Movie poster of "Dream Tour Ring"
As the Dream Tour Ring says:
Therefore, great musicians will never die, because their music has been sung by the world; Similarly, great mathematicians will never die, because their mathematics has been interpreted by the world.
The lives of Ka Kui Wong and Leslie Cheung are continued through Days of Our Lives and Ghost Story, and Jin Yong's martial arts novels will always have readers. Atiyah is remembered because his exponential theorem (together with Singer) has been used repeatedly, just as we still mention Euler, the great mathematician of18th century. I believe that after several years, "there are still (faint) whispers in the world, pursuing their legends."
In essence, they-whether musicians, actors, writers or mathematicians-are all one kind of people: artists. Artists are immortal because they have immortal works of art, for example, Cao Pi said in "Dian Lun Paper": "Building a chapter is a great cause of governing the country and an immortal event." The article is like this, and so is music mathematics.
Of course, the slight difference is that it often takes much more effort to appreciate mathematics (in essence, to understand mathematics), so only a few people can realize that mathematics is an art like music and articles.
Perhaps the best shortcut to truly understand this point is to listen to what these great mathematicians themselves have to say. We once shared the stories of some great mathematicians in the Series of Contemporary Great Mathematicians. Today, we will add the stories of three mathematicians. They are:
Sir Michael Atia.
Sir Michael Francis Atiyah.
algebraic topology
Fields Prize, Abel Prize
Former Dean of Trinity College, Cambridge University, the first director of Newton Institute, and honorary professor of mathematics at Edinburgh University.
Many scientists in the 20th century had complicated immigrant backgrounds and were forced to emigrate to other countries because of the persecution of German Nazis. This forced cosmopolitanism may broaden the horizons of these immigrant scientists and promote their subsequent careers. Although I am not a Hitler refugee, I spent my childhood wandering between Europe and the Middle East. My mother is Scottish and my father is Lebanese. We live in Khartoum. I attended high school in Egypt until I was 16 years old. My grandmother lives in Lebanon.
1945 We moved to England. After I finished my studies at Cambridge University, we stayed in the United States for a long time. I find it difficult to answer this question: where are you from? Similarly, when asked what kind of mathematician you are, I find it equally difficult to answer. I usually answer this question like this, but simply say that I am a geometer in a broad sense, which seems to find comfort in the famous saying "God is a geometer". For me, it seems that there is only one world, although some parts of it are more familiar than others, so there is only one math. I don't like political or cultural barriers. I find that ignoring them is an important stimulus to creative thinking. Ideas should flow out naturally without hindrance.
My mathematical development started with algebraic geometry, and then slowly and naturally turned to topology and differential geometry, then to analysis, and finally to theoretical physics. Every stage is a wonderful process, and I have established close friendship with many collaborators and broadened my horizons. Fritz Hirzebruch of Bonn is my first colleague and mentor, and his annual math meeting will be a gathering place for my generation. In Paris and Princeton, Jean-Pierre Serre educated me through his clear and beautiful views and explanations.
At Princeton, Harvard and Massachusetts Institute of Technology, I have established close cooperation with Raoul Bott and Singh, who have taught me column group and functional analysis. Back in Oxford, under the guidance of my old friend roger penrose, I took the first tentative step towards modern physics. Stimulated and guided by edward witten, this moderate participation later developed into the mainstream. In the next few years, I was lucky enough to attract many smart graduate students, some of whom eventually became my colleagues and collaborators. I learned a lot from them, and I also realized how math taste and skills reflect a person's personality. The diversity of styles and viewpoints is welcome, and creativity is most prosperous with the least guidance and the most freedom and encouragement.
Mathematicians are usually regarded as intelligent machines, and their brains can process numbers and output theorems. In fact, as Herman Weller said, we are more like creative artists. Although we are strongly bound by logic and physical experience, we use our imagination to jump into the unknown. The development of mathematics for thousands of years is a great civilization achievement. Some mathematicians, most notably G.H. Hardy, admire and despise anything with practical application value because of the "purity" of mathematics. I hold the opposite view. If anything I do finally finds practical value, I will be very happy. More generally, I think mathematics should contribute to science and society, and mathematics is one of the main parts of education and learning.
Because of these views, I always think it is my responsibility to play some general roles, such as Pugwash, President of the Royal Society and Dean of Trinity College, Cambridge. [Note: Pugwash is an organization composed of influential scholars and public figures who are concerned about reducing the danger of armed conflict and seeking cooperation to solve global problems. ] chairman. The future of mathematicians and their research privileges ultimately depend on society. Therefore, in return, we must repay this debt in various ways and urge our compatriots to adopt a friendly and tolerant attitude towards this strange profession.
Phoenix Braud
Felix Browder
Functional analysis, partial differential equation
Professor of mathematics, former vice president of Rutgers University; Max Mei Sen is an emeritus professor of mathematics at the University of Chicago.
1927 was born in Moscow, Russia in July, and was brought to the United States at the age of five. My father, Earl Braud, was the leader of a dismissed American political party. He didn't even finish primary school. My grandfather is an unemployed primary school teacher. He is tutoring children, while my father is basically self-taught. My father opposed the first world war. He was the social leader of the anti-war movement in Kansas City, Missouri. Because he opposed war, he was imprisoned in 19 17- 1920. He has accumulated a library with more than 10,000 books in his life.
My mother was interested in astronomy at first, but she got a law degree from St. Petersburg University. This was very difficult before the Russian revolution, because she was Jewish and Kharkov was the only city where she could practice law. She became the mayor's secretary. Unlike her, the mayor is not from party member. My parents met in Moscow in 1926, when my father was visiting Lenin School, which was a school for training party leaders. At that time, he worked for the Kremlin in the Red Trade Union International (that is, a international trade union confederation). He is one of the American representatives of an international organization.
My two brothers Andrew and William and I are mathematicians. My brother William and I are the only brothers and academicians of the National Academy of Sciences. We are both presidents of the American Mathematical Association. 1970- 1980 during these eleven years, I was the head of the Department of Mathematics at the University of Chicago. In the middle period, William and Andrew were the heads of mathematics departments of Princeton University and Brown University respectively. I don't know why we are all attracted to mathematics.
I 1944 graduated from yonkers high school, and then went to MIT to study mathematics. I graduated from 1946 with a bachelor's degree. I am one of the top five winners of Putnam Competition, a math competition for American undergraduates. 1946, entered Princeton University. 1948, aged 20, received his doctorate with a paper on nonlinear functional analysis and its application. In the next 60 years, this field and partial differential equations have become my main interests, especially the nonlinear monotone operators from Banach space to its dual space.
From 1948- 195 1, I was one of the first two Moore mentors at MIT. Before 1955, there was no difficult time for mathematics employment, and I only had a lecturer position. Although I was recommended by the Department of Mathematics, any permanent or long-term position was rejected by MIT. 1953 I got the Guggenheim research fund. At the same time, I was assigned to the American army. In the army, I was listed as a dangerous person, and finally I was tested for it, and finally my innocence was cleared. From 65438 to 0955, I left the army and became a teaching assistant at brandeis University. From 65438 to 0956, I went to Yale University, where I went through all the academic steps and became a professor. 1963, I came to the University of Chicago and stayed there for 23 years. 1986, I retired from the University of Chicago and went to Rutgers University as the vice president. From 65438 to 0999, I won the National Science Medal of Mathematics and Computer Science.
You may want to know why I am sitting in a seemingly empty room. This is because we are going to move into this new house. One reason why we want to move is that I need more space to store my 35 thousand books. This library has many books on different subjects, including mathematics, physics and science, philosophy, literature and history, as well as some books on modern politics and economics. This is a rich library. I am interested in everything, and my library reflects all my interests. Taking mathematics as my profession is an adventure in my life. Among mathematicians I know, it is very rare to be interested in everything. One exception is the recent Gyan-carlo rota.
Harold Kuhn
Harold William Kuhn
Game theory, mathematical economy
Honorary Professor of Mathematical Economics, Princeton University.
As I grow older, I believe more and more that our lives are controlled by accidents and the influence of others. My own life confirms this argument. Let me just talk about my life experience.
My math career will start with my electrical teacher, Mr. Brockway from Fuxi Junior High School in south-central Los Angeles. When I was eleven years old, he taught me the miracle of logarithm and let me solve some problems-setting switches (unipolar and bipolar) to control lighting in a complicated way. These "puzzles" are essentially combinatorial problems and play a central role in all my research. Mr. Broakeway also provides high-simulation, long-term audio equipment for Hollywood studios on a part-time basis, which gives me the ambition to become a radio engineer.
In arts and crafts high school, we benefited from the fact that teachers were stable jobs during the Great Depression. So our high school teachers are all doctors in chemistry or physics. Moreover, it was my physics teacher, Mr. Patten, who took me to visit the science and technology exhibition of California Institute of Technology, laying the groundwork for me to become an electrical engineer at California Institute of Technology one day. I have a letter of guarantee at UCLA, which accepts any high school student in California with an average grade of ~B~ or above. However, UCLA has one drawback. As a university established by the government, it bothers me that students are required to participate in military training of the reserve forces.
So, in the autumn of 1942, I became one of the 60 freshmen of Caltech/kloc-0, and the only one who didn't live on campus. The reason is simple: my parents are poor and can't afford my room and board at California Institute of Technology, so they moved to Pasadena and rented a house near the campus for $25 a month. My father suffered from severe heart disease in 1939, and the annual income of the whole family came from a disability insurance of about 1200 US dollars. My parents have never been to the fifth grade of primary school, so my academic ambition is a miracle for them. In the middle of the third year of California Institute of Technology,/kloc-0 was drafted into the army in July, 1944, and he changed from an electrical engineer to a double degree in mathematics and physics.
After completing the basic training of infantry regiment, he obtained the qualification of Japanese military professional training program and was sent to Yale University. E.T. Bell, who taught me several courses, introduced me to Oroy Steiner, who allowed me to listen to his abstract algebra class for graduate students. At the same time, Earnie Rauch, a friend of California Institute of Technology who joined the army with me, retired due to physical reasons and has transferred to Princeton University to complete his undergraduate degree in mathematics. I managed to cheat a week's leave from Yale to visit him, so I sat in the classes of Emil Artin, Claude Chevalier and Botshner, which convinced me that Princeton was a paradise for mathematics graduate students.
1946 after I was discharged from the army, I returned to California Institute of Technology and completed my undergraduate study in June 1947. At that time, I knew very well that mathematics was my mission. This feeling was further strengthened by the appearance of Flederick Born Brewster at California Institute of Technology, who was brought to Princeton by Herman Weil. Bonenburst brought a breeze to the mathematics of California Institute of Technology, and he provided a modern point of view for the English stylistic analysis that was blocked in the early 20th century. He also supported my application for postgraduate study in Princeton. One weekend, he came to my home (the home was poor and there was no telephone) and invited me to meet Lefschetz, who was then the head of the mathematics department of Princeton University.
In this way, along this winding road full of accidents, I was finally led to the real training as a mathematician. However, opportunities once again played a role in shaping my career. When I finished my doctoral thesis on group theory with Ralph Fox and proved some algebraic results by topological methods, I cooperated with al tucker and graduate student David Gale on a summer project to study the relationship between the newly born game theory and linear programming. This project determined the direction of my subsequent academic career, focusing on the application of mathematics in economics.
Every mathematician has his "favorite child". Personally, they are: using tree (a concept in mathematics) to represent extended game, Hungarian method, rotating shaft method approaching fixed point, and an elementary proof of the basic theorem of algebra. These are all combination problems, so they belong to the same type as the switch design problems I encountered when I was eleven years old.
Acknowledgement: Lin thanked college volleyball friends Li Ru, Su and Li Ideality for their strong support!
Reprinted to the WeChat public platform "Fun Mathematics"
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