The unnamed lake is an ocean.
In July, 2007, I began to read the enrollment brochure of Peking University Institute of Mathematics, which impressively stated that "dozens of students go to MIT and Princeton University for further study every year". This is a sentence that changed my life. It let me know that there are two schools in America besides Harvard and Yale. Also let me know that "going abroad for further study" is a decent thing that can be written into the enrollment brochure. Let me find my next life goal after the national examination. A month later, a newspaper in Harbin interviewed me and asked me about my plans in four years. "Go to MIT for further study", I pretended to be very clear and blurted out the name I had just heard for a month. In this way, my life in Peking University began, with the dream of going abroad for further study.
After coming to the School of Mathematics, I quickly understood the elements and steps of studying abroad and established a set of simple logic: learning mathematical analysis well means getting good grades and going to a good school. Therefore, my academic life in the first two years of college was a down-to-earth academic analysis. Later, I deeply felt that the competition in the college was fierce, and it was not enough to have good optical analysis. So I took a deviation and began to learn the direction of probability theory, which seemed to be very close to analysis, and other students paid little attention to it. The longing for going abroad has given me the motivation to review in senior three, and I have been immersed in my work. Looking back now, this stupid experience, in addition to being ridiculous, also helped me lay a solid foundation in mathematics.
But analysis and probability alone are not enough to pass the time, so I decided to open my eyes and see the world. In this way, the unnamed lake became an ocean, leaving me free to wander in it. Listen to lectures four or five times a week: listen to Yu Dan telling jokes, listen to Chen Danqing swearing, listen to Jia talking about movies, and listen to Rao Yi expressing intellectual ideals; Study various courses: study the East Asian game behind the Six-Party Talks and think about the philosophical thoughts of Hume, Kant and Foucault; I go to the math report every week. What impressed me most were the reports of Xia Zhihong, Yan Jiaan, Dingzhu Du, Smale, Wang Shizhen, Chen Mufa, Kong Liang and others. They told me that there are many interesting things in mathematics besides the analysis and probability that I concentrate on every day. Looking for books in the library: the most important books by Russell and Fromm, the core part of my world view comes from them; Listening to Hu Tao's Principles of Economics and Liu Xufeng's Mathematical Economy made me respect a subject. Listen to Mr Zhu Qingsheng's art history. He explained the Mona Lisa's smile and the exquisiteness of Wang Xizhi's calligraphy, and explained the world history with the help of an art history. Listening to Mr. Ma's introduction to theoretical physics, I am excited about the excitement of physics, which ultimately determines my research direction in the next five to ten years. The rest of the time, I daydreamed by the unnamed lake. Later, it proved that these casual explorations were worthwhile, and their most profound changes were brewed in this process, and Peking University gave the best resources to a person who explored inadvertently.
The culture of discussion classes in several colleges has also deeply influenced me. When I was a sophomore, I attended the seminar of Senior Brother Liu Zhiyu. Liu Zhiyu's broad mind and passion for the world and others deeply infected me. He let me know what a selfish and narrow-minded person he is. In my junior year, I formed a math discussion class with three students, namely Yu Yue and Shen. Yu Yue, who is versatile, well-informed and particularly playful, and Zhang Li, who was still studying the final GRE of Zhuge Liang's collected works the day before the GRE exam (no way, he seems to know Greek and Latin, and is the originator of English), took two IMO discussion classes.
In these explorations and exchanges, some ideas were established and some were subverted. It can be said that four years' life has subverted all the ideas I lived on before I entered school. One of the important things is swimming. Junior year began to learn breaststroke. Because of my clumsiness, cowardice and modesty, I am the only student in my class who has not studied. The teacher called me "stupid", which hurt me deeply. I'm determined to learn it. Finally, I studied for another semester and took 28 classes to learn breaststroke. Later, I asked my classmates from the Swimming Association to learn freestyle. After three times, I swam very well. The coach praised me: "You are really good at swimming, and you are learning so fast at such an age." I don't know how to answer at once. I admit that I am good at swimming, because I really feel like a duck to water now, but I seem to hear the laughter of the breaststroke teacher. I realized that the concept of "talent" that I had believed for many years was false. At the beginning, a person is attracted by something for some reason, immersed in it, and naturally has a "talent." Swimming is my most important achievement in four years. In addition to doing one thing well through hard work, it also freed me from a state: when I was growing up, I would unconsciously ask myself, "Is his talent better than mine?" When no one is around, I often ask myself, "Do I have this talent?" It turns out that I have been obsessed with a wrong concept!
In April 2009, I started my research under the guidance of teacher Wang Zhengdong, with the goal of a paper and a letter of recommendation. I didn't expect this job, which was purely for going abroad, to become the most far-reaching event in my four years at Peking University. In the first year, Dr. Liu Dangzheng and I worked together to solve the central limit theorem of random Toeplitz matrices. This is the first time in my life to answer an unknown question, and it is also the first time in my life to feel the joy of discovery and creation that I have been fantasizing about since I was a child. Later, I began to pay attention to a counting problem that Li Yiting was studying. Cheng Zheng, a senior in Grade 06, unexpectedly linked it with surface topology, which suddenly opened a world. Later, I developed the topological view of Cheng Zheng Brothers and added my own group theory. With the combination skills of Master Li Yiting, I gradually advanced this counting problem and got satisfactory results. It was in this process that I began to find that topology and algebra, which were once looked down upon by people, were not so terrible. On the contrary, they can be powerful tools when interests are stimulated. On the contrary, I have learned so much about analysis and probability, but it is not as simple as I thought.
However, just as Li and I were preparing to write a paper, Dr. Liu Dangzheng found that our results were obtained in 2004, and they were based on a group theory method similar to mine. But at the same time, Liu Faxian, a result in algebraic geometry of counting, is helpful to fully understand this counting problem, thus obtaining an expression of probability density that we have been trying to calculate. So we didn't lose heart and went on along this road. Liu showed superb calculation skills and almost worked out this expression. Later he went to Chile, and the task fell to me.
1 1 new year's day, I searched for keywords related to the problem with curiosity, and a magnificent picture that shocked me was displayed. It turns out that the counting problem and Cheng Zheng Brothers' topological ideas were discovered as early as the 1970s when physicists studied quantum gravity. After the birth of string theory, this problem became a channel between string theory and quantum gravity, and string theory is closely related to counting algebraic geometry. Witten(Fields 1990) put forward the famous Witten conjecture in this field along this line of thought. It was solved by the technique developed by kontsevich (Fields 1998), and later Okounkov(Fields 2006) solved the BDJ conjecture along this road, which is related to many growth phenomena in nature and Riemann hypothesis that stands out in number theory. The unity of mathematics and the exquisite harmony of nature have completely shocked the soul of a young man. It turns out that scientific exploration is to swim to that mysterious and beautiful realm in the hazy water vapor. Didn't Mona Lisa's mysterious smile and Wang Xizhi's calligraphy lead people to this state? Science radiates her energy like the sun, shining on farmland and even on rocks, and crops grow. I think this is what science means to the people who work for her and to the whole world.
The significance of this scientific research to me is not only to free me from the study of analysis and probability, but also to let me see the true beauty of science. It fundamentally changed my outlook on life. I always think that only scientific research is a noble cause, and not being a scientist is a failure in life. And this experience made me understand that a good life can't be achieved by being a scientist or not being a scientist. A good life should be spent like this: a pure-hearted person will devote himself to the career he has chosen, and constantly realize and surpass himself, without end. This is the true feeling I have experienced in scientific research, and it is also the most worthy pursuit for a person. This kind of feeling must exist in human activities. Brave athletes, courageous businessmen and resourceful politicians can all reach this level in their own way. Moreover, this profession is not necessarily doing scientific research, but feeding the baby, cooking a table and climbing mountains. I think it is because of this feeling of transcendence and realization that an Olympic champion can become a successful businessman, a skilled magician can become a statistician and an excellent geometer can become a top fund manager. This is the core of Russell and Fromm's humanistic thought.
Finally, I have to mention the teacher's help in the process of applying for going abroad. In order to go abroad smoothly, I tried my best to seek the help of teachers, including Wang Zhengdong, Chen Dayue and Wang Baoxiang from Peking University, professors from Northwest University, Professor Shu Qiwang from Brown University, Professor Wu Sijue and Professor Smoler from the University of Michigan, Professor chatterjee from the College, Professor Dembo from Stanford University, Professor Borodin from MIT, Professor Strauch and Professor Yao from Harvard University. I can't wait to type the draft 100 times in every interview, and I can't wait to type the draft 20 times in every email. Every communication proves that I am trying to be a gentleman with the heart of a villain. Communication with them is like spring breeze. They taught me how to be a real scholar. They let me know that embarrassment breeds evil thoughts. A person always helps others calmly in a calm state. For me, the entrance to the country is like a high wall that needs to be climbed. I don't know whether it is the Peach Blossom Garden or the abyss behind the high wall. It was the guidance of these teachers combined with my own tossing in an unknown lake that gradually turned this high wall into a transparent glass wall, through which I saw the real picture on the other side of the wall. "Going abroad" is no longer the most attractive word for me, but has become a heavy burden that I have to bear for further study.
Looking back on four years of college life, the only picture in my mind is a person swimming in an unknown lake, growing, feeling and surpassing in the water. Now he is going to swim out of the unnamed lake, cross the Atlantic via the North Pole and enter the Charles River in Boston. That new water area is waiting for him to explore. How much he hopes to return to the unnamed lake along the same route after many years, because it is his spiritual hometown.