TED2016
Cédric Villani: What's so sexy about math?
Sedrik Vilani (Cédric Villani): Šta je tako privlačno u matematici?
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2,006,708 views
Skrivene istine prožimaju naš svet; njih je nemoguće otkriti kroz naša čula, ali matematika nam dozvoljava da idemo dalje od naše intuicije ka otkriću misterija sveta. U ovom pregledu matematičkih otkrića, dobitnik Fildsove medalje, Sedrik Vilani, govori o uzbuđenju otkrića i detaljima ponekad zbunjujućeg života matematičara. „Lepa matematička objašnjenja nisu samo zarad našeg zadovoljstva“, kaže on. „Ona menjaju naš pogled na svet.“
Cédric Villani - Mathematician
Cédric Villani tackles perplexing problems in mathematical physics, analysis and geometry with rigor, wit and a signature personal style. Full bio
Cédric Villani tackles perplexing problems in mathematical physics, analysis and geometry with rigor, wit and a signature personal style. Full bio
Double-click the English transcript below to play the video.
00:12
What is it that French people
do better than all the others?
do better than all the others?
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Šta to Francuzi rade bolje od svih drugih?
00:18
If you would take polls,
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Ako biste sproveli istraživanje,
00:20
the top three answers might be:
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najčešća tri odgovora bi možda bila:
00:22
love, wine and whining.
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ljubav, vino i žaljenje.
00:26
(Laughter)
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(Smeh)
00:27
Maybe.
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Možda.
00:29
But let me suggest a fourth one:
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Ali, dozvolite mi da predložim i četvrti:
00:31
mathematics.
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matematika.
00:33
Did you know that Paris
has more mathematicians
has more mathematicians
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Da li znate da Pariz ima više matematičara
00:36
than any other city in the world?
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od bilo kog drugog grada u svetu?
00:38
And more streets
with mathematicians' names, too.
with mathematicians' names, too.
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I više ulica sa imenima
matematičara, takođe.
matematičara, takođe.
00:42
And if you look at the statistics
of the Fields Medal,
of the Fields Medal,
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I ukoliko pogledamo statistiku
Fildsove medalje,
Fildsove medalje,
00:45
often called the Nobel Prize
for mathematics,
for mathematics,
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često nazivane Nobelovom
nagradom za matematičare,
nagradom za matematičare,
00:48
and always awarded to mathematicians
below the age of 40,
below the age of 40,
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koja se uvek dodeljuje
matematičarima ispod 40 godina,
matematičarima ispod 40 godina,
00:52
you will find that France has more
Fields medalists per inhabitant
Fields medalists per inhabitant
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otkrićete da Francuska ima više
dobitnika ove medalje po glavi stanovnika
dobitnika ove medalje po glavi stanovnika
00:56
than any other country.
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od bilo koje druge države.
00:58
What is it that we find so sexy in math?
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Šta nam je tako privlačno u matematici?
01:02
After all, it seems to be
dull and abstract,
dull and abstract,
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Naposletku, deluje
da je dosadna i apstraktna;
da je dosadna i apstraktna;
01:05
just numbers and computations
and rules to apply.
and rules to apply.
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samo brojevi, računanje i pravila
koja treba primeniti.
koja treba primeniti.
01:10
Mathematics may be abstract,
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Matematika je možda apstraktna,
01:12
but it's not dull
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ali nije dosadna
01:13
and it's not about computing.
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i nije u vezi sa proračunima.
01:16
It is about reasoning
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U vezi je sa razmišljanjem
01:17
and proving our core activity.
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i dokazivanjem naše suštinske aktivnosti.
01:20
It is about imagination,
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U vezi je sa maštom,
01:22
the talent which we most praise.
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talentom koji cenimo više od svega.
01:24
It is about finding the truth.
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U vezi je sa nalaženjem istine.
01:27
There's nothing like the feeling
which invades you
which invades you
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Nema ničega boljeg
od osećaja koji te prožme
od osećaja koji te prožme
01:30
when after months of hard thinking,
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kada, posle meseci teškog razmišljanja,
01:32
you finally understand the right
reasoning to solve your problem.
reasoning to solve your problem.
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konačno razumeš
kako da rešiš svoj problem.
kako da rešiš svoj problem.
01:37
The great mathematician
André Weil likened this --
André Weil likened this --
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Veliki matematičar,
Andre Vejl, je uporedio to -
Andre Vejl, je uporedio to -
01:40
no kidding --
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bez šale -
01:41
to sexual pleasure.
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sa seksualnim zadovoljstvom.
01:44
But noted that this feeling
can last for hours, or even days.
can last for hours, or even days.
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S tim da ovaj osećaj može da traje
satima ili čak danima.
satima ili čak danima.
01:50
The reward may be big.
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Nagrada može biti velika.
01:53
Hidden mathematical truths
permeate our whole physical world.
permeate our whole physical world.
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Skrivene matematičke istine
prožimaju sav naš fizički svet.
prožimaju sav naš fizički svet.
01:57
They are inaccessible to our senses
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Do njih se ne može doći putem čula,
02:00
but can be seen
through mathematical lenses.
through mathematical lenses.
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ali se mogu uočiti
kroz matematička sočiva.
kroz matematička sočiva.
02:04
Close your eyes for moment
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Zatvorite oči na trenutak
02:05
and think of what is occurring
right now around you.
right now around you.
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i mislite o tome šta se dešava
trenutno oko vas.
trenutno oko vas.
02:10
Invisible particles from the air
around are bumping on you
around are bumping on you
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Nevidljive čestice iz vazduha
se sudaraju sa vama,
se sudaraju sa vama,
02:13
by the billions and billions
at each second,
at each second,
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milijarde i milijarde svake sekunde,
02:16
all in complete chaos.
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potpuno haotično.
02:19
And still,
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Ali, ipak,
02:20
their statistics can be accurately
predicted by mathematical physics.
predicted by mathematical physics.
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njihova statistika se može
tačno predvideti putem matematičke fizike.
tačno predvideti putem matematičke fizike.
02:25
And open your eyes now
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Otvorite oči sada
02:28
to the statistics of the velocities
of these particles.
of these particles.
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da vidite statistiku brzina ovih čestica.
02:32
The famous bell-shaped Gauss Curve,
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Poznata Gausova kriva u obliku zvona,
02:35
or the Law of Errors --
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ili zakon grešaka -
02:37
of deviations with respect
to the mean behavior.
to the mean behavior.
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odstupanja koja se odnose
na srednjestatističko ponašanje.
na srednjestatističko ponašanje.
02:41
This curve tells about the statistics
of velocities of particles
of velocities of particles
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Kriva pokazuje statistiku brzina čestica
02:45
in the same way as a demographic curve
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na isti način kao što i demografska kriva
02:48
would tell about the statistics
of ages of individuals.
of ages of individuals.
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pokazuje statistiku
godina uzrasta pojedinaca.
godina uzrasta pojedinaca.
02:52
It's one of the most
important curves ever.
important curves ever.
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To je jedna od najvažnijih
krivih u istoriji.
krivih u istoriji.
02:56
It keeps on occurring again and again,
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Ponavlja se iznova i iznova
02:59
from many theories and many experiments,
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u mnogim teorijama i eksperimentima,
03:01
as a great example of the universality
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kao divan primer univerzalnosti
03:05
which is so dear to us mathematicians.
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koja je nama, matematičarima, tako draga.
03:09
Of this curve,
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O ovoj je krivoj
03:10
the famous scientist Francis Galton said,
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poznati naučnik Francis Galton rekao:
03:14
"It would have been deified by the Greeks
if they had known it.
if they had known it.
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„Da su znali za nju,
Grci bi je obogotvorili.
Grci bi je obogotvorili.
03:19
It is the supreme law of unreason."
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To je viši zakon iracionalnosti.“
03:23
And there's no better way to materialize
that supreme goddess than Galton's Board.
that supreme goddess than Galton's Board.
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Nema boljeg načina za materijalizovanje te
visoke boginje nego kroz Galtonovu tablu.
visoke boginje nego kroz Galtonovu tablu.
03:31
Inside this board are narrow tunnels
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Unutar ove table su uski tuneli
03:34
through which tiny balls
will fall down randomly,
will fall down randomly,
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kroz koje će male loptice padati
nadole nasumično,
nadole nasumično,
03:40
going right or left, or left, etc.
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idući desno, ili levo, ili levo itd.
03:46
All in complete randomness and chaos.
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U potpunoj nasumičnosti i haosu.
03:50
Let's see what happens when we look
at all these random trajectories together.
at all these random trajectories together.
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Da vidimo šta se dešava kada pogledamo
sve ove nasumične putanje zajedno.
sve ove nasumične putanje zajedno.
03:56
(Board shaking)
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(Tabla se trese)
Ovo je pomalo poput sporta,
04:01
This is a bit of a sport,
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04:04
because we need to resolve
some traffic jams in there.
some traffic jams in there.
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zato što se moramo rešiti
saobraćajne gužve ovde.
saobraćajne gužve ovde.
04:11
Aha.
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Aha.
04:13
We think that randomness
is going to play me a trick on stage.
is going to play me a trick on stage.
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Mislimo da će nasumičnost
da me prevari na sceni.
da me prevari na sceni.
04:19
There it is.
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Evo je.
04:22
Our supreme goddess of unreason.
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Naša visoka boginja iracionalnosti.
04:24
the Gauss Curve,
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Gausova kriva,
04:26
trapped here inside this transparent box
as Dream in "The Sandman" comics.
as Dream in "The Sandman" comics.
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zarobljena ovde unutar ove providne
kutije poput Sna u stripu „Sandman“.
kutije poput Sna u stripu „Sandman“.
04:34
For you I have shown it,
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Vama sam je pokazao,
04:37
but to my students I explain why
it could not be any other curve.
it could not be any other curve.
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ali svojim studentima objašnjavam
zašto to ne može biti neka druga kriva.
zašto to ne može biti neka druga kriva.
04:43
And this is touching
the mystery of that goddess,
the mystery of that goddess,
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I tu se približavamo misteriji te boginje,
04:46
replacing a beautiful coincidence
by a beautiful explanation.
by a beautiful explanation.
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zamenjujući prelepu slučajnost
prelepim objašnjenjem.
prelepim objašnjenjem.
04:51
All of science is like this.
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Sva nauka je takva.
04:54
And beautiful mathematical explanations
are not only for our pleasure.
are not only for our pleasure.
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A prelepa matematička objašnjenja
nisu tu samo zbog našeg zadovoljstva.
nisu tu samo zbog našeg zadovoljstva.
04:59
They also change our vision of the world.
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Ona takođe menjaju naš pogled na svet.
05:03
For instance,
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Na primer,
05:04
Einstein,
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Ajnštajn, Perin, Smolučovski,
05:05
Perrin,
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05:06
Smoluchowski,
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koristili su matematičku analizu
nasumičnih putanja
nasumičnih putanja
05:07
they used the mathematical analysis
of random trajectories
of random trajectories
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05:11
and the Gauss Curve
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i Gausovu krivu
05:13
to explain and prove that our
world is made of atoms.
world is made of atoms.
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da objasne i dokažu
da je naš svet izgrađen iz atoma.
da je naš svet izgrađen iz atoma.
05:19
It was not the first time
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To nije prvi put
05:21
that mathematics was revolutionizing
our view of the world.
our view of the world.
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da je matematika iz korena
menjala naš pogled na svet.
menjala naš pogled na svet.
05:25
More than 2,000 years ago,
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Pre više od 2 000 godina,
05:27
at the time of the ancient Greeks,
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u vreme antičke Grčke,
05:31
it already occurred.
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to se već dogodilo.
05:33
In those days,
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U to vreme,
05:35
only a small fraction of the world
had been explored,
had been explored,
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samo mali procenat sveta je bio otkriven,
05:38
and the Earth might have seemed infinite.
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a Zemlja je možda delovala
kao da je beskonačna.
kao da je beskonačna.
05:42
But clever Eratosthenes,
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Ali, umni Eratosten,
05:43
using mathematics,
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koristeći se matematikom,
05:45
was able to measure the Earth
with an amazing accuracy of two percent.
with an amazing accuracy of two percent.
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bio je u stanju da izmeri Zemlju
sa sjajnom preciznošću
od dva procenta greške.
od dva procenta greške.
05:51
Here's another example.
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Evo ga još jedan primer.
05:54
In 1673, Jean Richer noticed
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Godine 1673. Žan Rišer je primetio
05:58
that a pendulum swings slightly
slower in Cayenne than in Paris.
slower in Cayenne than in Paris.
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da se klatno malčice sporije ljulja
u Kajenu nego u Parizu.
u Kajenu nego u Parizu.
06:06
From this observation alone,
and clever mathematics,
and clever mathematics,
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Iz samo ove observacije
i uz lukavu matematiku,
i uz lukavu matematiku,
06:10
Newton rightly deduced
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Njutn je pravilno zaključio
06:13
that the Earth is a wee bit
flattened at the poles,
flattened at the poles,
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da je Zemlja malo ravnija na polovima,
06:18
like 0.3 percent --
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negde oko 0,3 procenta -
06:20
so tiny that you wouldn't even
notice it on the real view of the Earth.
notice it on the real view of the Earth.
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toliko malo da to ne možete
ni primetiti na pravoj slici Zemlje.
ni primetiti na pravoj slici Zemlje.
06:26
These stories show that mathematics
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Ovakve priče pokazuju da uz matematiku
06:30
is able to make us go out of our intuition
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možemo da idemo dalje od naše intuicije,
06:35
measure the Earth which seems infinite,
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da izmerimo Zemlju
koja deluje kao beskonačna,
koja deluje kao beskonačna,
06:39
see atoms which are invisible
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da vidimo atome koji su nevidljivi
06:41
or detect an imperceptible
variation of shape.
variation of shape.
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ili da detektujemo
nevidljive varijacije oblika.
nevidljive varijacije oblika.
06:44
And if there is just one thing that you
should take home from this talk,
should take home from this talk,
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I ako biste izdvojili samo jednu stvar
koju treba da zapamtite iz ovog govora,
koju treba da zapamtite iz ovog govora,
06:48
it is this:
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to je ovo:
06:49
mathematics allows us
to go beyond the intuition
to go beyond the intuition
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matematika nam dopušta
da idemo dalje od naše intuicije
da idemo dalje od naše intuicije
06:54
and explore territories
which do not fit within our grasp.
which do not fit within our grasp.
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i da istražujemo teritorije
koje ne možemo da zamislimo.
koje ne možemo da zamislimo.
06:59
Here's a modern example
you will all relate to:
you will all relate to:
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Evo modernog primera
koji je blizak svima:
koji je blizak svima:
07:03
searching the Internet.
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pretraživanje interneta.
07:06
The World Wide Web,
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Svetska mreža,
07:07
more than one billion web pages --
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više od milijardu veb-stranica -
07:09
do you want to go through them all?
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da li biste pretraživali kroz sve njih?
07:11
Computing power helps,
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Računarska moć pomaže,
07:13
but it would be useless without
the mathematical modeling
the mathematical modeling
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ali bi bila beskorisna
bez matematičkog modelovanja
bez matematičkog modelovanja
07:16
to find the information
hidden in the data.
hidden in the data.
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kojim se nalazi informacija
skrivena u podacima.
skrivena u podacima.
07:20
Let's work out a baby problem.
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Hajde da prođemo kroz mali zadatak.
07:23
Imagine that you're a detective
working on a crime case,
working on a crime case,
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Zamislite da ste detektiv
koji radi na slučaju zločina,
koji radi na slučaju zločina,
07:27
and there are many people
who have their version of the facts.
who have their version of the facts.
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i imate mnogo ljudi koji imaju
svoju verziju toga šta se dogodilo.
svoju verziju toga šta se dogodilo.
07:32
Who do you want to interview first?
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Koga biste prvo intervjuisali?
07:34
Sensible answer:
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Razuman odgovor:
07:36
prime witnesses.
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glavne svedoke.
07:38
You see,
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Vidite,
07:40
suppose that there is person number seven,
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pretpostavimo da vam osoba broj sedam
07:44
tells you a story,
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ispriča priču,
07:45
but when you ask where he got if from,
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ali kada je upitate odake ona to zna,
07:47
he points to person
number three as a source.
number three as a source.
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ona vam kaže da je njen
izvor osoba broj tri.
izvor osoba broj tri.
07:50
And maybe person number three, in turn,
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I možda osoba broj tri dalje
07:52
points at person number one
as the primary source.
as the primary source.
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istakne osobu broj jedan
kao primarni izvor.
kao primarni izvor.
07:56
Now number one is a prime witness,
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Sada je osoba broj jedan glavni svedok.
07:58
so I definitely want
to interview him -- priority
to interview him -- priority
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tako da definitivno hoću
nju da intervjuišem - prioritet.
nju da intervjuišem - prioritet.
08:02
And from the graph
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I iz grafika
08:03
we also see that person
number four is a prime witness.
number four is a prime witness.
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možemo da pročitamo da je osoba
broj četiri takođe među glavnim svedocima.
broj četiri takođe među glavnim svedocima.
08:06
And maybe I even want
to interview him first,
to interview him first,
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I možda ja mogu i nju
prvo da intervjuišem,
prvo da intervjuišem,
08:09
because there are more
people who refer to him.
people who refer to him.
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zato što ima više osoba
koje upućuju na nju.
koje upućuju na nju.
08:12
OK, that was easy,
146
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2664
U redu, to je bilo lako,
08:15
but now what about if you have
a big bunch of people who will testify?
a big bunch of people who will testify?
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5246
ali šta ako imate gomilu ljudi
koji treba da svedoče?
koji treba da svedoče?
08:20
And this graph,
148
488864
1352
Ovaj grafik
08:22
I may think of it as all people
who testify in a complicated crime case,
who testify in a complicated crime case,
149
490240
5619
može da se razume kao da su to svi svedoci
ovog komplikovanog kriminalnog slučaja,
ovog komplikovanog kriminalnog slučaja,
08:27
but it may just as well be web pages
pointing to each other,
pointing to each other,
150
495883
4022
ali to isto tako mogu biti i veb-stranice
koje ukazuju jedna na drugu,
koje ukazuju jedna na drugu,
08:31
referring to each other for contents.
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2071
čiji sadržaj usmerava sa jedne na drugu.
08:34
Which ones are the most authoritative?
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2336
Koje stranice su najautoritativnije?
08:37
Not so clear.
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1334
Nije sasvim jasno.
08:40
Enter PageRank,
154
508091
1900
Pristupimo „Pejdž ranku“,
08:42
one of the early cornerstones of Google.
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2536
jednom od kamena temeljaca Gugla.
08:45
This algorithm uses the laws
of mathematical randomness
of mathematical randomness
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4242
Ovaj algoritam koristi zakone
matematičke nasumičnosti
matematičke nasumičnosti
08:49
to determine automatically
the most relevant web pages,
the most relevant web pages,
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3857
da automatski odredi
najrelevantnije veb-stranice,
najrelevantnije veb-stranice,
08:53
in the same way as we used randomness
in the Galton Board experiment.
in the Galton Board experiment.
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na isti način kako smo
koristili nasumičnost
koristili nasumičnost
u eksperimentu Galtonove table.
08:59
So let's send into this graph
159
527341
2341
Onda, propustimo kroz ovaj grafik
09:01
a bunch of tiny, digital marbles
160
529706
2850
gomilu malih, digitalnih klikera
09:04
and let them go randomly
through the graph.
through the graph.
161
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3749
i pustimo ih da idu nasumično kroz grafik.
09:08
Each time they arrive at some site,
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Svaki put kad su na nekom sajtu,
09:10
they will go out through some link
chosen at random to the next one.
chosen at random to the next one.
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4166
izaći će sa tog sajta i preći na drugi
koristeći se nekim nasumičnim linkom.
koristeći se nekim nasumičnim linkom.
09:14
And again, and again, and again.
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1753
I ponovo, i ponovo, i ponovo.
09:16
And with small, growing piles,
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544358
1628
I malim, rastućim gomilama,
09:18
we'll keep the record of how many
times each site has been visited
times each site has been visited
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3753
merićemo koliko puta
su ovi digitalni klikeri
su ovi digitalni klikeri
09:21
by these digital marbles.
167
549787
1945
posetili svaki sajt.
09:24
Here we go.
168
552243
1151
Krećemo.
09:25
Randomness, randomness.
169
553418
1848
Nasumičnost, nasumičnost.
09:27
And from time to time,
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1448
I s vremena na vreme,
09:29
also let's make jumps completely
randomly to increase the fun.
randomly to increase the fun.
171
557283
3952
da bi bilo zabavnije,
preskačimo sasvim proizvoljno.
preskačimo sasvim proizvoljno.
09:34
And look at this:
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1216
I pogledajte ovo:
09:36
from the chaos will emerge the solution.
173
564358
2785
iz haosa se pojavljuje rešenje.
09:39
The highest piles
correspond to those sites
correspond to those sites
174
567483
2485
Najviše hrpe odgovaraju onim sajtovima
09:41
which somehow are better
connected than the others,
connected than the others,
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569992
3511
koji su na neki način
bolje povezani od drugih,
bolje povezani od drugih,
09:45
more pointed at than the others.
176
573527
2273
koji češće od drugih
upućuju na druge stranice.
upućuju na druge stranice.
09:47
And here we see clearly
177
575824
1722
I ovde jasno vidimo
09:49
which are the web pages
we want to first try.
we want to first try.
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577570
3032
koje veb-stranice hoćemo
prvo da isprobamo.
prvo da isprobamo.
09:53
Once again,
179
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1151
Opet,
09:54
the solution emerges from the randomness.
180
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2460
rešenje se pojavljuje iz nasumičnosti.
09:57
Of course, since that time,
181
585775
2251
Naravno, od tada,
10:00
Google has come up with much more
sophisticated algorithms,
sophisticated algorithms,
182
588050
3707
Gugl je smislio mnogo
sofisticiranije algoritme,
sofisticiranije algoritme,
10:03
but already this was beautiful.
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591781
2280
ali je već tada ovo bilo prelepo.
10:06
And still,
184
594981
1476
Ipak,
10:08
just one problem in a million.
185
596481
1611
to je samo jedan problem
iz milion problema.
iz milion problema.
10:10
With the advent of digital area,
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2270
Sa razvojem digitalne oblasti,
10:13
more and more problems lend
themselves to mathematical analysis,
themselves to mathematical analysis,
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601028
5016
sve više i više problema se može
podvrgnuti matematičkoj analizi,
podvrgnuti matematičkoj analizi,
10:18
making the job of mathematician
a more and more useful one,
a more and more useful one,
188
606068
4365
čineći posao matematičara sve korisnijim,
10:23
to the extent that a few years ago,
189
611166
2722
do tog nivoa da je pre par godina,
10:25
it was ranked number one
among hundreds of jobs
among hundreds of jobs
190
613912
3779
bio broj jedan na listi
među stotinama poslova
među stotinama poslova
10:29
in a study about the best and worst jobs
191
617715
3968
u istraživanju o najboljim
i najgorim poslovima
i najgorim poslovima
10:33
published by the Wall Street
Journal in 2009.
Journal in 2009.
192
621707
2975
koje je „Vol strit džurnal“
objavio 2009. godine.
objavio 2009. godine.
10:37
Mathematician --
193
625445
1852
Matematičar -
10:39
best job in the world.
194
627321
1433
najbolji posao na svetu.
10:41
That's because of the applications:
195
629646
3068
To je zbog primena:
10:44
communication theory,
196
632738
2139
komunikaciona teorija,
10:46
information theory,
197
634901
1820
informaciona teorija,
10:48
game theory,
198
636745
1260
teorija igara,
10:50
compressed sensing,
199
638029
1446
kompresija signala,
10:51
machine learning,
200
639499
1562
mašinsko učenje,
10:53
graph analysis,
201
641085
1567
teorija grafova,
10:54
harmonic analysis.
202
642676
1742
harmonijska analiza.
10:56
And why not stochastic processes,
203
644442
2640
I zašto da ne, stohastički procesi,
10:59
linear programming,
204
647106
1630
linearno programiranje
11:00
or fluid simulation?
205
648760
2028
ili simulacija dinamike tečnosti?
11:03
Each of these fields have
monster industrial applications.
monster industrial applications.
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651292
3895
Svaka od ovih oblasti ima
ogromnu primenu u industriji.
ogromnu primenu u industriji.
11:07
And through them,
207
655211
1151
I kroz primenu,
11:08
there is big money in mathematics.
208
656386
1999
matematika donosi mnogo novca.
11:11
And let me concede
209
659400
2040
I da potvrdim da su,
11:13
that when it comes to making
money from the math,
money from the math,
210
661464
2477
kada je reč o zarađivanju od matematike,
11:15
the Americans are by a long shot
the world champions,
the world champions,
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3824
Amerikanci daleko najbolji
svetski šampioni u tome,
svetski šampioni u tome,
11:19
with clever, emblematic billionaires
and amazing, giant companies,
and amazing, giant companies,
212
667813
4619
sa mudrim, realnim milijarderima
i sjajnim, ogromnim kompanijama,
i sjajnim, ogromnim kompanijama,
11:24
all resting, ultimately,
on good algorithm.
on good algorithm.
213
672456
3280
a svi počivaju, na kraju krajeva,
na dobrim algoritmima.
na dobrim algoritmima.
11:29
Now with all this beauty,
usefulness and wealth,
usefulness and wealth,
214
677091
3972
Sada, uzimajući u obzir svu ovu lepotu,
praktičnu primenu i bogatstvo,
praktičnu primenu i bogatstvo,
11:33
mathematics does look more sexy.
215
681087
2284
matematika doista izgleda privlačnije.
11:36
But don't you think
216
684399
1617
Ali, nemojte misliti
11:38
that the life a mathematical
researcher is an easy one.
researcher is an easy one.
217
686040
4120
da je život matematičara istraživača lak.
11:42
It is filled with perplexity,
218
690959
2741
Ispunjen je zbunjenošću,
11:46
frustration,
219
694347
1150
frustracijom,
11:48
a desperate fight for understanding.
220
696172
2445
očajnom borbom da se nešto razume.
11:51
Let me evoke for you
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699955
2140
Da vam predstavim
11:54
one of the most striking days
in my mathematician's life.
in my mathematician's life.
222
702119
4380
jedan od najboljih dana
u mom matematičkom životu.
u mom matematičkom životu.
11:58
Or should I say,
223
706523
1151
Ili bolje,
11:59
one of the most striking nights.
224
707698
1737
jednu od mojih najboljih noći.
12:02
At that time,
225
710713
1151
U to vreme, bio sam u Institutu
za primenjeno istraživanje u Prinstonu -
za primenjeno istraživanje u Prinstonu -
12:03
I was staying at the Institute
for Advanced Studies in Princeton --
for Advanced Studies in Princeton --
226
711888
3151
koji je mnogo godina
bio dom Albertu Ajnštajnu
bio dom Albertu Ajnštajnu
12:07
for many years, the home
of Albert Einstein
of Albert Einstein
227
715063
2139
12:09
and arguably the most holy place
for mathematical research in the world.
for mathematical research in the world.
228
717226
4428
i koji je možda najsvetije mesto
za istraživanje matematike u svetu.
za istraživanje matematike u svetu.
12:14
And that night I was working
and working on an elusive proof,
and working on an elusive proof,
229
722878
3844
Te noći sam radio i radio
na jednom teškom dokazu,
na jednom teškom dokazu,
12:18
which was incomplete.
230
726746
1378
koji je bio nepotpun.
12:21
It was all about understanding
231
729304
2208
Reč je bila o razumevanju
12:23
the paradoxical stability
property of plasmas,
property of plasmas,
232
731536
3823
paradoksalnog svojstva stabilnosti plazmi,
12:27
which are a crowd of electrons.
233
735383
1958
koje su suštinski skupina elektrona.
12:30
In the perfect world of plasma,
234
738423
2736
U savršenom svetu plazmi,
12:33
there are no collisions
235
741183
1778
nema sudara
12:34
and no friction to provide
the stability like we are used to.
the stability like we are used to.
236
742985
3658
i nema trenja koji bi obezbedili
stabilnost na koju smo navikli.
stabilnost na koju smo navikli.
12:39
But still,
237
747392
1151
Ipak, ako se malčice naruši
ekvilibrijum plazme,
ekvilibrijum plazme,
12:40
if you slightly perturb
a plasma equilibrium,
a plasma equilibrium,
238
748567
3033
primetiće se da električno polje
koje se pojavilo kao posledica toga
koje se pojavilo kao posledica toga
12:43
you will find that the
resulting electric shield
resulting electric shield
239
751624
2688
12:46
spontaneously vanishes,
240
754336
2339
spontano nestaje
12:48
or damps out,
241
756699
1975
i gasi se,
12:50
as if by some mysterious friction force.
242
758698
3294
kao da je pod dejstvom
neke tajanstvene sile trenja.
neke tajanstvene sile trenja.
12:54
This paradoxical effect,
243
762728
1835
Ovaj paradoksalni efekat
12:56
called the Landau damping,
244
764587
1477
pod nazivom Landauovo prigušenje
12:58
is one of the most important
in plasma physics,
in plasma physics,
245
766088
2989
jedan je od najvažnijih u fizici plazme
13:01
and it was discovered
through mathematical ideas.
through mathematical ideas.
246
769101
3002
i otkriven je kroz matematičke ideje.
13:04
But still,
247
772970
1151
Ipak, nedostajalo je potpuno
matematičko razumevanje ovog fenomena.
matematičko razumevanje ovog fenomena.
13:06
a full mathematical understanding
of this phenomenon was missing.
of this phenomenon was missing.
248
774145
4230
13:10
And together with my former student
and main collaborator Clément Mouhot,
and main collaborator Clément Mouhot,
249
778399
4786
I zajedno sa svojim bivšim studentom
i glavnim saradnikom, Klementom Muoom,
i glavnim saradnikom, Klementom Muoom,
13:15
in Paris at the time,
250
783209
1492
tada u Parizu,
13:16
we had been working for months
and months on such a proof.
and months on such a proof.
251
784725
4086
radili smo mesecima
i mesecima na tom dokazu.
i mesecima na tom dokazu.
13:21
Actually,
252
789832
1335
U stvari,
13:23
I had already announced by mistake
that we could solve it.
that we could solve it.
253
791191
4746
ja sam već greškom objavio
da možemo to da rešimo.
da možemo to da rešimo.
13:27
But the truth is,
254
795961
1725
Ali, istina je bila
13:29
the proof was just not working.
255
797710
2147
da dokaz jednostavno nije funkcionisao.
13:32
In spite of more than 100 pages
of complicated, mathematical arguments,
of complicated, mathematical arguments,
256
800196
4349
Bez obzira na to što je postojalo
više od 100 stranica komplikovanih
matematičkih pretpostavki,
matematičkih pretpostavki,
13:36
and a bunch discoveries,
257
804569
1690
kao i niz otkrića
13:38
and huge calculation,
258
806283
1267
i ogromni proračuni,
13:39
it was not working.
259
807574
1169
dokaz nije funkcionisao.
13:41
And that night in Princeton,
260
809290
1681
I te noći u Prinstonu,
13:42
a certain gap in the chain of arguments
was driving me crazy.
was driving me crazy.
261
810995
4301
određena nelogičost u lancu
pretpostavki me je izluđivala.
pretpostavki me je izluđivala.
13:47
I was putting in there all my energy
and experience and tricks,
and experience and tricks,
262
815658
4593
Uložio sam svu svoju energiju,
iskustvo i trikove,
iskustvo i trikove,
13:52
and still nothing was working.
263
820275
1742
a ipak ništa nije funkcionisalo.
13:54
1 a.m., 2 a.m., 3 a.m.,
264
822553
3882
Jedan ujutru, dva ujutru, tri ujutru;
13:58
not working.
265
826459
1308
ne funkcioniše.
14:00
Around 4 a.m., I go to bed in low spirits.
266
828545
4321
Oko četiri ujutru,
ležem u rđavom raspoloženju.
ležem u rđavom raspoloženju.
14:05
Then a few hours later,
267
833915
2460
Onda, nekoliko sati kasnije,
14:08
waking up and go,
268
836399
1151
budim se i mislim:
14:09
"Ah, it's time to get
the kids to school --"
the kids to school --"
269
837574
3357
„Ah, vreme je da odvedem decu u školu - “
14:12
What is this?
270
840955
1151
Šta je ovo?
14:14
There was this voice in my head, I swear.
271
842130
2142
Čuo sam glas u glavi, kunem se.
14:16
"Take the second term to the other side,
272
844894
1913
„Prebaci drugi član na drugu stranu,
14:18
Fourier transform and invert in L2."
273
846831
1919
Furijeova transformacija
i invertuj na L2.“
i invertuj na L2.“
14:21
(Laughter)
274
849257
1151
(Smeh)
14:22
Damn it,
275
850432
1702
Dođavola,
to je bio početak rešenja!
14:24
that was the start of the solution!
276
852158
2113
14:27
You see,
277
855519
1151
Vidite, mislio sam da sam se odmorio,
14:28
I thought I had taken some rest,
278
856694
2283
14:31
but really my brain had
continued to work on it.
continued to work on it.
279
859001
3388
ali je moj mozak u stvari
nastavio da radi na tome.
nastavio da radi na tome.
14:35
In those moments,
280
863008
1597
U tim trenucima,
14:36
you don't think of your career
or your colleagues,
or your colleagues,
281
864629
2601
ne misliš na svoju karijeru ili na kolege;
14:39
it's just a complete battle
between the problem and you.
between the problem and you.
282
867254
3690
to je prosto potpuna bitka
između problema i tebe.
između problema i tebe.
14:44
That being said,
283
872098
1328
Imajući to u vidu,
14:45
it does not harm when you do get
a promotion in reward for your hard work.
a promotion in reward for your hard work.
284
873450
3949
ne škodi ni kada se dobije unapređenje
kao nagrada za naporan rad.
kao nagrada za naporan rad.
14:49
And after we completed our huge
analysis of the Landau damping,
analysis of the Landau damping,
285
877808
5160
I pošto smo završili našu
ogromnu analizu Landauovog prigušenja,
ogromnu analizu Landauovog prigušenja,
14:54
I was lucky enough
286
882992
1615
bio sam dovoljno srećan
14:56
to get the most coveted Fields Medal
287
884631
3030
da dobijem najpoželjniju Fildsovu medalju
14:59
from the hands of the President of India,
288
887685
2867
koju mi je uručila predsednica Indije,
15:02
in Hyderabad on 19 August, 2010 --
289
890576
3920
u Hajderabadu 19. avgusta 2010. -
15:07
an honor that mathematicians
never dare to dream,
never dare to dream,
290
895453
3251
čast o kojoj se matematičari
i ne usuđuju da sanjaju,
i ne usuđuju da sanjaju,
15:10
a day that I will remember until I live.
291
898728
2399
dan koji ću pamtiti dok sam živ.
15:14
What do you think,
292
902366
1447
O čemu misliti
15:15
on such an occasion?
293
903837
2141
u takvoj prilici?
15:18
Pride, yes?
294
906002
1150
Ponos, zar ne?
15:19
And gratitude to the man collaborators
who made this possible.
who made this possible.
295
907791
3640
I zahvalnost mnogim saradnicima
koji su učinili to mogućim.
koji su učinili to mogućim.
15:24
And because it was a collective adventure,
296
912304
2212
I zato što je to bio zajednički poduhvat,
15:26
you need to share it,
not just with your collaborators.
not just with your collaborators.
297
914540
4142
potrebno ga je podeliti
ne samo sa saradnicima.
ne samo sa saradnicima.
15:31
I believe that everybody can appreciate
the thrill of mathematical research,
the thrill of mathematical research,
298
919548
5692
Verujem da su svi u stanju da cene
uzbuđenje matematičkog istraživanja
uzbuđenje matematičkog istraživanja
15:37
and share the passionate stories
of humans and ideas behind it.
of humans and ideas behind it.
299
925264
4318
i da strastveno dele priče
o ljudima i idejama iza njih.
o ljudima i idejama iza njih.
15:42
And I've been working with my staff
at Institut Henri Poincaré,
at Institut Henri Poincaré,
300
930494
4774
Moje osoblje pri Institutu
Anri Poenkare i ja smo radili,
Anri Poenkare i ja smo radili,
15:47
together with partners and artists
of mathematical communication worldwide,
of mathematical communication worldwide,
301
935292
5181
zajedno sa partnerima i umetnicima
matematičke komunikacije širom sveta,
matematičke komunikacije širom sveta,
15:52
so that we can found our own,
very special museum of mathematics there.
very special museum of mathematics there.
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na osnivanju sopstvenog,
veoma specijalnog muzeja matematike tamo.
veoma specijalnog muzeja matematike tamo.
15:58
So in a few years,
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Tako, kroz par godina
16:00
when you come to Paris,
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kada dođete u Pariz,
16:02
after tasting the great, crispy
baguette and macaroon,
baguette and macaroon,
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posle isprobavanja sjajnog,
hrskavog bageta i makaruna,
hrskavog bageta i makaruna,
16:08
please come and visit us
at Institut Henri Poincaré,
at Institut Henri Poincaré,
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molim vas dođite i posetite nas
u Institutu Anri Poenkare
u Institutu Anri Poenkare
16:11
and share the mathematical dream with us.
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i sanjajte matematički san
zajedno sa nama.
zajedno sa nama.
16:14
Thank you.
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Hvala.
16:15
(Applause)
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(Aplauz)
ABOUT THE SPEAKER
Cédric Villani - MathematicianCédric Villani tackles perplexing problems in mathematical physics, analysis and geometry with rigor, wit and a signature personal style.
Why you should listen
His Byronesque hair, colorful ascots and spider brooches have earned Cédric Villani the nickname “the Lady Gaga of Mathematics.” But this moniker has not obscured Villani’s deeper, serious mission: inspiring students to delve into the mysteries of mathematics.
Villani’s fame is based on his work resolving difficult problems of kinetic theory, for which he received the Fields Medal in 2010. His book Birth of a Theorem is an exhilarating journey into the nocturnal dilemmas of mathematicians hot on the trail of discovery.
Villani was elected to the French National Assembly in June 2017.
Cédric Villani | Speaker | TED.com