Imagine you're in a bar, or a club, and you start talking, and after a while, the question comes up, "So, what do you do for work?" And since you think your job is interesting, you say, "I'm a mathematician." (Laughter) And inevitably, during that conversation one of these two phrases come up: A) "I was terrible at math, but it wasn't my fault. It's because the teacher was awful." (Laughter) Or B) "But what is math really for?" (Laughter) I'll now address Case B. (Laughter)
Zamisli da se nalaziš u kafiću ili klubu, kreneš razgovarati i nakon nekog vremena pojavi se pitanje: „A čime se ti baviš?“ Budući da misliš da ti je posao zanimljiv kažeš: „Ja sam matematičar.“ (Smijeh) Tijekom razgovora, u jednom trenutku neizbježno se javi jedna od ovih dviju rečenica: A) „Užasno mi je išla matematika, ali ne mojom krivnjom. To je zato što je profesor bio užasan." (Smijeh) I B) „Ali čemu uopće služi matematika?“ (Smijeh) Pozabavit ću se slučajem B. (Smijeh) Kada te netko pita čemu služi matematika,
When someone asks you what math is for, they're not asking you about applications of mathematical science. They're asking you, why did I have to study that bullshit I never used in my life again? (Laughter) That's what they're actually asking. So when mathematicians are asked what math is for, they tend to fall into two groups: 54.51 percent of mathematicians will assume an attacking position, and 44.77 percent of mathematicians will take a defensive position. There's a strange 0.8 percent, among which I include myself.
ne pita te za primjenu znanstvene matematike. Pita te: „Zašto sam morao učiti to sranje koje nikad više u životu nisam upotrijebio?“ (Smijeh) To je ono što te zaista pita. Stoga kada matematičare pitaju čemu služi matematika, mi, matematičari, podijelimo se u dvije grupe. 54,51% matematičara zauzima napadački stav, a 44.77% matematičara zauzima obrambeni stav. Postoji i neobičnih 0,8%, unutar kojih sam i ja.
Who are the ones that attack? The attacking ones are mathematicians who would tell you this question makes no sense, because mathematics have a meaning all their own -- a beautiful edifice with its own logic -- and that there's no point in constantly searching for all possible applications. What's the use of poetry? What's the use of love? What's the use of life itself? What kind of question is that? (Laughter) Hardy, for instance, was a model of this type of attack.
Tko su oni koji napadaju? Oni koji napadaju su matematičari koji bi ti rekli da ovo pitanje nema smisla jer matematika ima značenje sama po sebi. To je prekrasno zdanje sa svojom vlastitom logikom i nema smisla stalno tražiti sve moguće primjene. Čemu služi poezija? Čemu služi ljubav? Čemu služi sam život? Kakvo je to pitanje? (Smijeh) Hardy je, primjerice, eksponent takvog napada.
And those who stand in defense tell you, "Even if you don't realize it, friend, math is behind everything." (Laughter) Those guys, they always bring up bridges and computers. "If you don't know math, your bridge will collapse." (Laughter) It's true, computers are all about math. And now these guys have also started saying that behind information security and credit cards are prime numbers. These are the answers your math teacher would give you if you asked him. He's one of the defensive ones.
Oni koji stoje u obrani ti kažu: „Čak i ako to ne shvaćaš, prijatelju, matematika se nalazi u osnovi svega.“ (Smijeh) Takvi uvijek spominju mostove i računala. „Ako ne znaš matematiku, srušit će ti se most.“ (Smijeh) Realno, računala se svode na matematiku. I sada su oni također počeli govoriti da se iza informacijske sigurnosti i kreditnih kartica nalaze primarni brojevi. To su odgovori koje bi ti dao tvoj profesor matematike kad bi ga pitao. On je jedan od onih obrambenih.
Okay, but who's right then? Those who say that math doesn't need to have a purpose, or those who say that math is behind everything we do? Actually, both are right. But remember I told you I belong to that strange 0.8 percent claiming something else? So, go ahead, ask me what math is for.
Ok, ali tko je onda u pravu? Oni koji kažu da matematika ne treba imati svrhu ili oni koji kažu da je iza svega što radimo? Zapravo, obje strane su u pravu. No rekao sam vam da sam ja u onih 0,8% koji tvrde nešto drugo, zar ne? Dakle, samo naprijed, pitajte me čemu služi matematika. Publika: „Čemu služi matematika?“
Audience: What is math for?
Ok, 6,34% vas postavilo je pitanje, 23,41% nije reklo ništa,
Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question, 23.41 percent didn't say anything, and the 0.8 percent -- I'm not sure what those guys are doing. Well, to my dear 76.31 percent -- it's true that math doesn't need to serve a purpose, it's true that it's a beautiful structure, a logical one, probably one of the greatest collective efforts ever achieved in human history. But it's also true that there, where scientists and technicians are looking for mathematical theories that allow them to advance, they're within the structure of math, which permeates everything.
a onih 0,8% – nisam siguran što oni rade. Pa, dragih mojih 76,31%, istina je da matematika ne treba služiti svrsi, istina je da se radi o lijepoj strukturi, logičnoj, i vjerojatno jednom od najvećih zajedničkih napora ikad ostvarenih u ljudskoj podsvijesti. Ali isto tako istina je da tamo gdje znanstvenici i tehničari traže matematičke teorije koje im omogućuju napredak, oni su unutar matematičke strukture koja prožima sve. Istina je da moramo otići nešto dublje
It's true that we have to go somewhat deeper, to see what's behind science. Science operates on intuition, creativity. Math controls intuition and tames creativity. Almost everyone who hasn't heard this before is surprised when they hear that if you take a 0.1 millimeter thick sheet of paper, the size we normally use, and, if it were big enough, fold it 50 times, its thickness would extend almost the distance from the Earth to the sun. Your intuition tells you it's impossible. Do the math and you'll see it's right. That's what math is for.
da vidimo što je iza znanosti. Znanost funkcionira pomoću intuicije, pomoću kreativnosti, a matematika kontrolira intuiciju i ukroćuje kreativnost. Gotovo svi koji ovo nisu čuli ranije su iznenađeni kada čuju da kada bi uzeli papir debljine 0,1 mm, kakav obično koristimo, i, kada bi bio dovoljno velik, presavinuli ga 50 puta, njegova bi debljina bila jednaka udaljenosti Zemlje do Sunca. Intuicija ti kaže: „To je nemoguće.“ Izračunaj i vidjet ćeš da je istina. To je ono čemu služi matematika. Istina je da znanost i sve vrste znanosti imaju smisla samo zato što nam omogućuju
It's true that science, all types of science, only makes sense because it makes us better understand this beautiful world we live in. And in doing that, it helps us avoid the pitfalls of this painful world we live in. There are sciences that help us in this way quite directly. Oncological science, for example. And there are others we look at from afar, with envy sometimes, but knowing that we are what supports them. All the basic sciences support them, including math. All that makes science, science is the rigor of math. And that rigor factors in because its results are eternal.
da bolje razumijemo ovaj lijepi svijet u kojem živimo. Čineći to, znanost nam pomaže izbjeći zamke ovog bolnog svijeta u kojem živimo. Ima znanosti koje nam u tom smislu pomažu prilično izravno. Onkološka znanost, na primjer. Postoje i druge koje gledamo izdaleka, ponekad sa zavišću, ali i znajući da smo mi ono što ih podupire. Podupiru ih sve osnovne znanosti, među njima i matematiku. Sve to čini znanost, znanost je strogost matematike. I ta strogost se javlja jer su njezini rezultati vječni.
You probably said or were told at some point that diamonds are forever, right? That depends on your definition of forever! A theorem -- that really is forever. (Laughter) The Pythagorean theorem is still true even though Pythagoras is dead, I assure you it's true. (Laughter) Even if the world collapsed the Pythagorean theorem would still be true. Wherever any two triangle sides and a good hypotenuse get together (Laughter) the Pythagorean theorem goes all out. It works like crazy. (Applause)
Vjerojatno ste rekli ili vam je nekad netko rekao da su dijamanti vječni, zar ne? Ovisi o tome što podrazumijevate pod tim pojmom. Teorem – to zaista jest zauvijek! (Smijeh) Pitagorin teorem, on je i dalje istinit iako je Pitagora mrtav, uvjeravam te. (Smijeh) Čak i da se svijet sruši, Pitagorin teorem bi i dalje nastavio biti istinit. Gdjegod se dodiruju par kateta i dobra hipotenuza (Smijeh) Pitagorin teorem funkcionira izvrsno. (Pljesak)
Well, we mathematicians devote ourselves to come up with theorems. Eternal truths. But it isn't always easy to know the difference between an eternal truth, or theorem, and a mere conjecture. You need proof. For example, let's say I have a big, enormous, infinite field. I want to cover it with equal pieces, without leaving any gaps. I could use squares, right? I could use triangles. Not circles, those leave little gaps. Which is the best shape to use? One that covers the same surface, but has a smaller border. In the year 300, Pappus of Alexandria said the best is to use hexagons, just like bees do. But he didn't prove it. The guy said, "Hexagons, great! Let's go with hexagons!" He didn't prove it, it remained a conjecture. "Hexagons!" And the world, as you know, split into Pappists and anti-Pappists, until 1700 years later when in 1999, Thomas Hales proved that Pappus and the bees were right -- the best shape to use was the hexagon. And that became a theorem, the honeycomb theorem, that will be true forever and ever, for longer than any diamond you may have. (Laughter)
Mi, matematičari, posvećeni smo pronalasku teorema. Vječnih istina. Ali nije uvijek tako lako razabrati vječnu istinu, ili teorem, od obične pretpostavke. Treba vam dokaz. Primjerice, recimo da ovdje imam veliko, golemo, beskonačno polje. Želim ga prekriti jednakim dijelovima, ne ostavljajući nikakvih praznina. Mogao bih upotrijebiti kvadrate, zar ne? Mogao bih upotrijebiti trokute. Ne krugove, oni ostavljaju praznine. Koji je najbolji oblik koji mogu upotrijebiti? Onaj koji pokriva jednaku površinu, ali ima manje stranice. Pap Aleksandrijski je 300. godine rekao da je najbolje upotrijebiti heksagone, kao što to čine pčele. Ali nije to i dokazao! Tip je rekao: „Heksagoni, odlično! Daj mi heksagone!“ On to nije dokazao, ostalo je na pretpostavci. „Heksagoni!“ I svijet se, kao što znate, podijelio na papiste i antipapiste, sve do 1700 kasnije kada je 1999. Thomas Hales dokazao da su Pap i pčele bili u pravu, da je najbolje upotrijebiti heksagone. I to je postalo teorem, teorem o pčelinjem saću, koji će biti istinit uvijek i zauvijek, dulje od bilo kojeg dijamanta. (Smijeh)
But what happens if we go to three dimensions? If I want to fill the space with equal pieces, without leaving any gaps, I can use cubes, right? Not spheres, those leave little gaps. (Laughter) What is the best shape to use? Lord Kelvin, of the famous Kelvin degrees and all, said that the best was to use a truncated octahedron which, as you all know -- (Laughter) -- is this thing here! (Applause) Come on. Who doesn't have a truncated octahedron at home? (Laughter) Even a plastic one. "Honey, get the truncated octahedron, we're having guests." Everybody has one! (Laughter)
Ali što se dogodi ako pređemo na tri dimenzije? Ako želim ispuniti prostor jednakim dijelovima, ne ostavljajući praznine, mogu upotrijebiti kocke, zar ne? Ne kugle, one ostavljaju male praznine. (Smijeh) Koji je najbolji oblik koji mogu upotrijebiti? Lord Kelvin, onaj po kojemu su nazvani čuveni Kelvinovi stupnjevi, rekao je da je najbolje upotrijebiti skraćeni oktaedar (Smijeh) koji je, kao što svi znate, (Smijeh) ovo ovdje! (Pljesak) Tko još nema skraćeni oktaedar kod kuće? (Smijeh) Makar i plastični. „Dušo, uzmi skraćeni oktaedar, imamo goste.“ Svi imaju jednog! (Smijeh) Ali Kelvin to nije dokazao.
But Kelvin didn't prove it. It remained a conjecture -- Kelvin's conjecture. The world, as you know, then split into Kelvinists and anti-Kelvinists (Laughter) until a hundred or so years later, someone found a better structure. Weaire and Phelan found this little thing over here -- (Laughter) -- this structure to which they gave the very clever name "the Weaire-Phelan structure." (Laughter) It looks like a strange object, but it isn't so strange, it also exists in nature. It's very interesting that this structure, because of its geometric properties, was used to build the Aquatics Center for the Beijing Olympic Games.
Ostalo je na pretpostavci, Kelvinovoj pretpostavci. Svijet se, kao što znate, tada podijelio na kelviniste i antikelviniste (Smijeh) sve dok netko stotinjak godina kasnije nije pronašao bolju strukturu. Weaire i Phelan pronašli su ovu stvarčicu ovdje (Smijeh) ovu strukturu kojoj su nadjenuli vrlo dovitljivo ime „Weaire-Phelanova struktura“. (Smijeh) Izgleda kao čudna stvar, ali nije tako čudna, postoji i u prirodi. Vrlo je zanimljivo da je ova struktura, zbog svojih geometrijskih svojstava, bila korištena u izgradnji Centra za vodene sportove za Olimpijske igre u Pekingu.
There, Michael Phelps won eight gold medals, and became the best swimmer of all time. Well, until someone better comes along, right? As may happen with the Weaire-Phelan structure. It's the best until something better shows up. But be careful, because this one really stands a chance that in a hundred or so years, or even if it's in 1700 years, that someone proves it's the best possible shape for the job. It will then become a theorem, a truth, forever and ever. For longer than any diamond.
Tamo je Michael Phelps osvojio osam zlatnih medalja i postao najbolji plivač svih vremena. Dobro, sve dok se ne pojavi netko bolji, zar ne? Kao što se može dogoditi i Weaire-Phelanovoj strukturi. Najbolja je sve dok se ne pojavi nešto bolje. No pazite jer ova zaista ima šanse da za stotinjak godina, ili čak njih 1700, netko dokaže da je ovo najbolji mogući oblik. Tada će postati teorem, istina, uvijek i zauijek. Dulje od bilo kojeg dijamanta.
So, if you want to tell someone that you will love them forever you can give them a diamond. But if you want to tell them that you'll love them forever and ever, give them a theorem! (Laughter) But hang on a minute! You'll have to prove it, so your love doesn't remain a conjecture.
Dakle, ako želiš nekome reći da ćeš ga voljeti zauvijek, (Smijeh) možeš mu pokloniti dijamant, ali ako mu želiš reći da ćeš ga voljeti uvijek i zauvijek, daj mu teorem! (Smijeh) Ali samo malo! Morat ćeš to dokazati da vaša ljubav ne bi ostala pretpostavka. (Pljesak)
(Applause)