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Science in English, 05b. What's so sexy about math? Cédric Villani. Part 2/2.

05b. What's so sexy about math? Cédric Villani. Part 2/2.

{Video: 08:12}

OK, that was easy, but now what about if you have a big bunch of people who will testify? And this graph, I may think of it as all people who testify in a complicated crime case, but it may just as well be web pages pointing to each other, referring to each other for contents. Which ones are the most authoritative? Not so clear. Enter PageRank, one of the early cornerstones of Google.

This algorithm uses the laws of mathematical randomness to determine automatically the most relevant web pages, in the same way as we used randomness in the Galton Board experiment. So let's send into this graph a bunch of tiny, digital marbles and let them go randomly through the graph. Each time they arrive at some site, they will go out through some link chosen at random to the next one. And again, and again, and again. And with small, growing piles, we'll keep the record of how many times each site has been visited by these digital marbles. Here we go. Randomness, randomness. And from time to time, also let's make jumps completely randomly to increase the fun. And look at this: from the chaos will emerge the solution. The highest piles correspond to those sites which somehow are better connected than the others, more pointed at than the others. And here we see clearly which are the web pages we want to first try.

Once again, the solution emerges from the randomness. Of course, since that time, Google has come up with much more sophisticated algorithms, but already this was beautiful. And still, just one problem in a million.

With the advent of digital area, more and more problems lend themselves to mathematical analysis, making the job of mathematician a more and more useful one, to the extent that a few years ago, it was ranked number one among hundreds of jobs in a study about the best and worst jobs published by the Wall Street Journal in 2009.

Mathematician -- best job in the world. That's because of the applications: communication theory, information theory, game theory, compressed sensing, machine learning, graph analysis, harmonic analysis. And why not stochastic processes, linear programming, or fluid simulation?

Each of these fields have monster industrial applications. And through them, there is big money in mathematics. And let me concede that when it comes to making money from the math, the Americans are by a long shot the world champions, with clever, emblematic billionaires and amazing, giant companies, all resting, ultimately, on good algorithm.

Now with all this beauty, usefulness and wealth, mathematics does look more sexy. But don't you think that the life a mathematical researcher is an easy one. It is filled with perplexity, frustration, a desperate fight for understanding.

Let me evoke for you one of the most striking days in my mathematician's life. Or should I say, one of the most striking nights. At that time, I was staying at the Institute for Advanced Studies in Princeton -- for many years, the home of Albert Einstein and arguably the most holy place for mathematical research in the world.

And that night I was working and working on an elusive proof, which was incomplete. It was all about understanding the paradoxical stability property of plasmas, which are a crowd of electrons. In the perfect world of plasma, there are no collisions and no friction to provide the stability like we are used to.

But still, if you slightly perturb a plasma equilibrium, you will find that the resulting electric shield spontaneously vanishes, or damps out, as if by some mysterious friction force.

This paradoxical effect, called the Landau damping, is one of the most important in plasma physics, and it was discovered through mathematical ideas.

But still, a full mathematical understanding of this phenomenon was missing. And together with my former student and main collaborator Clément Mouhot, in Paris at the time, we had been working for months and months on such a proof. Actually, I had already announced by mistake that we could solve it. But the truth is, the proof was just not working. In spite of more than 100 pages of complicated, mathematical arguments, and a bunch discoveries, and huge calculation, it was not working.

And that night in Princeton, a certain gap in the chain of arguments was driving me crazy. I was putting in there all my energy and experience and tricks, and still nothing was working. 1 a.m., 2 a.m., 3 a.m., not working. Around 4 a.m., I go to bed in low spirits. Then a few hours later, waking up and go, "Ah, it's time to get the kids to school" What is this? There was this voice in my head, I swear. "Take the second term to the other side, Fourier transform and invert in L2." (Laughter)

Damn it, that was the start of the solution! You see, I thought I had taken some rest, but really my brain had continued to work on it.

In those moments, you don't think of your career or your colleagues, it's just a complete battle between the problem and you. That being said, it does not harm when you do get a promotion in reward for your hard work. And after we completed our huge analysis of the Landau damping, I was lucky enough to get the most coveted Fields Medal from the hands of the President of India, in Hyderabad on 19 August, 2010 -- an honor that mathematicians never dare to dream, a day that I will remember until I live.

What do you think, on such an occasion? Pride, yes? And gratitude to the man collaborators who made this possible. And because it was a collective adventure, you need to share it, not just with your collaborators. I believe that everybody can appreciate the thrill of mathematical research, and share the passionate stories of humans and ideas behind it. And I've been working with my staff at Institut Henri Poincaré, together with partners and artists of mathematical communication worldwide, so that we can found our own, very special museum of mathematics there. So in a few years, when you come to Paris, after tasting the great, crispy baguette and macaroon, please come and visit us at Institut Henri Poincaré, and share the mathematical dream with us.

Thank you.

(Applause)

Thank you.

(Applause)


05b. What's so sexy about math? Cédric Villani. Part 2/2. 05b. Was ist so sexy an Mathe? Cédric Villani. Teil 2/2. 05b. Τι είναι τόσο σέξι στα μαθηματικά; Cédric Villani. Μέρος 2/2. 05b. What's so sexy about math? Cédric Villani. Part 2/2. 05b. ¿Qué tienen de sexy las matemáticas? Cédric Villani. Parte 2/2. 05b. Qu'y a-t-il de si sexy dans les maths ? Cédric Villani. Partie 2/2. 05b. Cosa c'è di così sexy nella matematica? Cédric Villani. Parte 2/2. 05b.数学の何がそんなにセクシーなのか？セドリック・ヴィラーニパート2/2 05b. 수학의 매력은 무엇일까요? 세드릭 빌라니. 파트 2/2. 05b. Co jest takiego seksownego w matematyce? Cédric Villani. Część 2/2. 05b. O que há de tão sexy na matemática? Cédric Villani. Parte 2/2. 05b. Что такого сексуального в математике? Седрик Виллани. Часть 2/2. 05b. Matematiğin nesi bu kadar seksi? Cédric Villani. Bölüm 2/2. 05b. Що такого сексуального в математиці? Седрік Віллані. Частина 2/2. 05b.数学有什么性感的？塞德里克·维拉尼。第 2/2 部分。 05b.數學有什麼性感的？塞德里克·維拉尼。第 2/2 部分。

{Video: 08:12}

OK, that was easy, but now what about if you have a big bunch of people who will testify? OK, isso foi fácil, mas agora e se você tiver um monte de gente que vai testemunhar? Гаразд, це було легко, але що робити, якщо у вас є велика група людей, які будуть давати свідчення? And this graph, I may think of it as all people who testify in a complicated crime case, but it may just as well be web pages pointing to each other, referring to each other for contents. E este gráfico, posso pensar nele como todas as pessoas que testemunham em um caso de crime complicado, mas também pode ser páginas da web apontando umas para as outras, referindo-se umas às outras por conteúdo. І цей графік, я можу думати про нього як про всіх людей, які дають свідчення у складній кримінальній справі, але з таким же успіхом це можуть бути веб-сторінки, які вказують одна на одну, посилаючись одна на одну за змістом. Which ones are the most authoritative? Not so clear. Не все так однозначно. Enter PageRank, one of the early cornerstones of Google.

This algorithm uses the laws of mathematical randomness to determine automatically the most relevant web pages, in the same way as we used randomness in the Galton Board experiment. So let's send into this graph a bunch of tiny, digital marbles and let them go randomly through the graph. Então, vamos enviar para este gráfico um monte de bolinhas de gude digitais minúsculas e deixá-las passar aleatoriamente pelo gráfico. Each time they arrive at some site, they will go out through some link chosen at random to the next one. Кожного разу, коли вони потрапляють на якийсь сайт, вони виходять через випадково вибране посилання на наступний сайт. And again, and again, and again. And with small, growing piles, we'll keep the record of how many times each site has been visited by these digital marbles. E com pilhas pequenas e crescentes, manteremos o registro de quantas vezes cada local foi visitado por essas bolinhas digitais. І за допомогою невеликих, зростаючих купок ми будемо вести облік того, скільки разів кожен сайт відвідали ці цифрові кульки. Here we go. Randomness, randomness. And from time to time, also let's make jumps completely randomly to increase the fun. І час від часу давайте також робити стрибки абсолютно випадковим чином, щоб збільшити задоволення. And look at this: from the chaos will emerge the solution. The highest piles correspond to those sites which somehow are better connected than the others, more pointed at than the others. Найвищі палі відповідають тим ділянкам, які якимось чином краще пов'язані з іншими, більш націлені на них, ніж інші. And here we see clearly which are the web pages we want to first try. І тут ми чітко бачимо, які веб-сторінки ми хочемо спробувати в першу чергу.

Once again, the solution emerges from the randomness. І знову рішення з'являється з випадковості. Of course, since that time, Google has come up with much more sophisticated algorithms, but already this was beautiful. Звичайно, з того часу Google придумав набагато складніші алгоритми, але вже це було прекрасно. And still, just one problem in a million. І все ж, це лише одна проблема на мільйон.

With the advent of digital area, more and more problems lend themselves to mathematical analysis, making the job of mathematician a more and more useful one, to the extent that a few years ago, it was ranked number one among hundreds of jobs in a study about the best and worst jobs published by the Wall Street Journal in 2009. З появою цифрової сфери все більше проблем піддаються математичному аналізу, що робить роботу математика все більш корисною, аж до того, що кілька років тому вона посіла перше місце серед сотень професій у дослідженні про найкращі та найгірші професії, опублікованому Wall Street Journal у 2009 році.

Mathematician -- best job in the world. That's because of the applications: communication theory, information theory, game theory, compressed sensing, machine learning, graph analysis, harmonic analysis. Це пов'язано із застосуваннями: теорія зв'язку, теорія інформації, теорія ігор, стиснене зондування, машинне навчання, аналіз графів, гармонійний аналіз. And why not stochastic processes, linear programming, or fluid simulation? А чому не стохастичні процеси, лінійне програмування чи моделювання рідини?

Each of these fields have monster industrial applications. Кожна з цих галузей має величезне промислове застосування. And through them, there is big money in mathematics. А через них у математику приходять великі гроші. And let me concede that when it comes to making money from the math, the Americans are by a long shot the world champions, with clever, emblematic billionaires and amazing, giant companies, all resting, ultimately, on good algorithm. І дозвольте мені визнати, що коли справа доходить до заробляння грошей на математиці, американці з великим відривом є чемпіонами світу, з розумними, символічними мільярдерами та дивовижними, гігантськими компаніями, які, в кінцевому рахунку, базуються на хорошому алгоритмі. 让我承认，从数学上赚钱时，美国人遥遥领先于世界冠军，他们拥有聪明的，象征性的亿万富翁和令人惊叹的巨型公司，所有这些最终都取决于良好的算法。

Now with all this beauty, usefulness and wealth, mathematics does look more sexy. Тепер, з усією цією красою, корисністю та багатством, математика виглядає більш сексуальною. But don't you think that the life a mathematical researcher is an easy one. Але вам не здається, що життя математика-дослідника легке. It is filled with perplexity, frustration, a desperate fight for understanding. Вона сповнена розгубленості, розчарування, відчайдушної боротьби за розуміння.

Let me evoke for you one of the most striking days in my mathematician's life. Deixe-me evocar para você um dos dias mais marcantes da vida do meu matemático. 让我为您唤起我数学家一生中最惊人的日子之一。 Or should I say, one of the most striking nights. Ou devo dizer, uma das noites mais marcantes. Або, краще сказати, одна з найяскравіших ночей. At that time, I was staying at the Institute for Advanced Studies in Princeton -- for many years, the home of Albert Einstein and arguably the most holy place for mathematical research in the world. Naquela época, eu estava hospedado no Instituto de Estudos Avançados em Princeton - por muitos anos, a casa de Albert Einstein e sem dúvida o lugar mais sagrado para a pesquisa matemática do mundo. У той час я перебував в Інституті перспективних досліджень у Прінстоні - протягом багатьох років це був дім Альберта Ейнштейна і, можливо, найсвятіше місце для математичних досліджень у світі.

And that night I was working and working on an elusive proof, which was incomplete. E naquela noite eu estava trabalhando e trabalhando em uma prova indescritível, que estava incompleta. І тієї ночі я працював і працював над невловимим доказом, який був неповним. It was all about understanding the paradoxical stability property of plasmas, which are a crowd of electrons. Tratava-se de entender a propriedade paradoxal de estabilidade dos plasmas, que são uma multidão de elétrons. Йшлося про розуміння парадоксальної властивості стабільності плазми, яка є натовпом електронів. 这完全是为了理解等离子体的矛盾性，该等离子体是一群电子。 In the perfect world of plasma, there are no collisions and no friction to provide the stability like we are used to. В ідеальному світі плазми немає зіткнень і тертя, які б забезпечували звичну для нас стабільність.

But still, if you slightly perturb a plasma equilibrium, you will find that the resulting electric shield spontaneously vanishes, or damps out, as if by some mysterious friction force. Mas ainda assim, se você perturbar ligeiramente o equilíbrio do plasma, descobrirá que o escudo elétrico resultante desaparece espontaneamente, ou amortece, como se por alguma misteriosa força de atrito. Але все ж, якщо ви трохи порушите рівновагу плазми, ви побачите, що електричний екран спонтанно зникає, або загасає, немов під дією якоїсь таємничої сили тертя. 但是，即使您稍稍扰动等离子体平衡，您也会发现生成的电屏蔽会自发消失或衰减，就像受到某种神秘的摩擦力一样。

This paradoxical effect, called the Landau damping, is one of the most important in plasma physics, and it was discovered through mathematical ideas. Esse efeito paradoxal, chamado de amortecimento de Landau, é um dos mais importantes da física dos plasmas e foi descoberto por meio de ideias matemáticas. Цей парадоксальний ефект, названий загасанням Ландау, є одним з найважливіших у фізиці плазми, і був відкритий завдяки математичним ідеям.

But still, a full mathematical understanding of this phenomenon was missing. Mas ainda faltava uma compreensão matemática completa desse fenômeno. Але повного математичного розуміння цього явища все ще бракувало. And together with my former student and main collaborator Clément Mouhot, in Paris at the time, we had been working for months and months on such a proof. E junto com meu ex-aluno e principal colaborador Clément Mouhot, na época em Paris, trabalhávamos meses e meses nessa prova. І разом з моїм колишнім студентом і головним співавтором Клеманом Мухо, який на той час перебував у Парижі, ми працювали над таким доказом місяцями і місяцями. Actually, I had already announced by mistake that we could solve it. Na verdade, eu já havia anunciado por engano que poderíamos resolvê-lo. Власне, я вже помилково оголосив, що ми можемо це вирішити. But the truth is, the proof was just not working. Але правда в тому, що докази просто не працювали. In spite of more than 100 pages of complicated, mathematical arguments, and a bunch discoveries, and huge calculation, it was not working. Apesar de mais de 100 páginas de argumentos matemáticos complicados e um monte de descobertas e cálculos enormes, não estava funcionando.

And that night in Princeton, a certain gap in the chain of arguments was driving me crazy. E naquela noite em Princeton, uma certa lacuna na cadeia de argumentos estava me deixando louco. 那天晚上在普林斯顿，争论的某些缝隙使我发疯。 I was putting in there all my energy and experience and tricks, and still nothing was working. Eu estava colocando toda a minha energia, experiência e truques, e ainda assim nada estava funcionando. Я вкладав туди всю свою енергію, досвід і хитрощі, і все одно нічого не виходило. 1 a.m., 2 a.m., 3 a.m., not working. Around 4 a.m., I go to bed in low spirits. Por volta das 4 da manhã, vou para a cama desanimado. Then a few hours later, waking up and go, "Ah, it's time to get the kids to school" What is this? Então, algumas horas depois, acordando e dizendo: "Ah, é hora de levar as crianças para a escola" O que é isso? А через кілька годин, прокинувшись, ви думаєте: "О, час збирати дітей до школи!" Що це таке? There was this voice in my head, I swear. Havia essa voz na minha cabeça, eu juro. "Take the second term to the other side, Fourier transform and invert in L2." "Leve o segundo termo para o outro lado, transforme Fourier e inverta em L2." "Перенесіть другий доданок на іншу сторону, перетворіть Фур'є та інвертуйте в L2". “将第二项带到另一端，在L2中进行傅立叶变换和求逆。” (Laughter) (Risada)

Damn it, that was the start of the solution! Droga, esse foi o começo da solução! You see, I thought I had taken some rest, but really my brain had continued to work on it. Você vê, eu pensei que tinha descansado um pouco, mas realmente meu cérebro continuou trabalhando nisso. 你看，我以为我已经休息了，但实际上我的大脑一直在继续努力。

In those moments, you don't think of your career or your colleagues, it's just a complete battle between the problem and you. 在那些时刻，您不会想到自己的职业或同事，这只是问题和您之间的一场完整的战斗。 That being said, it does not harm when you do get a promotion in reward for your hard work. Dito isto, não faz mal quando você recebe uma promoção em recompensa pelo seu trabalho duro. Тим не менш, не зашкодить, якщо ви отримаєте підвищення в якості винагороди за свою наполегливу працю. 话虽如此，当您的辛勤工作获得晋升奖励时，这并不会有害。 And after we completed our huge analysis of the Landau damping, I was lucky enough to get the most coveted Fields Medal from the hands of the President of India, in Hyderabad on 19 August, 2010 -- an honor that mathematicians never dare to dream, a day that I will remember until I live. E depois que concluímos nossa enorme análise do amortecimento de Landau, tive a sorte de receber a mais cobiçada Medalha Fields das mãos do Presidente da Índia, em Hyderabad, em 19 de agosto de 2010 - uma honra que os matemáticos nunca ousam sonhar, um dia que vou lembrar até viver. І після того, як ми завершили наш величезний аналіз загасання Ландау, мені пощастило отримати найбажанішу медаль Філдса з рук президента Індії в Хайдарабаді 19 серпня 2010 року - честь, про яку математики не сміють і мріяти, день, який я пам'ятатиму до кінця життя.

What do you think, on such an occasion? O que você acha, em tal ocasião? Pride, yes? Orgulho, sim? And gratitude to the man collaborators who made this possible. І вдячність чоловікам-колаборантам, які зробили це можливим. And because it was a collective adventure, you need to share it, not just with your collaborators. I believe that everybody can appreciate the thrill of mathematical research, and share the passionate stories of humans and ideas behind it. And I've been working with my staff at Institut Henri Poincaré, together with partners and artists of mathematical communication worldwide, so that we can found our own, very special museum of mathematics there. E tenho trabalhado com minha equipe no Institut Henri Poincaré, junto com parceiros e artistas da comunicação matemática em todo o mundo, para que possamos fundar nosso próprio museu de matemática muito especial lá. So in a few years, when you come to Paris, after tasting the great, crispy baguette and macaroon, please come and visit us at Institut Henri Poincaré, and share the mathematical dream with us. Assim, daqui a alguns anos, quando você vier a Paris, depois de provar a grande e crocante baguete e macaroon, venha nos visitar no Institut Henri Poincaré e compartilhe o sonho matemático conosco. Тож за кілька років, коли ви приїдете до Парижа, скуштувавши чудовий, хрусткий багет і макарон, будь ласка, завітайте до нас в Інститут Анрі Пуанкаре і поділіться з нами математичною мрією. 因此，几年后，当您来巴黎品尝美味脆皮的法式长棍面包和杏仁饼后，请到HenriPoincaré研究所参观我们，与我们分享数学梦想。

Thank you.

(Applause)

Thank you.

(Applause)