves mathematics,
it's natural to try and bring
the two together.
You don't force them together.
And the mathematics on The Simpsons
never gets in the way of the plot.
But if there is an opportunity
to drop something in that you love...
In the very first episode of The Simpsons
one of the kids has a lunch box
with Anatoly Karpov's picture on it.
Now, I remember Anatoly Karpov
as a great chess player of the early 70's.
Now, I guess somebody on The Simpsons
writing team is also a fan of chess,
and also a fan of Anatoly Karpov.

English: 
And so these things get dropped in.
And as there were so many
mathematical writers on The Simpsons,
they dropped in an awful lot of
these mathematical knobs.
Brady Haran: If you like to help
Simon buy some new monkeys
to hang on those bookshelves of his,
why don't you have a look at his book?
It's out this week,
it's all about mathematics in The Simpsons,
Of course, I'll put a link so you can check out
the book in the video description.
There will also be links to our other videos
about Fermat's Last Theorem,
that we filmed with Simon and released
earlier this week,
And lastly, I'm also including a link to
a Sixty Symbols video I uploaded this week,
all about the physics of water balloons
and filming them in slow motion.
It's really good, and I know
a lot of people were having problems
with their subscription boxes
on YouTube this week.
So, if you subscribe
to Sixty Symbols,
which is like our sister channel
but about physics,
and you missed that one,
well, now you've got no excuse.

Serbian: 
Takve stvari se ubacuju u seriju...
Imajući u vidu da ima tako mnogo scenarista matematičara na Simpsonovima
Ubacivali su jako puno matematičkih smicalica.
(Brejdi) Ako hoćete da podržite Sajmona, kupite one majmuničiće
da bi visili sa njegovih polica za knjige
Bacite pogled i na njegovu knjigu.
Izašla je ove nedelje i bavi se matematikom u Simpsonovima.
Dole u informacijama ispod videa je link ka knjizi.
Dole su i linkovi ka ostalim našim videima o Fermaovoj poslednjoj teoremi.
koje smo snimili sa Sajmonom ranije,
i na kraju, staviću i link ka novom videu na kanalu Sixty Symbols,
koji se tiče fizike vodenih balona, i snimanja u slow motion-u.
Odličan je. Znam da su mnogi od vas imali problem sa
dugmetom za prijavu na YouTube kanale, ove nedelje.
pa ako ste prijavljeni na Sixty Symbols,
što je sestrinski kanal ovom kanalu, samo o fizici
a propustili ste taj video, sada više nemate opravdanje...
