Translator: Tomás Guarna
Reviewer: Gisela Giardino How remarkable it is
that for so many years there has been such a prominent
negative view against math. And then we should say, “Let’s not enter through there,
through technicalities.” We should say,”You’re entering
through the wrong door.” It’s not that it’s not math,
it doesn’t have its beauty. You don’t invite someone home
and say, “This way, madam.” and lead her to the toilet. You don’t enter a restaurant through
the place where they put the garbage. No! Or if someone never played soccer before,
you take 10 kids and say, “Teach soccer to someone
who never played before, where would you start?” “We’ll form a kick line. You go here, I’ll kick
a ball towards you.” (Laughter)
“You can’t use your hands.” Who wants to play soccer like that? Math has an extraordinary peculiarity but they show it to us
in a way we can’t grasp it. No one says with such pride. Do you know any adult who says,
“I’m a mess, I can’t read, I actually communicate
very badly with other people”? However, saying,
“I’m not one for math.” Anywhere I go the first thing people say is: “It’s a pleasure, I always watch you.” Not really, right?
(Laughter) “I always watch your show.” It wears well to say they watch my show. “But don’t ask me anything
because I don’t get a thing of math.” And they seem to say it
with such pride, as if there was a small group of people who has access to understanding something, distant from the general public. Do you think I’m someone special? The only thing we have,
those who had the chance to do something related to math,
is that we went through all the obstacles they set up for us. Believe me, it’s something incredible. I would like that when today’s talk ends, all of you go home saying,
“Today, I learned something new.” If I could have each of you
here today to leave thinking, “We were in TED and I learned
something I didn’t know.” That would be enough. Do you realize?
If we could incorporate one idea a day, we would have 365 ideas a year. It would be crazy. Math has a peculiarity:
it’s like magicians. Why do magicians attract people? Why is it that a magician draws
the attention of all adults and children? Because the first thing you want
is to uncover the trick. We know that magic doesn’t exist,
but we want to know how it’s done. It’s the same as detectives.
Math is not all uncovered yet. In fact, around 200,000 theorems
are written per year. In other words, 200,000 problems
are solved each year. There’s a lot to know still unknown. We like detective TV shows,
detectives movies, because we want to uncover the murderer. In math there’s a lot
of hidden things still unknown. I could spend hours talking to you
about problems that are still unsolved. However, it seems as if that is banned. There are things
that go against intuition. Now, I’ll ask you a question,
but I need those who know the answer, and possibly many of you do,
to please don’t say it. If I told you the following,
notice how it goes against intuition: suppose someone buys something
that doesn’t exist anymore, a CD, that has ten songs. Ten songs in some order. Now you’ll see why I ask this. 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
Okay? This is the order in which the songs come. Suppose someone goes to work everyday
and listens to the ten songs in that way. But one day they say,
“Every CD player has a shuffle feature.” What is that? What does it do? It picks songs randomly.
You know that, right? So we’ll suppose,
as it takes this person, just enough time since they leave home
until they reach work to listen to the ten songs, they want to listen to them every day
in a different order, so they use the shuffle feature. Let’s suppose they listen to them
every day in a different order. How many days will it take
until they have no choice but to repeat one of the previous orders? Before I go on: is the question clear? Does everybody understand? How long will it take until someone
that wants to listen to the songs each day in a different order
has no choice but to repeat that order? If there were two songs,
how many days would it take? If there are only two songs? Two, because one day he listens to 1-2,
and the next to 2-1. And if there are 3, how many days? Six days, because
there’s 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2 and 3-2-1. Alright? Six. With 4, there’s 24. With 5, there’s 120. And you do know how much is it with 10? With 10
it’s 3,628,800. And it’s okay. To those who say
it’s an atrocity notice that people die
before they can repeat the order. (Laughter) Because it’s almost 10,000 years. People go on their cars desperate,
thinking, “Will it repeat itself or not? Because I’m dying, mom.” (Applause) What’s curious is that we can ask
what’s the importance of this. Well, one could have a bookshelf, for example, a bookseller
has a bookshelf with 10 books. In reality, imagine that with 10 books
there’s 3,628,800 ways. Simply with a case of 100 books there are more possibilities
than atoms in the universe. Imagine the booksellers,
trying to change them, a librarian who gets bored
and starts to move them. Now, why am I also telling you this? Because it goes against intuition. Had I asked this to you before coming in,
to those who didn’t know the answer, I’m sure this would’ve surprised you. But they don’t tell us this. Recently, something about Roland Garros
tennis tournament came up, in which there’s usually 128 contestants, but what I’ll say now applies to every
tournament; it doesn’t need to be tennis. Let’s suppose there’s 128 participants. I want to ask you a question.
How many matches should you plan? How many matches will be played
until the tournament ends? Is the question clear? You know tennis is played
by eliminating the one who loses. The word “eliminating” is understood. They play against each other,
and the one eliminated leaves. If there’s 128 of them.
– I can see you from here! Those faces! “Don’t look at me because I can’t. I only came for the ideas.”- (Laughter) If they are 128, how many matches
should be played the first day? 64. And if 64 are eliminated there,
the next day 32 matches are played, and the next 16, and then 8…
Alright? We would have to add up 64+32+16+8+4+2+1. What is the 1? The final match.
Do you follow? Well then. One could do that sum. Now I’ll show you what math can provide.
This is also doing math. But now I ask you this: how many matches
will the 128 participants lose except for the champion? All the others,
how many matches will they lose? One. To lose they must have played,
they can’t lose without playing. How many matches the participants
had to lose, save the champion? How many matches were lost? The 127 other participants,
that are not the champion, must have lost, right? Then, how many matches were played? Without doing any calculation; 127! The only one that didn’t lose
is the champion. All the rest lost one.
Do you agree? Elaborating a strategy of this type
is doing mathematics. Only that they don’t tell us this. Now, if one has 2,5 billion participants,
how many matches will be played? One could to the calculation again.
2,5 billion divided by two, and all. (Laughter) But now we won’t do it anymore. And looking for this type
of patterns is doing math. What’s more, and I would really like that you to take this with you
after this talk. If you stopped one person in the street and asked them, “What does
a mathematician do?” “What does a Ph.D. in Mathematics do?”
“They make calculations.” (Laughter) “Very fast.” (Laughter) “Really big calculations, sir.”
“I’ve seen them”. No. There’s a notion that mathematicians
do something we don’t do, that we’re not even good at doing… I’d be an idiot if I did calculations,
having computers and calculators. Why would I do them? And even though I look old, – and I’m 65 years old, but not 400 – when I was born there was no TV,
but when I was a kid my father told me that the wise men were those who knew many things
and about many things. And I imagined them
in another stratosphere, I guess. What was what these guys knew? That took us all
to an encyclopedist culture. It’s always better the person
who “knows more”. What is “to know more”? What is
what I have to know? I Google it. What one needs to have is creativity. What we should ban from schools
is the word “no”. That thing they write in red,”wrong”. What is “wrong”?
Can we have “wrong” in math? Scientists never publish their mistakes.
They never publish what’s wrong. They publish the result, the last step. And all the steps in between?
But you know what the real problem is? Society is always looking
for the person that gets there first, that runs the fastest,
that jumps the highest. The best.
Who is the best? And the one that gets there second,
tenth, fifth, 143th? Are we all losers? We can’t make the rules
for a small group of people. We’re looking for the child prodigy.
Child prodigy? The privileged child. We need to be generous at distributing
knowledge, by socializing it. If someone knows something,
they have to share it. And us, let’s end the myth that someone who did something
is better than another one who didn’t. They aren’t either better or worse. Let’s all learn from all. So math also offers
a branch called game theory. A kid wants to play, and wants
to keep playing their whole life. Adults too. In fact, this is what it came about when I was talking about
how to slice a cake. That’s part of the game theory. Trying to understand human behavior. I could show you how we can demonstrate that there are two people in Buenos Aires with the exact amount of hairs
in their head. Once again. The word “head”, yes,
but I get you at “hairs”. And let’s exclude bald people,
as they have zero hairs. See how math can come to our rescue
in this question. How can you demonstrate
that at least two people in Buenos Aires have the same amount of hairs? How can it be done?
I’ll give you the answer. Do you know how many hairs one person has
on their head, more or less? If we stretched out the scalp
–don’t try this at home today–, (Laughter)
I didn’t mean that, but if we could, we’d see that a person
with 200,000 hairs is a guy that has hair
growing out from everywhere. We has less than 200,000 hairs. Question: if one can’t have 200,000 hairs, does this prove there has to be
at least two people in Buenos Aires with the same number of hairs? Why? Because let’s suppose,
how many people are there in Buenos Aires? More than 2 million people? If they all had different number of hairs,
there would be people with hair like this. There’d be one with 2 million hairs,
I don’t know how it’d look like. Then, it has to inevitably repeat itself. Math says,
“Keep looking, because you’ll find them.” It doesn’t say which ones,
but that there are. So regarding today, I hope I get to see when programming is taught in schools,
both primary and secondary, because programming
is the language of the 21st century. In my time, all it took to be literate
was to be able to read and write. Today, reading and writing is the minimum
you can aim for. We need to have at least
another language to communicate, and the language of programming. Otherwise, they are teaching you
to play a video game, but not to let you modify it. I want to know how to read,
but also how to write. And that’s what programming allows. So, somehow, you, the young people need to motivate that,
learn how to say “I don’t know”. What’s wrong with saying “I don’t know”,
“I don’t get it”, “say it again”? If they didn’t get it, what’s the problem? What guarantee do we have
that the one who understood is better? Let’s learn to say “I don’t know”. That’s what happens to us with math.
We need to display it so someone sees it. We need to break this notion,
“Not me, I’ve nothing to do with math. I don’t understand anything!
My son does, he knows the 15 times table.” I suggest you to do the following: keep in mind that value
goes through creativity, through learning to solve problems. In school they often teach us
first how to solve a problem we don’t have and then they send us home
to try to solve it. In life is backwards, first we have the problem,
then we look for the solution. We don’t have the solution first
for problems we don’t have. (Applause) And the second thing:
give yourselves a chance, give math the following alternative:
don’t go in through that door, that door is useless, that’s clear,
we don’t need to diagnose it anymore. We know it, let’s stop saying
“we have failed”. Let’s give it another chance. Because soccer and life
are also like magic and detective stories: there are lots of things to do
and you are the ones to achieve them. Thank you. (Applause)