Eduardo Sáenz de Cabezón: Math is forever (with English subtitles) | TED

190,792 views ・ 2015-04-07

TED


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Translator: Tomás Guarna Reviewer: Sebastian Betti
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Imagine you're in a bar, or a club,
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and you start talking, and after a while, the question comes up,
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"So, what do you do for work?"
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And since you think your job is interesting,
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you say, "I'm a mathematician." (Laughter)
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And inevitably, during that conversation
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one of these two phrases come up:
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A) "I was terrible at math, but it wasn't my fault.
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It's because the teacher was awful." (Laughter)
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Or B) "But what is math really for?"
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(Laughter)
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I'll now address Case B.
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(Laughter)
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When someone asks you what math is for, they're not asking you
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about applications of mathematical science.
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They're asking you,
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why did I have to study that bullshit I never used in my life again? (Laughter)
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That's what they're actually asking.
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So when mathematicians are asked what math is for,
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they tend to fall into two groups:
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54.51 percent of mathematicians will assume an attacking position,
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and 44.77 percent of mathematicians will take a defensive position.
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There's a strange 0.8 percent, among which I include myself.
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Who are the ones that attack?
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The attacking ones are mathematicians who would tell you
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this question makes no sense,
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because mathematics have a meaning all their own --
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a beautiful edifice with its own logic --
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and that there's no point
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in constantly searching for all possible applications.
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What's the use of poetry? What's the use of love?
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What's the use of life itself? What kind of question is that?
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(Laughter)
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Hardy, for instance, was a model of this type of attack.
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And those who stand in defense tell you,
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"Even if you don't realize it, friend, math is behind everything."
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(Laughter)
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Those guys,
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they always bring up bridges and computers.
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"If you don't know math, your bridge will collapse."
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(Laughter)
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It's true, computers are all about math.
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And now these guys have also started saying
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that behind information security and credit cards are prime numbers.
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These are the answers your math teacher would give you if you asked him.
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He's one of the defensive ones.
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Okay, but who's right then?
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Those who say that math doesn't need to have a purpose,
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or those who say that math is behind everything we do?
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Actually, both are right.
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But remember I told you
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I belong to that strange 0.8 percent claiming something else?
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So, go ahead, ask me what math is for.
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Audience: What is math for?
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Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question,
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23.41 percent didn't say anything,
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and the 0.8 percent --
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I'm not sure what those guys are doing.
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Well, to my dear 76.31 percent --
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it's true that math doesn't need to serve a purpose,
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it's true that it's a beautiful structure, a logical one,
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probably one of the greatest collective efforts
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ever achieved in human history.
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But it's also true that there,
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where scientists and technicians are looking for mathematical theories
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that allow them to advance,
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they're within the structure of math, which permeates everything.
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It's true that we have to go somewhat deeper,
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to see what's behind science.
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Science operates on intuition, creativity.
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Math controls intuition and tames creativity.
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Almost everyone who hasn't heard this before
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is surprised when they hear that if you take
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a 0.1 millimeter thick sheet of paper, the size we normally use,
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and, if it were big enough, fold it 50 times,
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its thickness would extend almost the distance from the Earth to the sun.
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Your intuition tells you it's impossible.
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Do the math and you'll see it's right.
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That's what math is for.
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It's true that science, all types of science, only makes sense
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because it makes us better understand this beautiful world we live in.
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And in doing that,
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it helps us avoid the pitfalls of this painful world we live in.
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There are sciences that help us in this way quite directly.
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Oncological science, for example.
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And there are others we look at from afar, with envy sometimes,
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but knowing that we are what supports them.
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All the basic sciences support them,
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including math.
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All that makes science, science is the rigor of math.
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And that rigor factors in because its results are eternal.
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You probably said or were told at some point
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that diamonds are forever, right?
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That depends on your definition of forever!
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A theorem -- that really is forever.
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(Laughter)
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The Pythagorean theorem is still true
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even though Pythagoras is dead, I assure you it's true. (Laughter)
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Even if the world collapsed
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the Pythagorean theorem would still be true.
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Wherever any two triangle sides and a good hypotenuse get together
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(Laughter)
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the Pythagorean theorem goes all out. It works like crazy.
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(Applause)
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Well, we mathematicians devote ourselves to come up with theorems.
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Eternal truths.
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But it isn't always easy to know the difference between
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an eternal truth, or theorem, and a mere conjecture.
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You need proof.
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For example,
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let's say I have a big, enormous, infinite field.
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I want to cover it with equal pieces, without leaving any gaps.
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I could use squares, right?
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I could use triangles. Not circles, those leave little gaps.
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Which is the best shape to use?
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One that covers the same surface, but has a smaller border.
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In the year 300, Pappus of Alexandria said the best is to use hexagons,
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just like bees do.
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But he didn't prove it.
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The guy said, "Hexagons, great! Let's go with hexagons!"
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He didn't prove it, it remained a conjecture.
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"Hexagons!"
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And the world, as you know, split into Pappists and anti-Pappists,
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until 1700 years later
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when in 1999, Thomas Hales proved
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that Pappus and the bees were right -- the best shape to use was the hexagon.
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And that became a theorem, the honeycomb theorem,
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that will be true forever and ever,
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for longer than any diamond you may have. (Laughter)
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But what happens if we go to three dimensions?
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If I want to fill the space with equal pieces,
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without leaving any gaps,
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I can use cubes, right?
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Not spheres, those leave little gaps. (Laughter)
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What is the best shape to use?
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Lord Kelvin, of the famous Kelvin degrees and all,
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said that the best was to use a truncated octahedron
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which, as you all know --
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(Laughter) --
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is this thing here!
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(Applause)
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Come on.
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Who doesn't have a truncated octahedron at home? (Laughter)
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Even a plastic one.
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"Honey, get the truncated octahedron, we're having guests."
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Everybody has one! (Laughter)
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But Kelvin didn't prove it.
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It remained a conjecture -- Kelvin's conjecture.
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The world, as you know, then split into Kelvinists and anti-Kelvinists
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(Laughter)
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until a hundred or so years later,
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someone found a better structure.
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Weaire and Phelan found this little thing over here --
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(Laughter) --
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this structure to which they gave the very clever name
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"the Weaire-€“Phelan structure."
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(Laughter)
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It looks like a strange object, but it isn't so strange,
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it also exists in nature.
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It's very interesting that this structure,
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because of its geometric properties,
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was used to build the Aquatics Center for the Beijing Olympic Games.
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There, Michael Phelps won eight gold medals,
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and became the best swimmer of all time.
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Well, until someone better comes along, right?
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As may happen with the Weaire-€“Phelan structure.
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It's the best until something better shows up.
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But be careful, because this one really stands a chance
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that in a hundred or so years, or even if it's in 1700 years,
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that someone proves it's the best possible shape for the job.
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It will then become a theorem, a truth, forever and ever.
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For longer than any diamond.
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So, if you want to tell someone
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that you will love them forever
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you can give them a diamond.
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But if you want to tell them that you'll love them forever and ever,
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give them a theorem!
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(Laughter)
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But hang on a minute!
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You'll have to prove it,
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so your love doesn't remain
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a conjecture.
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(Applause)
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