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  • Translator: Tomás Guarna Reviewer: Sebastian Betti

  • 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)

  • 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.

  • 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.

  • 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.

  • 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.

  • Audience: What is math for?

  • Eduardoenz 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.

  • 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.

  • 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.

  • 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)

  • 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)

  • 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)

  • 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.

  • 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.

  • 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.

  • (Applause)

Translator: Tomás Guarna Reviewer: Sebastian Betti

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

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    Zenn posted on 2018/03/27
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