La puerta equivocada | Adrián Paenza | TEDxRiodelaPlata

Translator: Tomás Guarna Reviewer: Gisela Giardino How remarkable it is that for so many years there has been such a prominent negative view against mathematics. And then we should say: "Let's not go there, on technicalities." We should say, "You are entering through the wrong door." It's not that it's not mathematics, it doesn't have its beauty. You don't invite someone home and say, "This way, ma'am." and she takes her to the bathroom. You don't enter a restaurant through the place where they throw the garbage. No! Or if someone never played soccer before, you take 10 kids and say, "Teach soccer to someone who never played soccer before, where would you start?" "We'll form a kick line.

Go here, I'll kick a ball toward you." (Laughter) "You can't use your hands." Who wants to play football like that? Mathematics has an extraordinary peculiarity but it shows it to us in a way that we cannot grasp. Nobody says it with so much pride. Do you know any adult who says: "I'm a disaster, I don't know how to read, in fact I communicate very poorly with other people"? However, saying, "I'm not a math person." Everywhere I go the first thing people say is: "It's a pleasure, I always look at you." Not really, right? (Laughs) "I always watch your show." It's nice to say that they watch my program. "But don't ask me anything because I don't understand anything about mathematics." And they seem to say it with such pride, as if there were a small group of people who have access to understanding something, away from the general public.

Do you think I'm someone special? The only thing that we, those of us who had the opportunity to do something related to mathematics, have is that we went through all the obstacles that were put before us. Believe me, it's something incredible. I would like that when I finish today's talk, all of you go home saying: "I learned something new today." If I could have each of you here today to walk away thinking, "We were at TED and I learned something I didn't know." That would be enough. You realize? If we could add one idea a day, we would have 365 ideas a year.

It would be crazy. Mathematics has a peculiarity: they are like magicians. Why do magicians attract people? Why does a magician attract the attention of all adults and children? Because the first thing you want is to discover the trick. We know that magic does not exist, but we want to know how it is done. It's the same as detectives. The mathematics is not fully figured out yet. In fact, around 200,000 theorems are written a year. That is, 200,000 problems are solved every year. There is much to know yet unknown. We like television series and detective movies because we want to discover the murderer.

In mathematics there are many hidden things that are still unknown. I could spend hours talking to you about problems that are still unresolved. However, it seems that this is prohibited. There are things that go against intuition. Now I will ask you a question, but I need those who know the answer, and possibly many of you know it, to please not say it. If I tell you the following, notice that it goes against intuition: suppose someone buys something that no longer exists, a CD, which has ten songs. Ten songs in some order. Now you will see why I ask this. 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Okay? This is the order the songs come in. Suppose someone goes to work every day and listens to all ten songs that way. But one day they say: "All CD players have a shuffle function." What's that? What are you doing? Choose songs at random. Do you know it well? Then we will assume that, since it takes this person enough time from leaving home to arriving at work to listen to all ten songs, he wants to listen to them every day in a different order, so he uses the shuffle function. Suppose you listen to them every day in a different order.

How many days will it be until they have no choice but to repeat one of the previous requests? Before continuing: is the question clear? Does everyone understand? How long will it be until someone who wants to listen to the songs in a different order every day 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 you hear 1-2, and the next day 2-1. And if it is 3, how many days? Six rounds, because there are 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2 and 3-2-1.

Alright? Six. With 4, there are 24. With 5, there are 120. And do you know what 10 is? With 10 that's 3,628,800. And it's OK. To those who say it is an atrocity, notice that people die before they can repeat the order. (Laughs) Because it's almost 10,000 years. People drive in their cars desperate, thinking: "Will it happen again or not? Because I'm dying, mom." (Applause) The curious thing is that we can ask ourselves what the importance of this is. Well, one could have a bookshelf, for example, a bookseller has a shelf with 10 books. Actually, imagine that with 10 books there are 3,628,800 ways. Simply with a box of 100 books there are more possibilities than there are atoms in the universe.

Imagine the booksellers, trying to move them, a librarian who gets bored and starts moving them. Now, why am I telling you this too? Because it goes against intuition. If I had asked this before entering, to those who didn't know the answer, I'm sure they would have been surprised. But they don't tell us this. Something recently came up about the Roland Garros tennis tournament, in which there are normally 128 contestants, but what I will say now applies to all tournaments; It doesn't have to be tennis. Let's assume there are 128 participants. I want to ask you a question. How many matches should you plan?

How many games will be played until the tournament ends? Is the question clear? You already know that tennis is played by eliminating the loser. The word "delete" is understood. They play against each other and the eliminated one leaves. If there are 128 of them. - I can see you from here! Those faces! "Don't look at me because I can't. I just came for ideas." - (Laughter) If there are 128, how many games should be played on the first day? 64. And if 64 are eliminated there, the next day 32 games will be played, and the next day 16, and then 8... Okay? We would have to add 64+32+16+8+4+2+1.

What is 1? The final match. Do you follow him? Well then. That sum could be made. Now I will show you what mathematics can provide. This is also doing mathematics. But now I ask you this: how many matches will the 128 participants lose except the champion? Everyone else, how many games will they lose? One. To lose they have to have played, they cannot lose without playing. How many matches did the participants have to lose to save the champion? How many games were lost? The other 127 participants, who are not champions, must have lost, right? So how many games were played?

Without doing any calculations; 127! The only one who didn't lose is the champion. Everyone else lost one. Do you agree? Developing a strategy of this type is doing mathematics. Only they don't tell us this. Now, if one has 2.5 billion participants, how many games will be played? The calculation could be done again. 2.5 billion divided by two, and everything. (Laughter) But now we won't do it anymore. And looking for these types of patterns is doing mathematics. What's more, I would really like you to take it with you after this talk. If you stopped a person on the street and asked him, "What does a mathematician do?" "What does a PhD in Mathematics do?" "They do calculations." (Laughs) "Very fast." (Laughter) "Really big calculations, sir." "I've seen them." No.

There is this idea that mathematicians do something that we don't do, that we are not even good at... I would be an idiot if I did calculations, having computers and calculators. Why should I do them? And although I look old - and I am 65 years old, but not 400 - when I was born there was no television, but when I was a child my father told me that the wise men were the ones who knew many things and about many things. And I guess I imagined them in another stratosphere. What did these guys know? That led us all to an encyclopedist culture.

The person who "knows more" is always better. What is "know more"? What do I have to know? I search for it on Google. What you have to have is creativity. What we should ban in schools is the word "no." What they write in red,"wrong." What is wrong"? Can we have "wrong" in mathematics? Scientists never publish their errors. They never publish what is wrong. They publish the result, the last step. And all the steps in between? But do you know what the real problem? Society always looks for the person who comes first, who runs the fastest, who jumps the highest.

Who is the best? And the one who comes second, tenth, fifth, 143? ?We cannot establish rules for a small group of people. We are looking for the child prodigy. The privileged child. We need to be generous in distributing knowledge. If someone knows something, they have to share it. the myth that someone who did something is better than someone who didn't. They are neither better nor worse. Let's all learn from everyone. So mathematics also offers a branch called game theory. his life. Adults too. In fact, this is what he was talking about when he talked about how to cut a cake.

That's part of game theory. Trying to understand human behavior. I could show you how we can prove that there are two people in Buenos Aires with the exact number of hairs on their heads. One more time. The word "head", yes, but I understand "hairs". And let's exclude bald people, who have no hair. See how mathematics can come to our rescue in this question. How can you prove that at least two people in Buenos Aires have the same number of hairs? How can this be done? I will give you the answer. Do you know how many hairs a person has on their head, more or less?

If we stretched the scalp -- don't try this at home today -- (Laughter) I didn't mean that, but if we could, we would see that a person with 200,000 hairs is a guy who has hair. growing from everywhere. We have less than 200,000 hairs. Question: if one cannot have 200,000 hairs, does that show that there have to be at least two people in Buenos Aires with the same number of hairs? Because? Because suppose how many people are there in Buenos Aires? More than 2 million people? If everyone had a different number of hairs, there would be people with hair like that.

There would be one with 2 million hairs, I don't know what it would be like. So, it inevitably has to be repeated. Mathematics says, "Keep looking, because you will find them." It doesn't say which ones, but there are. So, as for today, I hope to see when programming is taught in schools, both primary and secondary, because programming is the language of the 21st century. In my time, to be literate it was enough to know how to read and write. Nowadays, reading and writing is the minimum you can aspire to. We need to have at least another language to communicate, and the programming language.

Otherwise, they are teaching you how to play a video game, but not how to modify it. I want to know how to read, but also write. And that is what programming allows. So, somehow, you young people need to motivate them, learn to say "I don't know." What's wrong with saying "I don't know", "I don't understand", "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 mathematics. We need to show it so someone sees it.

We need to break with this notion: "Not me, I have nothing to do with mathematics. I don't understand anything! My son does, he knows the 15 multiplication table." I suggest you do the following: keep in mind that value comes from creativity, from learning to solve problems. At school they often teach us first how to solve a problem we don't have and then send us home to try to solve it. In life it is the other way around, 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 yourself a chance, give mathematics the following alternative: do not enter through that door, that door is useless, that is clear, there is no need to diagnose it further.

We know, let's stop saying "we have failed." Let's give it another chance. Because football and life are also like magic and police stories: there are many things to do and you are the ones who have to achieve them. Thank you. (Applause)