In January 2018, when I saw a familiar figure appearing on the team of French President Macron visiting China, dressed beautifully and with a retro look, I immediately recognized him as mathematician Cedric Villani.

In January 2018, when I saw a familiar figure appearing in the team of French President Macron visiting China, dressed beautifully and outstandingly retro, I immediately recognized him as the mathematician Cedric Verani . It turned out that he had already entered politics and became a member of parliament, and it might be more appropriate to call him "former mathematician". In 2016, when interviewing the Fields Award winner and French math star, what impressed me the most was of course his smart and elegant brain - no, it was actually his fashionable clothes . In a sense, his dress has become part of his personal symbols and has become an interface for him to communicate with the public.

Cedric Verani (left) and Macron (right)

"The best people learn mathematics"

has a few hours left before the agreed interview time, and Cedric Verani sent an email: "I We must rush back to our home in the Olympics (South Suburbs of Paris). Time is tight, can the interview be held in a taxi? After the interview with Le Monde, I went to Paris High Master to pick you up, and I will pass by a lot along the way I have a very important place for my math research career, and we can stop at these places. " "Is there any other choice?" I murmured in my heart and agreed.

A few hours later, Verani showed us an extremely busy image in the taxi window: the computer is placed on his knees, and his hands are tapping on it, while taking the time to free up one hand to hold the clip. The chin and the phone on the right shoulder were talking endlessly, while the other hand held the POS machine to pay the bill. The taxi parked in the middle of Yulem No. 45, which was parked on both sides of the street. The taxi behind were waiting patiently as if the French were queuing up in long queues. It seems that Villani hopes that his toes can come in handy. I have no doubt that he can really think about problems in a hurry. He won the mathematical theorem of Fields Medal many times he made breakthroughs on the way home from the museum or on the regional fast railway in Paris. As an analytical mathematician and expert in mathematical entropy, he mainly thinks about the problems of gas and plasma - a mathematical physics concept that reflects the degree of chaos in particle swarms, which has a thousand-fold relationship with probability, gas theory, plasma physics, galaxy dynamics, geometry, etc. A close connection. But after winning the award and becoming a public figure, what he thought might be different.

Paris High School Master graduate and mathematician Cedric Verani (photo by Yu Chuzhong)

got off the car and leaned against the gate from Paris High School Master (actually a small door, Going to a small room with a few square meters (about 10 meters away) about a corner of the wall, continue to call him to . We and his two black trolley boxes were hung on the edge of Yulem Street. He still had the iconic outfit that appeared frequently: the open black windbreaker showed the silver chain of the pocket watch, and the red tie (sometimes dark green); the weather was colder, and there were two royal blue and tender yellow with tassels on the outside. Knitted long scarf. Of course there are spider brooches on the chest - he collected a lot of spider jewelry from all over the world, some are African spiders made of carnation, and some are spiders with long green legs, which are said to symbolize hope. His charming dress style was formed during his student days at the High School in Paris. The dedicated mathematician has been wearing this eye-catchingly since he was 20 years old. Teachers and students kept coming in and out of the gate of the Paris Higher Teachers, and Verani remained calm. Until he put down the call and said to us, "At the Paris Higher Normal University, I spent 8 years of my most important study and research career. I got my PhD here and then worked as an assistant professor for a while." Then he pulled Get your luggage and take us to trot all the way down the streets of Yulem - as a French math star, he seems to be enjoying the fun of turning serious journalists into paparazzi.

passes through Yule m Street, which is Marie Curie Street. The Curie Institute, named after the French chemist Madame Curie who discovered polonium and radium, is located here, close to the biology department of the High Master.The two institutions have been neighbors on this street for more than 200 years, but there is a saying that people here pass by, but they have not spoken actively, until in recent years, universities are driven by the central administrative forces. Begin to merge. Verani turned into a door next to the Curie Institute and stood in front of the arch of a red brick building. This is the Poincaré research institute where he served as director at the time. This palace of mathematics and theoretical physics, founded in 1928, rescued the French mathematical community from the dilemma of isolation that year. Einstein once taught general relativity here, Volterra introduced biomathematical analysis to the French academic community here, and France's first statistical institute and the first computer development plan were also born here.

Poincaré Institute | wikicommon

Vilani has been running in these streets and alleys several times. In 2010, the Clay Mathematics Institute celebrated the Perelmann that finally solved the Poincaré conjecture. He ran from the Isle of St. Louis to this core area of ​​the fifth arrondissement of Paris, sweating all over and running. I was out of breath to catch up with the summary speech at the end of the report. That day, he was attending the funeral of his old friend, French mathematician Paul Mariavan. He gasped and told me that just before seeing us, he gave a math report to hundreds of people, gave a popular science class to the children, and conducted an interview in Le Monde. And those two suitcases have become his companionship for his life without touching the ground. I asked him if he enjoyed this kind of "celebrity" life. He stuck out his tongue mischievously and said naively and shyly: "I think it's quite interesting." "Interesting" is another mathematician's ambition: "A mathematician is not enough to be good at mathematical studies. Mathematical research requires many other skills. You must be very dedicated, constantly struggling, full of ambition, and you must also be good at communicating with others. ——Constant travel, constantly meet different people, constantly deal with them. In these gaps, you keep finding a balance between learning new things and trying new things. “

Get into a taxi, Villani finally has it Relax comfort. He told me that after winning the Fields Medal, people always wanted to hear a "divine" story in him where he decided to be a mathematician, but he was always disappointing. "I don't have the experience of God's enlightenment." "I never went to 'choose' to learn mathematics. In France, mathematics is highly valued. Usually, if your math is great, you end up in math research." Since elementary school, Verani has been very good at math. When he was a child, some teachers praised him as a "genius", but he didn't like this word very much. "There are many real geniuses in the history of mathematics: Gauss , Ramanujan , Riemann , etc. People often say that young people are 'geniuses', but who knows whether this teenager can have the future? What about making a career really happen? What's more, Americans like to praise everyone as geniuses! " He is more willing to attribute his mathematical achievements to the combination of personal efforts and the most stringent mathematical training in the French education system : "While the age of 17 to 19, I received very rigorous math training in the preparatory class near Paris and studied extremely hard. I was admitted to the Paris Higher Teacher from the preparatory class."

mathematician Gauss portrait | wikicommon

France's preparatory education is a very special level of French higher education and is a channel to enter the French "university". French preparatory courses are the most difficult and strictest examination-oriented and general education system in the world. French students must undergo rigorous training in calculus and linear algebra in preparatory schools to cope with exams that are as difficult as the "sophomore year". Only about 10% of the best middle school graduates have the opportunity to enter preparatory studies, and in the end, only a few percent of preparatory graduates can enter top "universities" such as Paris Higher Normal University and Paris Integrated Polytechnic. Compared with American students, French math skills are usually more solid and broad. American students can understand formulas and calculations, but French students understand the history behind formulas and calculations - usually what only exists in the footnotes of mathematics textbooks.This strict preparatory training and selection system is the most historically credible elite producer in France: Comprehensive science and engineering and senior teachers are not hiding, and the graduation colleges on the resume are like "identity seals" branded on their foreheads. France Most of the core positions of enterprises and governments are left to the best graduates in these schools.

When high school teachers were in school, Verani loved baking her proud Madeline cake for her neighbors in the dormitory, and liked to attend the dance party held in the historic building of 45 Yulem Street. "I was elected president of the Student Union in the third year of the High School Teachers. That year, my studies were not very good, social and organizational work took up a lot of time and energy, and I basically didn't do anything in mathematics." Teacher Gao's teacher still encouraged him: "You used to have good math grades, and we know you didn't work hard this year." The teacher also told him: "If you study hard, you can still get a doctorate degree and be an assistant professor. Since then I began to study hard again. "In the years of high school, he liked to walk in the dim corridor of the school at night, watching rays of light coming out from the doors, as if the cold light shone through the submarine portholes wave. Later at , when he was , he also saw the light coming out of the crack in the office of Jean Burgan, the most outstanding mathematical analyst, in the dark building late at night. Those who enjoy a high academic reputation work hard and eagerly.

The corridor in the teaching building of the High Teachers in Paris (photo by Yu Chuzhong)

Verani's doctoral supervisor is Pierre-Louis Lion, an expert in partial differential equations. 1994, Lion won the Fields Medal. "He was very powerful, he thought very fast, and he was extremely diligent," Verani recalled his mentor, "I thought, 'Ah, I can never be a world-class mathematician like him'." But as time passed, He became a Fields Medal winner without knowing it - winning the Fields Medal is so common in high school that it has become a secret ambition in everyone's heart. "The Higher Teacher put me in the tradition of French mathematics, in a historic system: almost all award-winning French mathematicians have studied at the Higher Teacher." "The French are not like Eastern European countries, Russia, Vietnam, and Chinese people like the Chinese. , he was good at Olympic mathematics competitions in high school. This competition is a special exercise, which is actually very different from the reality of mathematical research. When the French entered the preparatory class and senior teacher, a group of the best and energetic people Gathering together can create an atmosphere and create something great." Verani further explained that the tradition of French mathematics is - "very abstract. The French always ask some abstract questions, hoping to find Elegant beauty, Love the concept of universality and is passionate about topics that can influence everyone and the world. This abstract tradition of penetrates into various disciplines in France. Although it is difficult to define the 'style' of French mathematics, in the 19th century, France The influence of Germany is deeply rooted in each other. is a series of major discoveries in mathematics that define the identity and self-cognition of these two nations. ”

24, it was in the high-level teacher in Paris, Verani Working with Italian mathematician Giuseppe Toscani, he came up with the first important result of his mathematics career: the entropy increase of the Boltzmann equation, the Folk-Planck equation, and the entropy increase of the plasma contact. A year and a half later, he and German mathematician Felix Otto discovered the connection behind the inequality of Soberlev and the concentrated inequality of Taragran, and started an adventure in the field of optimal transportation. It was also in the High School Master that he completed his doctoral thesis. He said his doctoral dissertation benefited from four spiritual mentors: the mentor Pierre-Louis Lion, the study coach Jan Brennier, and Eric Karen and Michelle Ledu He had read a lot of the works of the latter two scholars, thus opening the door to the world of inequality. When he was defending his doctoral thesis, Yves Meyer, a teacher in the mathematics department of Higher Teachers, once said to him: "There are some magical relationships and identities in your doctoral thesis.If it were 20 years ago, people might not be concerned about this work, because no one believed in miracles at that time! "Only in the high-level teacher, you will be in a crowd with the wise vision to discover miracles and be encouraged by them.

Paris mathematician

0 The night before meeting Villani, a family called pho in the 13th district of Paris At the pho restaurant in 13, we chatted with a group of young people studying mathematics in Paris until late at night. The waiter's voice was as magical as a chattering parrot, and the pho noodles covered with 80% mature beef were served in bowls, steaming in a steaming heat. The young couple who were studying for a Ph.D. in Mathematics at the High School in Paris, Wang Hua and Liu Linyuan, had the simple expression that mathematicians often had. Wang Hua talked about the mathematicians in this city, and they almost knocked the chopsticks in Liu Linyuan's hand several times. Liu Linyuan ate pho quietly and echoed a few words in her mood.

The French are deeply proud of their cultural pride with a large number of mathematicians: Laplace , Lagrangian , Ferma , Fourier, Descartes , Poisson, Pascal, Galova , Poincaré, Joeldon, LeBerg ... These stars have become famous for their brilliant names. In the past, Moscow and Paris were two large cities where European mathematicians gathered, Gottingen Although It was also the center of mathematics and physics, but it was a small town with a population of 100,000. Today, Moscow's status as a mathematical metropolis has declined. The United States represented by Princeton and Berkeley, California has become the center of mathematics, but Paris The status of mathematics will remain stable.

"Paris" stills

At dinner that day, I remembered the Bourbaki school in a long list of mathematician names mentioned. A name closely linked to Paris and the Higher Teachers. Bourbac is a famous secret group of mathematicians active in southern Paris, with basically all members of the Higher Teachers. It was born when French mathematics began to decline and emerging mathematics branches flourished After World War II. In the book "Bulbaki's Career", French mathematician J. Dieudonne mentioned the mathematical education status of Paris Higher Teachers after World War I: "Open the student list of higher normal schools during the war When you are in trouble, you will find a huge fault, and two-thirds of the students have been destroyed by the war. This situation had catastrophic consequences for French mathematics. ”

Mathematics students who entered the high school after the war found that most of the young mathematicians who should have provided guidance for them had been destroyed by the war, and their influence was also wiped out. Although the remaining mathematicians are admired, they are all Nearly fifty, even older. These mathematicians are familiar with the mathematics they learned when they were 20 or 30, and only have a vague idea of ​​new mathematics. Diedone recalls that when he graduated from a high school , I just knew what a "group" is , and the algebraic knowledge he learned at the senior teacher does not exceed preparatory mathematics, determinants, solvability of equations and single-row curves.

In order to revive the French mathematical tradition, a group of young mathematicians from the senior teacher gathered together. They held discussion classes , the topics were the latest achievements in mathematics at that time; they also published papers and published books in the name of Bourbaki. Wang Hua talked about Bourbaki's anecdotes: "Anley Jiadang, who served as the director of the mathematics department of the senior teacher, once served as the head of the high-level mathematics department. (Henri Cartan), is the representative of the Bourbaki school. He once set up a position for the Burbakic School in the Higher Teachers. In recent years, they have become active again and often discuss issues in the form of quarrels. There is a saying that those who stand up very impolitely at math meetings and argue with people fiercely, are likely members of the Burbaki. "Bulbaki's seminar is still held in Paris, and Verani has participated. However, he refused to tell me if he is a member of Boulbaki, "because it is a secret organization, members cannot expose themselves."

Only big cities like Paris can produce such a gathering effect; here, mathematics is often not created by a single person alone, but by a group of people. The tradition of can be roughly back to the 17th century. French priest Mason.Pascal and his son attended the mathematics salon organized by Father Mason, living in remote mountainous areas, tight-lipped Ferma, and the secluded Descartes all kept in communication with him. The priest was keen on math, liked to travel and spread news, and arranged various mathematicians' gatherings regularly. This salon is the prototype of of the French Academy of Sciences. Today, the high-level master likes to describe Paris like this: "There is no secret in Paris." Verani also believes that "the era of "making great discoveries of mathematics alone like a knight or a hero may have passed." "However, sometimes there are still heroes who will fight alone, such as the Russian mathematician Perelman. He was born in the mathematical ecology of Russia and proved the Poincaré conjecture by himself. Andrew Wyer Si is also the one who absolutely fights alone to solve the Ferma theorem. "However, such "risk" is also regarded as a high-risk strategy. In order to keep it confidential, it is to not discuss or test with any mathematical colleagues before announcing the proof. The risk of any idea, at the cost of it, is that it is possible to make some fundamental mistakes in the end.

What makes me curious is why Paris, a city with glamor and colorful, can accommodate so many mathematicians? In my stereotype, mathematicians are a group of people who are out of place with "urban animals". They are immersed in the subtle world of mathematics, and the world is not their paradise. What's more, how can Paris's temptation and lifestyle in big cities make people focus on mathematics? Liu Linyuan told me that students in the mathematics department know an unwritten rule, that is, income after graduation is not positively correlated, or even negatively correlated. People entering the financial industry are often only those who are qualified in mathematical research, not the most outstanding; the more in-depth research in mathematical research, the higher the level, the less salary. Being a mathematician in Paris seems not easy.

After graduating from Velani, he worked as an assistant researcher in the senior high school teacher for several years. His life is relatively poor. He told me: "Hundreds of CDs almost embezzled all my salary when I was in the High Division in Paris." When asked him about the law that I had heard of "the level of mathematical research is negatively correlated with income", he sighed, "Oh! I hate being a financial analyst, boring job!" He enjoyed his career as a mathematician in Paris . "When doing PhD research, there were so many seminars and lectures in Paris to listen to, and it is still the richest place in the world's curriculum. Secret organizations like Bourbaki still exist, and they are still organizing seminars."

The mathematics courses of high-level teachers are very high-quality, but there are many things outside of mathematics that excite Verani. "It's very good in physics, chemistry, literature and philosophy, and I met a lot of people full of curiosity and passion. For me, the time of Gaoshi opened me up culturally. I often went to show, Watch movies, listen to concerts, for a while, I even went to the cinema every day. You know, Paris is the city of cinemas, and there are cinemas everywhere. Even if we can watch online movies today, Paris is still full of cinemas. I have a rich cultural experience. My favorite movie star at that time was Audrey Hepburn, and I also particularly like Russian director Andrei Tarkovsky . Japanese movies are also very popular in Paris, my university Times are accompanied by Akira Kurosawa's films. "In Paris, he has begun to carefully choose his own costumes. In addition to wearing suits, he also wore a hat for a long time.

Photo source wikipedia

In 2009, Verani spent 4 months at Princeton Institute of Advanced Studies. Princeton is very different from Paris. "In Princeton's quiet environment, you can focus on academic thinking without interruption, which is like an isolated monastery. But Paris is different, it keeps happening every day." Verani's description Princeton is closer to the academic wonderland in my heart. Everything else is perfect except for the ubiquitous Einstein watching the living from bronze statues, photos and oil paintings.

But Paris has its secret.The CDs that Verani bought marked the memories of many important moments in his mathematics career: at the age of 18, in the hall of , of the Paris Institute of Technology, he heard John Lennon's during the oral break of the entrance examination of the senior high school teacher. "Walrus"; at the age of 21, in the single dormitory of the High Master, he played Brahms' "The First Piano Concerto", and a young girl slapped his room hard; 1994, he listened to Mozart's every morning "Requiem" wakes up and prepares for the teacher qualification selection exam Exam - Exams that most senior teachers will face when they graduate; 1999 When he wrote his first book on optimal transport in Atlanta, Prokofiev's Second Symphony Four Movements made him cry; in the winter of 2003, when he was exploring the secrets of the subcompulsiveness in Reading, England, he was haunted by Mary Lafoley's Why These Clouds; in the winter of 2006, he wrote in Lyon During the days of Journal of the International Conference of Mathematicians, Juliet's "Mr. Venus".

In that book "The Birth of a Theorem", he wrote that in Princeton's independent courtyard wall, like von Neumann distributed the collected cocktails to everyone at the wild feast. , and people who occasionally play violin like Einstein and are versatile, gradually became the past of the 20th century. "Now, rational Apolloism has destroyed the romantic Dionysianism in the institute." Perhaps, in Paris, the ghost of Dionysia is still wandering in the streets and alleys.

Paris is essentially different from Beijing and New York. You can't imagine being a mathematician in Beijing or New York, but in Paris, it comes naturally. You can do what you like with the money you have to make a living. Although leftist political thoughts have been challenged by financial deficits and refugee issues, their impact on French society is far-reaching: from having children to going to college, ordinary people do not have any material concerns. Paris still maintains its heavy taxes, and it is still difficult for the rich to get rich, while ordinary people live comfortably and have extraordinary sympathy for refugees. What's more, in high school teachers, formal students sign student civil servant contracts. Not only do they not pay tuition fees, they also accept French government allowance. Liu Linyuan told me that Master Gao gave her enough money every month to her. "A free museum, free public cultural venue, a swimming club season ticket of 19 euros, and exaggerated medical benefits are enough to make people concentrate on mathematical research. ”. In Paris, anti-market thinking remains vital: Here, artists are likely to be reluctant to sell their highest-valued artworks, and bankers are likely to give up their posts and go to university to serve as a school band conductor.

Since the age of 26 and 27, Villani has been invited to at Berkeley, California and Stanford University. At the age of 30, invitations from the United States came one after another. He said that although he likes the United States, he "never considered living in the United States for a long time." When Princeton invited him to extend his visit to the Institute of Advanced Studies, he returned to France without hesitation to take office as director of the Poincaré Institute. He joked that he "can't imagine living in a country with poor bread quality for a long time." Love for desserts and cheeses, like the sustenance of nostalgia, has almost become the huge traction for Verani to return to France: crisp baguettes, soft boat-shaped biscuits, fruity Conte, soft feta cheese, aromatic Escarp Shurniac cheese, soft Bria-Savalanche, spicy olive oil... these are all things that cannot be found in the United States.

The exquisite bakery on the streets of Paris

What is deeper is the inner sense of belonging. He told me: "I am a person who lives in the French cultural atmosphere. French language, literature and history all form part of me. I love Hugo's novels--although his thinking is different from mathematicians; I also love Balzac - my colleague Lafurge, who is also a Fields Medal winner, is very obsessed with Balzac and has read all his works twice."He also likes Dumas' adventure novels, and also likes to improvise the "Korak Adventure Story" for his children that never ends: a little raven abandoned by his parents and the young owner Arthur, in search of a password, Go deep into the circus and the Arabian market and embark on a thrilling journey across France and Egypt . For Villani, mathematics is "an adventure." The word "adventure" also often appears in French philosophers In the long speech, this behavior contains heroism that inspires human noble emotions and strong spiritual experience.

"Decoding Mathematics" Stills

In today's mathematics department, some mathematics majors related to chemistry and physics have adopted English as the thesis language. But Verani told me that even so, students are still thinking in French, "at least I am." . French thinking is rooted in its complex and subtle language. Verani once conjectured that the reason why Hungarian can produce Erdesh , von Neumann, Feyer, Riz, Wei Gner, Zirat, Lax, Polya and many other great mathematicians are because "Hungarian requires listeners to focus on all the time. Idiot, before the last word pops up, I can never guess whether the meaning of the other party being said will be completely subverted." In the eyes of foreigners, French is also a strange language, especially in the expression of numbers. French numbers are not pure decimal , but a mixture of decimal, decimal and hexadecimal. Numbers within 100, 1 to 16 are hexadecimal, 17 to 69 are decimal, 70 to 79 is decimal, 16 is hexadecimal The mixture of the calculating and hexadecimal system, 80 to 99 is a mixture of decimal, hexadecimal and 20. This strange expression was formed in history and was France Part of the tradition. There is a joke about

. When a French man approaches, he will not ask for a woman's phone number, but will directly get to the point because it is too troublesome to ask for a number. For example, the number 176988472 will be pronounced as: 100 plus 60 Add 16, 4 20 plus 18, 4 20 plus 4, 60 plus 12. Enlightenment in this unique language environment, the way of thinking about the world is probably more complicated. Verani told me: "The French believe that there is a universal solution to any problem, believing in abstract and pure beauty. This is a very idealist country. Many Parisian mathematicians were invited to teach at American universities for a while and had a good salary, but they would still return to Paris in a few years. Top American universities like Princeton and MIT Although there are the best teachers in the world, it is difficult to cultivate great American mathematicians. Many of them are "foreign aids" from other countries. is different from the Americans using engineers to train mathematicians. For the French, Mathematics is an aesthetic pursuit.

The journey from the High Master

Entering the fan record that the High Master was built after the French Revolution The stone gate of the school history, passes through the corridor with an inquiry, push open the thick door, and then passes through the atrium where Ennest Pond is located, enters the corridor on the other side, and then enters another atrium, passing by one to the right The modern library, the Department of Mathematics is hidden deep in No. 45 Yulem Street. Here, today's senior teachers still believe that the theoretical research that mathematicians are persistent in may not be applied immediately, but will be in a long time. The historical time produces value; understanding and understanding the world is the first priority of mathematicians, not changing the world.

Paris High Teacher’s atrium garden, with the famous Ernst pond (Yu Chuzhong Photo)

20th century 56 After the 1900s, mathematicians' interests were more focused on classical and specific problems, and were not enthusiastic about the construction of large theoretical systems. Mathematical research tends to be more specialized, technical, and technical. The combination is also closer, and the application of mathematics is everywhere. But in high school teachers, doctoral students in the Department of Mathematics told me that the main motivation to promote everyone's research is "interest and taste" Although they are much more sensitive to the actual needs of the industry and business world than their predecessors, they are also better at using digital technology to communicate and share their ideas.The discovery process of mathematics is becoming more and more open. I asked Claude Viterbo, then director of the mathematics department, what are the unique features of mathematicians who graduated from high school? He replied: "Trial. They have an elegant taste in mathematics, which is constantly polished in subtleties. It depends on what kind of people you meet and what kind of people you communicate with."

dimension Rani is such a high-level teacher. Starting from No. 45 Yulem Street, he entered a world where the best mathematicians gathered. Three years after completing his doctoral defense, he and his collaborator Langlo de Villet discovered the connection between Cohen's inequality in elastic theory and the increase in entropy in Boltzmann's theory; he and Dario Cordero later - Alausgan and Bruno Nassaret together reveal the relationship between optimal transport and the Saubrev inequality; in 2004, he came to Berkeley as a visiting professor and met the future American collaborator John Lott, who collaborated on how to apply the optimal transport idea from economics to non-Euclidean geometry and non-smooth geometry, the Rich comprehensive curvature problem, this theory connects the analysis and geometry. the boundaries. accidentally collided, deducing new mathematical theorems from scratch. It was these encounters that made him firmly devote himself to exploring various harmonious relationships that had already existed. He once sighed: "The world is full of many unexpected connections!" During his math journey, there was a French song "Sailor and the Rose", and one of the lyrics was deeply rooted in his heart: "People have never discovered it." , a love thread is connected from afar, starting at Dublin Garden, and ending at sailors are in the horizon. "

Vilani is often uncertain. When people you meet in life ask him "what are you studying", are they really interested in knowing the answer . He would sometimes take a deep breath and answer, "I developed a comprehensive concept of the lower boundary of Rich's curvature in a complete local tightness measurement space." The result was almost always a ignorant and amazed reaction. He would patiently popularize Einstein's theory of relativity, making the curvature of light bends, not the cornerstone of Euclidean geometry; he would also explain to people that when the curvature is positive, the light is close to each other, and when the curvature is negative, the light is bright Divergence. He will patiently continue to talk about the optical concept of curvature, which is combined with the concepts of density, entropy, kinetic energy, and extremely small energy in statistical physics, and what he does is to solve the problem of "how to be in one Discuss the issue of curvature in a space that is not smooth like a hedgehog”, which is "optimal transport", a concept involving engineering, meteorology, computer science and geometry.

When mathematicians say he is studying questions like "what makes atoms organize spontaneously, rather than quietly staying away from each other? Why do we connect into a whole, not dissolve in the universe" mathematical like Starry sky is as romantic. When physicists propose and solve this "matter stability problem" in mathematical form, the process is difficult again. Sometimes, people ask Verani to write a mathematical formula to keep it as a souvenir (this thing often happens in France). Those formulas and geometric figures that ordinary people cannot understand are more like an obscure but mysterious and mysterious contemporary art, and perhaps creates a certain impressionist atmosphere. He treated the public very tolerantly who were full of curiosity but could not understand his mathematics: "No one understood the mathematical formulas in my book "The Birth of a Theorem". They exist for decoration and atmosphere."

took office as Pang Before the director of the Calais Institute, he asked himself a question: "Now, who would like to be the head of a research institution who is bothered by administrative trivial matters all day long, succumbing to increasingly complex regulations every year? Leadership A research institute that is so complicated, this may be the end of his research career. "But he accepted the position anyway.After winning the Fields Medal, he continued to appear in newspapers, radio and television programs, constantly meeting various figures, from politicians, artists, college students, entrepreneurs, revolutionaries, MPs to the President of the French Republic... He always repeated The same question was asked by everyone: How did you start to become interested in mathematics? Why are French math so powerful? Did the Fields Medal change your life? After receiving the highest honor, what is the current driving force for scientific research? Are you a genius? Is it a point to wear a spider ornament?

Luxembourg Park (photo by Yu Chuzhong)

The secluded mathematical predecessor Descartes and Pascals is that Verani did not escape the lively world. Instead, he actively intervened. He told me that the Fields Medal did not change his life in the math circle. "Mathematicians around the world form an circle . There are not many people in this circle , and people have already known each other." The influence of the Fields Medal on him changed his relationship with the world outside of mathematics. Especially with politicians, industry and media. “I started to be interviewed by media, appeared in TV shows and documentaries, and I also started to give public speeches, with hundreds of invitations every year. I also recently participated in France’s application for the 2025 World Expo as a representative of French culture One of the six characters, along with five other representatives from French chefs, writers, astronauts, entrepreneurs and navigators, representing France. Politicians also began to respect you, seeking opinions from you, hoping to get you involved in various matters. "But mathematicians are usually critical of politics, and when the telecommunications industry, the cloud industry, and the optimization industry come to him to give advice, he doesn't have time to solve their problems, but points them out, Which fields and researchers can provide them with solutions.

At the beginning of the 21st century, the proof of the Poincaré conjecture changed the whole picture of mathematics. The bigger upheaval is that mathematics and technology have become closer, which has opened up a new world for mathematics. The great development of algorithms and digital science has made the application of mathematics more and more extensive. Vilani clearly knows the source of his reputation: "Mathematics plays a rising role in the economy, and therefore is more respected. The industry is increasingly in need of more mathematicians, and in many companies, mathematicians are At a high-level position. With the increasing use of mathematics, mathematics has become a good career for modern people. "Contemporary mathematicians may be more fortunate. The development of pure mathematics often transcends the times, or even theoretical physics. The theory established by Galova, worshipped by Verani, was only applied to quantum mechanics more than a century later; the same is true for non-European geometry to describe the application of gravitational fields and complex analysis in electrical dynamics; conical curves It has always been considered an unprofitable entertainment in a speculative mind. It plays a role in modern astronomy and the law of universal gravitation, which has happened more than 2,000 years after its birth. In the past, the work of mathematicians was difficult to understand by people, and they were like useless dreamers; now, the work of mathematicians is still difficult to understand, but people have long realized how our era has benefited from mathematics.

Verani's mathematical heroes, from Boltzmann, Maxwell, John Nash to Alan Turing , have applied the abstraction of mathematics to another scientific field with unprecedented creativity, such as economics, , physics, computer or industry. Verani thinks they "very good at proving the idea that mathematics is very effective in understanding reality." He feels that applications can truly integrate mathematics into the entire human society; between beauty and practice, mathematics has been repeatedly swaying, looking for balance.

But compared with the era of Einstein and Niels Bohr, the role of scientists has changed a lot. "Einstein became a well-known public figure, a God-like existence, and he was unique. Today, the context is different: compared with his time, there are much more scientists; the problems they study are also more. Complex, more global perspective, often spanning multiple continents.Scientists can still play public roles, and should be said to be representatives and symbols of the scientific community to influence young people. "Vilani does not hide the fact that the international reputation of the Fields Medal has caused mathematicians to receive too much attention from to , but its benefits are: "It always makes young faces appear in the public eye, and Unlike scientists who won the Nobel Prize in their 70s, they no longer have the energy to talk to the public and young people. "After all, the golden period of creation by mathematicians is mainly in the middle-aged and young age.

cars are constantly braked and bumping on the urban traffic in Paris and the roads in the suburbs. We try our best to resist the urge to vomit. During this more than an hour trip, Verani occasionally showed some fatigue and yawned twice with caution. Once, he almost used his mind to support his upper and lower eyelids that were moving closer together. During this journey to the southern suburbs, he Finally decided to answer a phone call that had ringed several times. I probably heard that he told the other party that there was no time yet. Put down the phone call

1. He told me that the caller was a Tunisian caller. He went to Africa several times a year, and people there were great enthusiasm for scientists. The calligrapher wanted to write a children's book with him. , from the perspective of mathematicians, choose some words that represent its own for the 26 English letters. "Oh, poor Assad, I'm always busy," said Verani.

(This article was first published in Sanlian Life Weekly Issue 45, 2016, has been deleted and modified.)

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