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Science in English, 04a. The search for answers and the romance of maths.Cédric Villani Part 1/2.

04a. The search for answers and the romance of maths.Cédric Villani Part 1/2.

Hello everybody. So, let me introduce me.

(Laughter)

I am a French mathematician, as was said. French, probably you have ideas about what this means: good food, great literature, cute girls, of course, all that is true. I believe that I need my crispy baguette, good cheese, raw milk to be happy in my daily life.

But it is less known that France is also a great country for science and in particular mathematics, and has been so for hundreds of years. As I was a high school student, shy, kind of nerdy, I went through this very elitist French system of preparatory classes and grandes écoles inherited from Napoleon.

I attended courses in École Normale Supérieure in Paris. It is the institution that claims the most Fields Medalists among its former students, more than any other institution in the world.

Last year my name was added to the list, and that was it. When you receive such an award of course you are full with joy and pride but also with a bit of terror like all of a sudden you become a spokesperson for your field and you will meet many people who will like to hear you talk about what you do.

So you meet everybody, you meet CEOs, you meet politicians, you meet kids in high schools, you meet musicians, you go in public newspapers, everybody sees you in the street. I even made my way to fashion magazines.

(Laughter)

You know, these French people, they like fashion. Ok. So I met everybody, from garbage men to presidents of republics, and all of them, they wanted me to talk about science and mathematicians. It is maybe a surprise for some people in the audience that there is a job called mathematician, what the hell is this?

Do they exist? What do they do? Compute? No, mathematics is not about figures. It is a job, a damned good job, (Laughter) and in fact when the very serious Wall Street Journal had the weird idea to rank all jobs in the world, guess what came first? Was it princess? Or lawyer? Or trader? No, my friends, it was mathematician.

(Laughter)

Well, I hate rankings but, well, knowing they are in the good direction, it's OK. Now, mathematician, these people define as somebody who applies mathematical theories and formulas to teach or solve problems in the business, educational or industrial climate.

To some extent this is fine but these guys forgot what for me is the most important: to create mathematics, to invent mathematics, to discover new mathematics. And that's my job. The world is full of mathematical problems that are still not solved.

Problems with numbers are the simplest to explain, there are problem about numbers that you can explain to eight year-old kids in a couple of minutes and though the smartest mathematician in the world would not be able to solve them.

My inspiration is not in numbers, it comes rather from physics. The world around us. It's so full of great problems, whenever you boil water, this is a problem, a mathematical problem that nobody has solved yet. Think about... in this room, there are all the particles of gas going around, the speech that I am making, waves of sound, the heat going on. Close your eyes for a second, maybe, and try to imagine the complexity of the surrounding gas, with its billions and billions of molecules going and bumping into each other and exchanges of energy all around your body and around you billions and billions of molecules.

This is crazy. The world is so difficult to understand. And still it is a marvel that Einstein was very surprised of, for instance, that the world in some sense can be explained and studied, thanks to mathematical formulas and physics. And it is our job, understanding the world with the help of mathematical formulas armed with only our logic.

Here are some of the objects we work with, take them as artistic objects if you want. Each of them for a mathematician's eyes stands for some natural feature. Here in blue you have the equation of fluids, incompressible fluids, all are equations.

Here the equation for gas, here the equation for plasmas and so on. And the first one on top, here, this is the Boltzmann equation, I made my PhD on this equation. When my adviser first wrote down the equation for me and told me: "You know, OK, we'll do this and this" and after a couple of years when you start to master the equation you even can do this: "Wait a minute! Am I going to spend two or three years of my life on this one-line damned equation? Aren't there better things to do?" And I did it and I loved it. (Laughter) Not only did I do it, but I spent ten years on the damned equation. (Laughter) And little by little I appreciated how rich it is, what beauty there is in it, what complexity of natural phenomena are hidden.

Many papers, many things that I still don't understand about this equation but some things I understood and this is part of what awarded me the Fields Medal. Boltzmann was a great scientist, this equation is from 140 years ago. He understood a concept that is universal deep and associated with the equation, the concept of Entropy.

Entropy is associated with uncertainty, disorder. When we look at some system and we can make some experiments like feeling the pressure with our hand, or something it always involves a great number of particles so we only have access to it in statistical sense, not the exact position of all the molecules. So there is a great deal of uncertainty, and Entropy captures this uncertainty, this disorder. Here is the formula of Entropy:

S=k.log W

This is me near the grave of Boltzmann in Vienna. I love this picture. It shows me like a heir of Boltzmann, thinking about his ideas you know there is communion throughout the centuries I worked at the same problem as he. And this formula is magical, I swear; when I met a stranger in this huge cemetery and I asked him if he knew about Boltzmann's grave the guy looked at me and said something like "S = k log W ..." like a secret, a secret password, you know for those who know.

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04a. The search for answers and the romance of maths.Cédric Villani Part 1/2. |||||||||Mathematik|Cédric Villani|Villani| 04a. Die Suche nach Antworten und die Romantik der Mathe.Cédric Villani Teil 1/2. 04a. The search for answers and the romance of maths.Cédric Villani Part 1/2. 04a. La búsqueda de respuestas y el romanticismo de las matemáticas.Cédric Villani Parte 1/2. 04a. La recherche de réponses et le romantisme des mathématiques.Cédric Villani Partie 1/2. 04a. La ricerca di risposte e il romanticismo della matematica.Cédric Villani Parte 1/2. 04a.答えの探求と数学のロマン.Cédric Villani Part 1/2. 04a. 해답 찾기와 수학의 낭만.세드릭 빌라니 파트 1/2. 04a. Poszukiwanie odpowiedzi i romans matematyki.Cédric Villani Część 1/2. 04a. A procura de respostas e o romance da matemática. Cédric Villani Parte 1/2. 04a. Поиск ответов и романтика математики.Седрик Виллани Часть 1/2. 04a. Cevap arayışı ve matematiğin romantizmi Cédric Villani Bölüm 1/2. 04a. Пошуки відповідей і романтика математики.Седрік Віллані Частина 1/2. 04a.寻找答案和数学的浪漫。Cédric Villani 第 1/2 部分。 04a.尋找答案和數學的浪漫。Cédric Villani 第 1/2 部分。

Hello everybody. So, let me introduce me.

(Laughter)

I am a French mathematician, as was said. French, probably you have ideas about what this means: good food, great literature, cute girls, of course, all that is true. |||||||||||||lindas||||||| I believe that I need my crispy baguette, good cheese, raw milk to be happy in my daily life. ||||||knusprig|Baguette||||||||||| Acredito que preciso da minha baguete crocante, queijo bom, leite cru para ser feliz no meu dia a dia.

But it is less known that France is also a great country for science and in particular mathematics, and has been so for hundreds of years. As I was a high school student, shy, kind of nerdy, I went through this very elitist French system of preparatory classes and grandes écoles inherited from Napoleon. ||||||||||||||||elitär||||vorbereitend|||große|Schulen|vererbt|| |||||||tímido|||empollón||||||elitista|||||||||heredado de||Napoleón Когда я был старшеклассником, застенчивым и ботанистым, я прошел через эту очень элитарную французскую систему подготовительных классов и grandes écoles, унаследованную от Наполеона. 当我还是一名高中生时,我很害羞,有点书呆子,我经历了这个非常精英的法国预备班制度,从拿破仑继承了格兰德·埃科莱斯。

I attended courses in École Normale Supérieure in Paris. ||||Schule|normale|Hochschule|| Frequentei cursos na École Normale Supérieure em Paris. It is the institution that claims the most Fields Medalists among its former students, more than any other institution in the world. |||||||||Medailleträger|||||||||||| |||||afirma tener|||Medallas Fields||||||||||||| Это учебное заведение, получившее наибольшее количество медалистов Филдса среди своих бывших студентов, больше, чем любое другое учебное заведение в мире.

Last year my name was added to the list, and that was it. When you receive such an award of course you are full with joy and pride but also with a bit of terror like all of a sudden you become a spokesperson for your field and you will meet many people who will like to hear you talk about what you do. ||||||||||||||||||||||||||||||Gesicht der Branche|||||||||||||||||||| ||||||||||||||||||||||||||||||portavoz|||||||||||||||||||| Quando você recebe tal prêmio, é claro, você fica cheio de alegria e orgulho, mas também com um pouco de terror, como se de repente você se tornasse um porta-voz do seu campo e conhecesse muitas pessoas que gostariam de ouvi-lo falar sobre o que você Faz. Когда вы получаете такую награду, конечно, вы полны радости и гордости, но также и немного ужаса, как будто вы внезапно становитесь представителем своей области, и вы встретите много людей, которые захотят услышать, как вы говорите о том, что вы делать.

So you meet everybody, you meet CEOs, you meet politicians, you meet kids in high schools, you meet musicians, you go in public newspapers, everybody sees you in the street. Итак, вы встречаетесь со всеми, вы встречаетесь с генеральными директорами, вы встречаете политиков, вы встречаете детей в старших классах, вы встречаете музыкантов, вы ходите в публичные газеты, все видят вас на улице. I even made my way to fashion magazines. Eu até fiz meu caminho para revistas de moda. Я даже заходила в модные журналы.

(Laughter)

You know, these French people, they like fashion. Ok. So I met everybody, from garbage men to presidents of republics, and all of them, they wanted me to talk about science and mathematicians. ||||||||Präsidenten||||||||||||||| Então eu conheci todo mundo, de lixeiros a presidentes de repúblicas, e todos eles queriam que eu falasse sobre ciência e matemática. Я познакомился со всеми, от мусорщиков до президентов республик, и все они хотели, чтобы я говорил о науке и математиках. It is maybe a surprise for some people in the audience that there is a job called mathematician, what the hell is this? Talvez seja uma surpresa para algumas pessoas na platéia que exista um trabalho chamado matemático, que diabos é isso? Возможно, для некоторых из аудитории будет сюрпризом, что есть работа под названием «математик», что это, черт возьми?

Do they exist? What do they do? Compute? No, mathematics is not about figures. Нет, математика - это не цифры. It is a job, a damned good job, (Laughter) and in fact when the very serious Wall Street Journal had the weird idea to rank all jobs in the world, guess what came first? É um trabalho, um trabalho danado de bom, (Risos) e, de fato, quando o muito sério Wall Street Journal teve a estranha ideia de classificar todos os empregos do mundo, adivinhem o que veio primeiro? 这是一份工作,一份该死的好工作,(笑声),实际上,当非常认真的《华尔街日报》提出了对世界上所有工作进行排名的怪异想法时,你猜首先是什么? Was it princess? ||Prinzessin Or lawyer? Or trader? |Händler No, my friends, it was mathematician.

(Laughter)

Well, I hate rankings but, well, knowing they are in the good direction, it's OK. |||Ranglisten||||||||||| 好吧,我讨厌排名,但是,知道他们的发展方向不错,就可以了。 Now, mathematician, these people define as somebody who applies mathematical theories and formulas to teach or solve problems in the business, educational or industrial climate.

To some extent this is fine but these guys forgot what for me is the most important: to create mathematics, to invent mathematics, to discover new mathematics. В какой-то степени это нормально, но эти ребята забыли, что для меня самое важное: создавать математику, изобретать математику, открывать новую математику. And that's my job. The world is full of mathematical problems that are still not solved.

Problems with numbers are the simplest to explain, there are problem about numbers that you can explain to eight year-old kids in a couple of minutes and though the smartest mathematician in the world would not be able to solve them. Проблемы с числами объяснить проще всего, есть проблемы с числами, которые можно объяснить восьмилетним детям за пару минут, хотя самый умный математик в мире не сможет их решить.

My inspiration is not in numbers, it comes rather from physics. Меня вдохновляют не числа, а физика. 我的灵感不是来自数字,而是来自物理学。 The world around us. It's so full of great problems, whenever you boil water, this is a problem, a mathematical problem that nobody has solved yet. Здесь так полно великих проблем, что всякий раз, когда вы кипятите воду, это проблема, математическая проблема, которую еще никто не решил. Think about... in this room, there are all the particles of gas going around, the speech that I am making, waves of sound, the heat going on. Подумайте ... в этой комнате вращаются все частицы газа, речь, которую я говорю, звуковые волны, тепло. 想想...在这个房间里,到处都是气体的微粒,我在说的话,声音的波动,以及不断散发的热量。 Close your eyes for a second, maybe, and try to imagine the complexity of the surrounding gas, with its billions and billions of molecules going and bumping into each other and exchanges of energy all around your body and around you billions and billions of molecules. |||||||||||||||||||||||||||||||Austausch|||||||||||||| Feche os olhos por um segundo, talvez, e tente imaginar a complexidade do gás ao seu redor, com seus bilhões e bilhões de moléculas colidindo umas com as outras e trocas de energia ao redor de seu corpo e bilhões e bilhões de moléculas ao seu redor. Может быть, закройте глаза на секунду и попытайтесь представить себе сложность окружающего газа с его миллиардами и миллиардами молекул, которые сталкиваются и сталкиваются друг с другом, и обмениваются энергией вокруг вашего тела и вокруг вас с миллиардами и миллиардами молекул. 也许闭上你的眼睛一秒钟,然后试着想象一下周围气体的复杂性,数十亿个分子相互碰撞,相互碰撞,能量在身体周围以及数十亿个分子之间交换。

This is crazy. The world is so difficult to understand. And still it is a marvel that Einstein was very surprised of, for instance, that the world in some sense can be explained and studied, thanks to mathematical formulas and physics. E ainda é uma maravilha que Einstein tenha ficado muito surpreso de, por exemplo, que o mundo em certo sentido possa ser explicado e estudado, graças a fórmulas matemáticas e físicas. И все же это чудо, чему Эйнштейн был очень удивлен, например, что мир в некотором смысле можно объяснить и изучить с помощью математических формул и физики. And it is our job, understanding the world with the help of mathematical formulas armed with only our logic. И это наша работа - понимать мир с помощью математических формул, вооруженных только нашей логикой.

Here are some of the objects we work with, take them as artistic objects if you want. Вот некоторые из предметов, с которыми мы работаем, примите их как художественные объекты, если хотите. Each of them for a mathematician's eyes stands for some natural feature. |||||Mathematikers|||||| Cada um deles para os olhos de um matemático representa alguma característica natural. Каждая из них для математика обозначает какую-то естественную особенность. Here in blue you have the equation of fluids, incompressible fluids, all are equations. |||||||||inkompressible|||| Здесь, выделенное синим цветом, у вас есть уравнения жидкостей, несжимаемых жидкостей, все это уравнения.

Here the equation for gas, here the equation for plasmas and so on. And the first one on top, here, this is the Boltzmann equation, I made my PhD on this equation. ||||||||||Boltzmann|||||||| When my adviser first wrote down the equation for me and told me: "You know, OK, we'll do this and this" and after a couple of years when you start to master the equation you even can do this: Когда мой советник впервые записал для меня уравнение и сказал мне: «Знаешь, хорошо, мы сделаем то и это», и через пару лет, когда вы начнете осваивать уравнение, вы даже сможете сделать это: "Wait a minute! Am I going to spend two or three years of my life on this one-line damned equation? Собираюсь ли я потратить два или три года своей жизни на это проклятое уравнение, состоящее из одной строки? Aren't there better things to do?" Não há coisas melhores para fazer?" Разве нет дела поинтереснее? " And I did it and I loved it. E eu fiz e adorei. (Laughter) Not only did I do it, but I spent ten years on the damned equation. (Смех) Я не только сделал это, но и потратил десять лет на проклятое уравнение. (Laughter) And little by little I appreciated how rich it is, what beauty there is in it, what complexity of natural phenomena are hidden. (Смех) И постепенно я осознал, насколько он богат, какая в нем красота, какая сложность скрытых природных явлений. (笑声)我一点一点地欣赏了它的丰富,里面有什么美,隐藏了什么自然现象的复杂性。

Many papers, many things that I still don't understand about this equation but some things I understood and this is part of what awarded me the Fields Medal. |||||||||||||||||||||||verliehen|||| Boltzmann was a great scientist, this equation is from 140 years ago. He understood a concept that is universal deep and associated with the equation, the concept of Entropy. Он понял универсальную глубокую концепцию, связанную с уравнением, концепцию энтропии.

Entropy is associated with uncertainty, disorder. Энтропия связана с неопределенностью, беспорядком. When we look at some system and we can make some experiments like feeling the pressure with our hand, or something it always involves a great number of particles so we only have access to it in statistical sense, not the exact position of all the molecules. |||||||||||||||||||||||||||||||||||||statistisch||||||||| Когда мы смотрим на какую-то систему и можем провести некоторые эксперименты, например, почувствовать давление рукой или что-то еще, это всегда связано с большим количеством частиц, поэтому мы имеем доступ к ней только в статистическом смысле, а не к точному положению всех молекул. 当我们查看某个系统时,我们可以进行一些实验,例如用手感觉压力,或者它总是涉及大量粒子,因此我们只能从统计学的角度访问它,而不能获得所有分子的确切位置。 So there is a great deal of uncertainty, and Entropy captures this uncertainty, this disorder. 因此存在很大的不确定性,而熵捕获了这种不确定性,即无序。 Here is the formula of Entropy:

S=k.log W |||Wahrscheinlichkeit S=k.log W

This is me near the grave of Boltzmann in Vienna. Este sou eu perto do túmulo de Boltzmann em Viena. Это я возле могилы Больцмана в Вене. 这就是我在维也纳玻尔兹曼(Boltzmann)坟墓附近的地方。 I love this picture. It shows me like a heir of Boltzmann, thinking about his ideas you know there is communion throughout the centuries I worked at the same problem as he. Это показывает меня, как наследника Больцмана, размышляющего о его идеях, вы знаете, что есть общение на протяжении веков, я работал над той же проблемой, что и он. 它向我展示了一个像玻尔兹曼的继承人,思考他的想法,您知道我在与他相同的问题上工作了多个世纪以来一直有交流。 And this formula is magical, I swear; when I met a stranger in this huge cemetery and I asked him if he knew about Boltzmann's grave the guy looked at me and said something like "S = k log W ..." like a secret, a secret password, you know for those who know. ||||||||||||||||||||||||Boltzmanns||||||||||||||||||||geheime Formel|||||| E essa fórmula é mágica, juro; quando eu encontrei um estranho neste enorme cemitério e perguntei se ele sabia sobre o túmulo de Boltzmann o cara olhou para mim e disse algo como "S = k log W ..." como um segredo, uma senha secreta, você sabe para aqueles quem sabe. И эта формула волшебна, клянусь; когда я встретил незнакомца на этом огромном кладбище, и я спросил его, знает ли он о могиле Больцмана, парень посмотрел на меня и сказал что-то вроде «S = k log W ...» как секрет, секретный пароль, вы знаете для тех кто знает.