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Dyson's writings not only give readers a sense of intimacy, but also give people a strong sense of mission as a scientist. Perhaps we can use a sentence that Sima Qian commented on Qu Yuan in the "Records of History" to evaluate Dyson as a writer: "His zhijie, so he is called Wufang".
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Author | Lin Kailiang
Note: The first draft of this article was published in Science and Culture Review, No. 3, 2013, under the title of "Freeman Dyson: The Life of a Scientist and a Writer", and was also reprinted as an appendix to Dyson's Chinese translation book "A Colorful Mirror" (translated by Xiao Mingbo and Yang Guangsong, Zhejiang University Press, 2014), and later published in Mathematical Culture, No. 3, 2015, and No. 9, 2016, and was pushed in the WeChat public account Mathematical Humanities and Mr. Sai in stages. Thanks to the feedback from some enthusiastic readers and friends (including Dyson himself, based on the English version of Professor Chan Kwan Wing of the City University of Hong Kong), some of the errors in the first draft have now been corrected. Today in Fun Math, this revision is released and the full text is pushed at once to commemorate Dyson, who passed away yesterday (February 28, 2020). Here is the text.
“
In my life the three most important things were family, friends and work, in that order. So my greatest contribution was to bring up six children who are all successful in various professions and now raising families of their own. My work was not as important as that. Also, my work as a writer was probably more important than my work as a scientist.
”“
[In my life, the three most important things are, in order: family, friends, and work.] So my biggest contribution is to raise six children who have all been successful in different industries and have their own families. My work is not as important as that. And maybe my job as a writer is more important than my job as a scientist. Freeman Dyson, November 21, 2012 letter to me
”
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Freeman Dyson (Photo by R. Hagadorn)
The name Freeman Dyson may already be familiar in China. As an outstanding popular science writer, he has a wide readership. Several of his books have been translated into Chinese, including his debut novel Cosmic Waves,[1] which was translated by Qiu Xianzheng in 2002 at the inaugural Wu Dayu Prize for Popular Science By the Taiwan Wu University Academic Foundation. "All-round Infinity", "Imaginary World", "Sun, Genome and Internet", "Rebellious Scientist" and "A Colorful Mirror" have also been published in Chinese translations. Presumably, many readers are attracted to Dyson's writing, but do not necessarily know much about his identity as a mathematician and physicist. This article will try to interpret this person who combines scientific talent and humanistic accomplishment.
Dyson is now about to turn ninety-two and continues to write articles and do research, including some interesting work in pure mathematics. More than a decade ago, Dyson was invited by Professor Ge Molin of the Institute of Mathematics at Nankai University to visit China and tour the capital Beijing and the ancient city of Xi'an. China's long culture and rapid development have left a deep impression on him. He has high hopes for China's role on the world stage. This is reflected in his July 26, 2013 email to his old friend Yang Zhenning:
You write that when we were young, the focus of research shifted from Europe to the United States. Now I see one of the most important facts of the twenty-first century, which is that the center of the world stage will shift from the United States to China. You can be proud of the opportunity to contribute to both of these shifts. The main task left to our children and grandchildren is to witness this transformation happen peacefully.
I often think of your beautiful essay "Father and Me". He[3] must have been proud of it.
Cosmic Waves Cover
Notes for this section
[1] Dyson 1979. Disturbing the Universe. New York: Harper & Row.
[2] Yang Zhenning 1991, "Father and I", by C. N. Yang 2013. Selected Papers II With Commentaries, World Scientific. There is a Chinese translation of "Father and Me", included in Yang Zhenning's "Shuguang Collection", Beijing Sanlian Bookstore, 2008.
[3] Yang Zhenning's father, Yang Wuzhi. Wuzhi Yang, 1896--1973, mathematician and mathematics educator, L. Dixon, algebra and number theory specialist at the University of Chicago in 1928. E. Dickson received his Ph.D. and was a pioneer in the dissemination of modern mathematics in China.
<h2 class= "pgc-h-arrow-right" > a talented teenager</h2>
Freeman S. Dyson was born in england on December 15, 1923. Mother M. L. Atkey) is a lawyer who gave birth to Alice Dyson at age 40 and Freeman Dyson at age 43, and has been working as a social worker ever since. His father, George Dyson, was a musician who taught at historic Winchester College in England before being promoted to president of the Royal College of Music in London. George was interested in science, and there were many science books on the shelves, such as A. Whitehead. N. Whitehead), A. Whitehead S. Eddington), J. Gins Jeans), L. Hogben and J. Haldane B. S. Haldane) works. This exposed Dyson to science from an early age. But Dyson said he was already a writer before he became a scientist. Because he wrote a science fiction novel when he was nine years old. This unfinished debut was later included as an opening in his popular collection from Eros to Gaia.[1]
Dyson siblings: Freeman and Alice
Dyson was very obsessed with Jules Verne as a child. Verne) Hector Servadac (1877). He read it as a true story, only to be disappointed when he later discovered that "everything was made up." Still, Verne's style inspired Dyson's own childhood writing. Here is a look at a painting he made in his notebook as a child.
Teen Dyson with a pair of creations from his childhood
Dyson showed extraordinary mathematical talent at an early age. He told such a story in a short autobiography he wrote for The Face of Science[2]. He was still very young and needed to take a nap in his crib. But he didn't want to sleep that day, so he used calculations to pass the time. He calculates 1+1/2+1/4+1/8+1/16+..., and finds that the final number is 2. Then, he calculated 1+1/3+1/9+1/27+..., and found that the final number was 3/2. He calculated 1+1/4+1/16+1/64+... again, and found that the final number was 4/3. In other words, he discovered infinite series. He didn't tell anyone about the amazing experience at the time, he thought it was just a game he liked.
In 1936, Dyson passed a highly competitive exam to enter Winchester College, where his father taught, until graduation in 1941. He was married to the Brothers Longko Higgins (H. Christopher Longuet-Higgins, Michael S. Longuet-Higgins), J. Wrighthill Lighthill) formed the Gang of Four, and both of them later made outstanding contributions to their respective fields of science, and were both elected to the Royal Society. Christophe Longko-Higgins (1923-2004) was a theoretical chemist and music cognitive. Michael Longko-Higgins (1925–2016) was a mathematician and oceanographer who worked with the geometrist H. Coxte. S.M. Coxeter) collaborated on a famous paper on homogeneous polyhedra [4]. Wrighthill (1924-1998) was a well-known fluid mechanics expert who served as p. A.M. Dirac) and S. Hawking Hawking) is a Lucas Chair Professor of Mathematics at the University of Cambridge.
Winchester College is not in favor of forcing gifted children to learn advanced math and science in advance. Teachers believe that it is better for students to learn autonomously, so they deliberately let students go, students have a lot of time at their disposal, and Dyson and other boys rely mainly on self-study. Dyson said the Gang of Four learns more from each other than from teachers.
In Dyson's view, the college has an excellent award mechanism. For each grade, the Academy holds three competitions per year, and the winner will receive thirty shillings, but must be spent in the Academy's bookstore. Dyson often won prizes in competitions and thus owned his own collection of books. From 1937 to 1940, he won a total of 19 books. These books played a decisive role in the development of his interest and intellectual development, and some books even became his lifelong favorites. Some of the most influential books are: E. Bell T. Bell's Mathematical Elite,[6] G. Bell's H. Hardy and E. Wright M. Wright) co-authored Introduction to Number Theory[7], G. Joos' Theoretical Physics and S. Ramanuean's Ramanujan's Collected Mathematical Papers.
Dyson's Bookshelf,
See http://paradigmmagazine.com/2015/01/08/paradigm-freeman-dyson-interview/
Dyson was fascinated by Bell's mathematical science book The Mathematical Elite. He recalled[8]:
When I was fourteen I read Bell's The Mathematical Elite. The book chronicles the legends of many great mathematicians. Bell is a professor of mathematics at the California Institute of Technology and a gifted writer. He convincingly introduces the reader to the elite of the mathematical community. He knows how to touch the heartstrings of emotionally sensitive teenagers. Bell's book produced an entire generation of young mathematicians. Although many of the details in the book do not match the facts, the main plot is true. In Bell's pen, mathematicians are flesh-and-blood people who do wrong things and have flaws. Mathematics has become a magical kingdom that all kinds of people can set foot in. The book's message to young readers is: "If they can do it, why can't you?" ”
Bell's book inspired Dyson's ambitions to become a mathematician. He even had the dream of one day proving the famous Riemann Hypothesis.
On September 3, 1939, British Prime Minister Neville Chamberlain was forced to declare war on Hitler and Britain joined World War II. During the Christmas holidays, in order to understand Einstein's theory of relativity, Dyson began to study a relatively advanced mathematical book, H. Piaggio . T. H. Piaggio's Differential Equations was a prize he received at school that same year. Dyson feared that he might be killed in the war, and that he might even be worse than The Most Miserable Mathematical Genius in Bell's book, É. Galois) is even more tragic, because Galois has created immortal mathematical achievements before the duel. All he had in mind was Galois's last words before the duel: "I have no time, I have no time." So Dyson devoted all his time to math, studying an average of fourteen hours a day from six a.m. to ten p.m., except for a two-hour break at noon. Although Dyson himself enjoyed it, it worried his parents. The mother quotes Chaucer (G. Chaucer) Chaucer's Oxford priesthood was "so preoccupied with his studies that he had no time to make a sound" and warned him that he would get sick or even damage his brain in the long run. His father repeatedly advised him to put down his books and go out together to help him do some farm work to relax. But Dyson ignored it and continued to indulge in Piagio's Differential Equations. Toward the end of the Christmas holidays, Dyson had completed nearly 700 exercises in the book and was almost done, so he was willing to take time to walk with his mother. My mother had been praying for this for a long time and had been preparing for it. What his mother said at the time had a profound impact on Dyson. We quote the following from Cosmic Waves[9]:
My mother was a lawyer, so she was very interested in people, and she liked Latin poets and Greek poets. Speaking to me, she first quoted a former African slave who later became the greatest Latin playwright, T. Eff. A line from Afer's play, The Self-Tormentor: "I am human, and I am by no means alienated from human beings." This was the proverb of her creed throughout her long life, until her death at the age of ninety-four. As we strolled along the embankment between the mud swamp and the sea, she said to me that this sentence should also be my credo. She understood my desire and love for The Abstract Beauty of Piaggio, but she asked me not to lose my human nature in my desire to be a mathematician. She said: "One day you become a great mathematician, but you are soberly aware that you have never had time to make friends, you will regret it." If you don't have a wife and children to share the joy of success, what's the point of even if you prove the Riemann hypothesis? If you are only interested in mathematics, then in the future you will feel that mathematics will become boring, like bitter wine.
As Dyson puts it in the book, "Mother's proverbs have gradually been deeply imprinted into my subconscious, and from time to time have unexpected effects." ”
Dyson also worked hard to read Hardy and Wright's Introduction to Number Theory and try to prove every theorem in the book. There are more than 400 theorems in the book, and Dyson was under 14 years old at the time! The book fostered Dyson's keen interest in number theory, and Hardy's lifelong influence on Dyson began.
In addition to reading his own award-winning collection, Dyson read two other books from the College Library with Wright Hill, Whitehead and B. Russell. Russell's Principia Mathematica and C. Jordaan's Jordan's Analytical Tutorial. These two books were accidental discoveries by Wright Hill. They quickly judged that Principia Mathematica was a failure, and that the Analytical Tutorial was the key to opening the doors of modern mathematics. They had always wondered how the Three-Volume Advanced Mathematics Textbook, written in French, could be placed in the Academy's library. It wasn't until many years later, when Dyson read Hardy's classic Confessions of a Mathematician, that he found a plausible explanation. In it, Hardy describes the influence of the Book of Analysis on him.[10]
I will never forget the surprise of reading this great book, which was the first enlightenment for many mathematicians of my time. Reading it I first learned what mathematics really means. Since then, I have embarked on the path of becoming a true mathematician with healthy mathematical aspirations and sincere passions and aspirations for mathematics.
Hardy's feelings must have resonated with Dyson. Dyson later learned that Hardy had also attended Winchester College 40 years earlier (Hardy had a bad time here, so he rarely mentioned the famous alma mater). Dyson once speculated that it was Hardy who deliberately left the book in the college library, hoping to "hide the famous mountains and pass it on to others". Dyson later entered Cambridge University and became a student of Hardy. But because Hardy was so high and inaccessible, Dyson didn't have the courage to ask Hardy himself for verification. After Hardy's death in 1947, this also became a major regret for Dyson.
During the college's final summer, Dyson's high school math teacher, Dreher (C.V. Thompson), was a high school math teacher. Durell) arranged for the geometrist Peter (D. Durell) to arrange for the geometrist Peter. Pedoe) came to give Dyson and Wright Hill special counseling. Peto, who was a junior lecturer at the University of Southampton twelve miles away, was the first true mathematician Dyson had ever met. Peto later recalled dyson at the age of 17.[12]
Dyson asked me if there was anything more interesting than the infinite series problem in middle school, so I suggested that he study the problem of representing the directed circles given by equations in the plane as points in three-dimensional space. I have published an extremely in-depth article discussing this beautiful representation. For example, a co-axis circle would be represented as a line in three-dimensional space. Dyson was fascinated and still remembers it.
As Dyson put it, although he did not become a geometrist, he learned from Peto an appreciation of geometric styles, and thus regarded mathematics as an art rather than just a science.
Dyson also befriended Frank Thompson, a literary young man three years his senior at the academy. Frank had a greater influence on Dyson than anyone else in the Academy. Frank earned the title of Academy Poet at the age of fifteen. He had a deep affection for poetry. For him, poetry is not only an intellectual pastime, but has always been the crystallization of wisdom that people have refined from the depths of the indescribable soul. As a sensitive poet, he was more concerned with the world beyond the Academy, especially the Spanish Civil War and the coming World War II. Dyson thus learned for the first time from Frank about the great moral issues of war and peace. But just as Frank couldn't live without poetry, Dyson's favorite was still mathematics. Frank was unfortunately killed in World War II, and his heroic deeds were written by Dyson in the "Poet's Blood" chapter of Cosmic Waves.
[1] F. Dyson 1992. From Eros to Gaia. New York : Pantheon Books.
[2] M. Cook 2005. Faces of Science. New York, London: Norton and Company.
[3] In the United Kingdom, members of the Royal Society are equivalent to members of the Academy of Natural Sciences (scholars of the humanities can be elected to the Academy of Sciences).
[4] H. S. M. Coxeter, M. S. Longuet-Higgins and J. C. P. Miller, Uniform Polyhedra， Philos. Trans. R. Soc. Lond. A 246 (1954), 401--450.
[5] Professor Yang Zhenning once told the story of Wright Hill in a letter to Professor Tong Yuanfang, see Chen Zhifan's "Ancient Clouds" (Beijing: Zhonghua Bookstore. 2014): He is physically fit and likes to do activities that ordinary people can't do. Once a swim around an island in the British Channel around the British Channel took ten hours. And 1. I have swam this seven times; Swim alone every time, do not have an airboat to follow; 3. 4. Do not wear a rubber jacket; Died on the eighth tour! Some say he died knowing he had cancer. ......
[6] E.T. Bell 1937, Men of Mathematics. Beijing: The Commercial Press.] 1991; The Great Mathematician. Jing Zhujun et al. translation. Taipei: Jiuzhang Publishing House.] 1998.
[7] There is a Chinese translation. Zhang Mingyao, Zhang Fanyi. Beijing: People's Post and Telecommunications Press.] 2008.
[8] M. Cook 2005.
[9] Dyson 1982. Cosmic Waves. Chen Shisu et al. translation. Shanghai: Shanghai Science and Technology Literature Publishing House.]
[10] G. H. Hardy，A Mathematician’s Apology. The book has four Chinese translations: two translations of "The Confession of a Mathematician", namely: Wang Xiyong Translation, Commercial Press, 2007; Li Wenlin, Dai Zongduo, Gao Rong Translation, Dalian University of Technology Press, 2014; He Sheng Translation (Bilingual Edition), Turing Company Publishing, 2020; and another translation of Confessions of a Mathematician, translated by Li Yong, Hunan Science and Technology Press, 2007.
[11] For Hardy, the following literature can be consulted: C. Snow P. Snow) for the preface to The Confession of a Mathematician, chinese translation of Which can be seen in Wang Xiyong's translation; Hu Zuoxuan, Hardy: Not Just Mathematicians, Bulletin of Dialectics of Nature, No. 4, 1993, 62--72.
[12] D. Pedoe , “In Love with Geometry” ,College Mathematics Journal, Vol. 29, No. 3 (May, 1998), pp. 170--188.
<h2 class= "pgc-h-arrow-right" > university of Cambridge</h2>
In September 1941, Dyson and Wrighthill both entered Cambridge University. Due to the extraordinary period in England at that time, all universities arranged as short courses as possible to enable students to enter the war as soon as possible, and many students left the school to join the army after only one year of study. Dyson was lucky enough to attend classes at Cambridge for two years before going into military service in 1943.
Only older professors remained at cambridge, and the mathematics departments included Hardy and J. Littlewood. E. Littlewood), W. V. D. Hodge), L. Modell J. Mordell) and A. Bersikovich S. Besicovitch), physics departments include Dirac, Eddington, and H. Jeffries. Jeffreys) and W. Prague L. Bragg）。 There were also very few students, and in many courses, Dyson and Wrighthill accounted for half of the audience, and Jeffries' fluid mechanics class was even pitiful to the point that dyson was the only student.
Of these professors, Dirac was the most famous. As one of the founders of quantum mechanics, Dirac published Principles of Quantum Mechanics in 1931, which later became one of the bibles of physics. Dirac was teaching almost verbatim, much to Dyson's disappointment. Because the course completely lacks the awareness of looking at the problem from a historical point of view, and Dirac does not teach students how to do specific calculations. Dyson always asked questions in class, and Dirac often had to pause for a long time to answer him, and once Dirac had to leave class early in order to answer Dyson's questions.
Dyson was very pleased with Hardy and Littlewood's course. He noticed that the two famous mathematical partners had very different styles: Hardy presented mathematics to his students as a mature and beautiful work of art, while Littlewood presented mathematics to students as a process of intellectual struggle. Dyson prefers Littlewood's style. However, what resonated most with Dyson was Bersikovich's style. In 1993, Dyson wrote a preface to the triptych edition of Cosmic Waves, specifically mentioning The Profound Influence of Bersikovich on him.
This Chinese edition gives me the opportunity to say what I would add if I were to rewrite the book today. First I'll add a chapter on pure mathematics. Pure mathematics is an important part of the universe in which we live. My scientific career began as a pure mathematician, and the teacher who most influenced my way of thinking was the Russian mathematician Bersikovich. In my style of study in physics and mathematics, traces of Bersikovich are clearly visible. ...... The style of Persekovich is architectural. He constructed a delicate architectural structure from simple mathematical elements according to a hierarchical plan, and when his building was completed, the whole structure led to unexpected conclusions through simple arguments. ...... After forty years of physics research, I recently returned to pure mathematics. Pure mathematics has once again become the main focus of my scientific activities. So I learned more about the artistic aspects of science. In a way, every scientist is an artist. As an artist, I use mathematical ideas as a tool, with Bersikovich as a model.
After completing his studies at Cambridge in 1943, Dyson served in the war, doing statistical work for the Royal Air Force. Until the end of the war in 1945, he earned a bachelor's degree in mathematics, but was still required to continue to serve for a year, and he was allowed to teach at the Royal College in London. The war consumed many young lives, the school was in a slump, and Dyson had few teaching tasks. His boss, S. Chapman. Chapman was a famous mathematician and geophysicist who encouraged him to do whatever he wanted. Dyson became H. Davenport, a number theorist at Birkbeck College, University of London. Davenport) discussion class regulars. Unlike The Cambridge Hardy, Littlewood, Persekovich and others who are alone, Davenport has a group of young graduate students around him, and the research atmosphere is very active. Dyson mentioned to Davenport his interest in Siegel's Conjecture, which was greatly encouraged.
In fact, at that time, Dyson already had the idea of switching from mathematics to physics. He had previously read about the physicist W. Hettler. Heitler's monograph, Quantum Theory of Radiation, which summarized the state of theoretical physics in the late 1930s and gave some suggestions to solve fundamental problems, captivated Dyson. But Davenport's friendship and the encouragement he gave mathematically made Dyson hesitate for a moment. So Dyson decided to use siegel conjecture to determine his direction: if he conquered the conjecture, he would continue to do mathematics; if he failed, he would convert to physics. After three months of hard work, Dyson conceded defeat. He did not fully conquer siege to siege, but he also achieved partial success, improving Siegel's earlier results.
1945-1946 was Dyson's golden age in mathematics. In addition to making some progress on the Siegel conjecture, he made important contributions to two other problems— Minkowski's Conjecture in geometric number theory and the Alpha-Beta conjecture in stack number theory. But the latter two issues are outside the mainstream, so the impact is not large. (The Alpha-Beta conjecture was demonstrated by H. Mann in 1942, and the Minkowski conjecture remains unresolved to date, and current research progress shows http://arxiv.org/pdf/1410.5743v1.pdf.) ）
After entering the military service in 1946, Dyson became a Fellow at Trinity College, Cambridge, with outstanding mathematical achievements. He had planned to relearn modern physics, but slowly realized that what he really needed was to talk to a theoretical physicist and learn from there what important unsolved problems were, so that he could use his mathematical skills to explore the depths and see if he was suitable for physics. Luckily, Chapman told him that there happened to be someone he was looking for in Cambridge: N. Kemer. Kemmer）。
Kemer was taught by W. Kelly at the University of Zurich. Pauli) and G. Winzell Wentzel), he taught dyson the quantum field theory he had learned from his mentor. Quantum field theory is mainly Dirac, Heisenberg (W. Heisenberg), Pauli, E. Fermi Fermi' creation, whose connoisseurs were mostly Europeans. At that time, very few people understood quantum field theory, and only one book on quantum field theory came out, and the author was Wintzel. Dyson learned of its importance from Kemer and mastered a one-handed skill, which was of great benefit to his later physics research. Kemer instructed Dyson with great patience, explaining to him in detail the difficulties in Wintzel's book and getting Dyson to accept the idea that quantum field theory provided the key to describing nature in a self-consistent mathematical way. Dyson, who had read countless people in his lifetime, said Kermel was the most selfless scientist he had ever met.
Although kemmer's guidance, there are more factors that prompt Dyson to leave Cambridge to start a new life in the United States. Dyson met G. Thompson, a fluid mechanics expert, in cavendish lab. I. Taylor), who worked at los Alamos National Laboratory in the United States during World War II. So Dyson asked which part of the United States was suitable for physics. Taylor immediately replied, "Oh, then you should go under Hans Bethe at Cornell University, where all the smart people in the postwar Los Alamos lab aspire." On Taylor's enthusiastic recommendation, Dyson went to the United States alone in 1947.
Interestingly, at the same time that Dyson decided to switch from math to physics, another man at Cambridge decided to switch from physics to math, Harish-Chandra, who later became a great mathematician. Harish Chandra, an Indian, came to Cambridge to follow Dirac as a PhD, but eventually left physics because he lacked Dirac's mysterious "sixth sense" of physics. Harish Chandra later visited the Institute for Advanced Study in Princeton with his mentor Dirac, where he met Dyson, who said, "I left physics for mathematics." I found physics messy, imprecise, and elusive. Dyson replied, "It was for the same reason that I left mathematics and threw myself into the arms of physics." ”
[1] Littlewood also has a famous popular mathematics book, A Mathematician s Miscellany. A new version of Littlewood s Miscellany has a Chinese translation of Littlewood's Collected Mathematical Essays. Translated by Li Peilian. Beijing: Higher Education Press.] 2014.
[2] Dyson 1998. Cosmic Waves. Qiu Xianzheng translation. Beijing: Sanlian Bookstore.]
[3] The ultimate glory goes to Dyson's compatriot K. Roth）。 See wikipedia entry: Thue–Siegel-Dyson-Roth theorem.
< h2 class="pgc-h-arrow-right" > three successfully changed careers</h2>
In September 1947, Dyson enrolled in Cornell under Bate. He immediately found that he had come to the right place: in the whole of Cornell University, he was the only one who understood quantum field theory. Quantum field theory is a mature mathematical construct, and when Europeans first created this theory, it was based more on consideration of mathematical beauty than on the success of explaining experiments, so most pragmatic American physicists are reluctant to bother to learn it. But it was later discovered that there were many experiments that needed to be explained with quantum field theory, which made learning quantum field theory necessary. Dyson's arrival came at the right time. So Dyson talked to instructor Bate and the bright young instructor R. Feinmann. P. Feynman) studied physics while teaching them how to deal with quantum field theory problems. Dyson brought the skills to calculate some atomic collision processes, and the data obtained could be confirmed by experiments, so he immediately got the favor of his mentors.
Bate was concerned with questions in quantum electrodynamics[1], a theory dedicated to precisely describing how atoms and electrons emit and absorb photons. It may seem inconceivable that in 1947, more than 20 years after the birth of quantum mechanics, there was no precise theory of the simplest and most basic particles, hydrogen atoms and light quanta! But there have been breakthroughs, with physicist W. Lamb Lamb) measured the so-called "Lamb shift" in the same year, which attracted the attention of its peers. In June of the same year, the American Academy of Sciences held a special meeting on Shelter Island in New York to discuss Lamb's displacement and related issues, a historic event that, although there were only 24 attendees, were all first-class figures. It was at this meeting that the idea of re-normalization was born. It was with this idea that Bate roughly calculated Lamb's shift on the train back to Cornell after the meeting. The theme he gave to Dyson was to delve into re-normalization and give strict treatment. This was the hottest and most cutting-edge theoretical question at the time.
From 1948 to 1949, Dyson followed Bate's advice and went to the Institute for Advanced Study in Princeton for a year. It was the most pivotal year of Dyson's scientific career. That year, at just 25 years old, Dyson made his most important contribution to physics — the reordering of quantum electrodynamics — and within a year, he had gone from being an unknown man to a shining new star in physics. He managed to change careers!
In the American physics community at that time, there were two active molecules studying reorganization: J. Schwenger of Harvard. Schwinger) with Cornell's Feynman. They are all physics wizards, but their tastes and styles are very different. [2] In 1948, with his excellent mathematical talent and interpersonal skills, Dyson learned directly from Feynman and Schwenger about their respective approaches to quantum electrodynamics, and perfectly drew on the advantages of both methods, mathematically giving a self-consistent formulation of quantum electrodynamics reormalization. In the sixth chapter of Cosmic Waves, he recalls a wonderful moment of sudden enlightenment:
On the third day, as the bus sped past Nebraska, a miracle happened—physics that I hadn't thought about for two weeks was flooding into my head. Feynman's image and Schwenger's equations began to correspond automatically in my mind, never before. For the first time in my life, I could connect these two perspectives. For an hour or two, I kept reassembling those fragments, and suddenly I realized that they could work together seamlessly. Although I didn't have a pen and paper on hand, everything was so clear that I didn't need to write it down at all. Feynmann and Schwenger are really just looking at the same idea from two different directions; if they combine their methods, they can get an ideal theory of quantum electrodynamics that combines Schwenger's mathematical rigor with Feenmann's application flexibility.
After learning about the Japanese physicist S. Asahina After Tomonaga's early contributions, Dyson crafted the paper "The Radiation Theory of Chaoyong, Schwenger, and Feynman," which became a far-reaching article. The title of the article more or less gives the reader the impression that the theory belongs to Chaoyong, Schwenger, and Feynman, and Dyson has simply integrated it. The truth is not so simple, for example, Nobel Laureate in Physics Yang Zhenning has a high opinion of Dyson's work[3]:
The program of re-normalization is a great development of physics. The main architects of this theory were Chaoyong, Schwenger, Feynman, and Dyson. When the Nobel Prize in Physics was awarded to Chaoyong, Schwenger, and Feynman in 1965, I thought that the Nobel Prize Committee had made a big mistake by not acknowledging Dyson's contributions at the same time. To this day, I still think so. Chaoyong, Schwenger, and Fehnmann did not complete the re-normalization program because they only did low-order calculations. Only Dyson dared to confront higher-order calculations and make this program complete. In his two high-level papers, which are extremely insightful, Dyson points out the main sticking points to this very difficult analysis and solves the problem. Renormalization is a program that transforms additive subtraction into multiplicative re-normalization. Its effectiveness also requires a far-means-extraordinary proof. This proof was given by Dyson. He defined concepts such as primordial divergence, skeletal diagrams, and overlapping divergences. Using these concepts, he made a profound analysis of the problem and completed the proof that quantum electrodynamics can be reordered. His insight and perseverance are amazing.
The two papers mentioned by Yang Zhenning here are "The Radiation Theory of Chaoyong, Schwenger, and Feynmann" and his sequel, "The Matrix of Quantum Electrodynamics". In an email to the author, Mr. Yang Zhenning specifically pointed out that these two papers have their own importance: the first paper proves the correctness of the Feynman diagram, while Before which Feynman only proposed the idea; the second paper overcame the problem of high-order computation and climbed to a height that Chaoyong, Schwenger and Feynman had never reached before. Later, almost everyone agreed that like Chaoyong, Schwenger, and Feynmann, Dyson was the founder of quantum electrodynamics. This is particularly evident in S. Schwebb. S. Schweber) 1994 book QED and Its Founders: Dyson, Feynman, Schwinger, and Chaoyong,[5] chapter 9 of which is devoted to Dyson's contributions.
Also lamenting Dyson's failure to win the Nobel Prize was the 1979 Nobel laureate steven Weinberg, who argued that "the Nobel Committee 'fledced' him." But Dyson has no regrets about missing the Nobel Prize. "One thing is almost invariably true[6]: in order to win the Nobel Prize, you have to have sustained attention, to grasp some deep and important issues, for at least a decade," he says. But that's not my style. [7] This big truth is to the point, and it is reminiscent of a famous statement by Mr. Yang Zhenning on the relationship between the style and contribution of scientists[8]:
In each field of creative activity, a man's taste, together with his abilities, temperament and encounters, determines his style, and this taste and style further determines his contribution. At first glance, it may seem surprising that a person's taste and style should be so closely related to his contributions to physics, which are generally considered to be an objective study of the material world. However, the material world has its structure, and a person's insight into these structures, his fondness for certain characteristics, his hatred of certain characteristics, are precisely the elements of his own style. It is therefore not unusual for taste and style to be as vital to scientific research as they are to literature, painting and music.
The above passage is also deeply appreciated by Dyson, because he also quoted this passage in his speech "Yang Zhenning - Conservative Revolutionary" at the dinner party for Yang Zhenning's honorary retirement in Stony Brook, New York. Dyson is well aware that he himself is a testament to the "decisive contribution of taste and style."
Borrowing a word that Mr. Yang Zhenning often says, we can say that Dyson completed his "push" as a young man in this year. An important result was that J. Oppenheimer, president of the Institute for Advanced Study in Princeton. R. Oppenheimer) gave him a long-term research position, which is extremely rare for a 25-year-old. Since then, Oppenheimer has always been very attached to Dyson, and even expected him to become the new Bohr (N. Bohr). Bohr) or Einstein. However, this is not Dyson's style. Dyson once said of this elder who treated him like a father.
Oppenheimer has a truly lifelong passion for physics. He always wanted to make a constant effort to understand the basic secrets of nature. I was disappointed that he didn't become a deep thinker. When he impulsively designated me for a permanent position at the Institute, he wished he had a young Bohr or Einstein. If he had asked for my opinion at that time, I would have told him that Dick [The nickname of Feinman's name Richard] was the person you wanted, and I wasn't. I have been and have always been a problem solver rather than a thought creator. I can't sit for years and pour all my effort into an esoteric problem, as Bohr and Feynman did. There are so many different things I'm interested in.
[1] Quantum electrodynamics, often abbreviated as QED, and in mathematics, Q.E.D., commonly used to denote the end of proof, is an abbreviation for the Latin quod erat demonstrandum.
[2] Mr. Yang Zhenning in Julian Schwinger (by C. N. Yang, 2013. The Chinese translation of Schwenger is included in the Dawning Collection) and makes the following interesting comments about Fehnmann and Schwenger: Feynmann and Schwenger are the two great physicists of our time. Each of them has made many profound contributions. They were all born in 1918. But in terms of personality, they are almost two diametrically opposed extremes. I often think that one might write a book titled Schwinger and Feynmann: Twenty Percent Emotionally Exposed Funny (impulsive clown), Twenty Percent Professional Nonconformist, Sixty Percent Brilliant Physicist, in order to be great performers, Feynman put in almost as much effort as he did to become a great physicist. Shy, erudite, and speaking and writing in beautifully crafted sentences, Schwinger exemplifies cultured perfectionist and quite inward-looking gentleman.
[3] C.N. Yang 1983, Selected Papers 1945-1980, With Commentary, W.H. Freeman & Company.
[4] F. J. Dyson (1949). "The radiation theories of Tomonaga, Schwinger, and Feynman". Phys. Rev. 75 (3): 486–502; "The S matrix in quantum electrodynamics". Phys. Rev. 75 (11): 1736--1755.
[5] S. S. Schweber 1994. QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga. Princeton University Press.
[6] The awards of Yang Zhenning and Li Zhengdao (awarded immediately after one year of publication) are perhaps a notable exception, as analyzed by Mr. Yang Zhenning, which shows Liu Du and Wang Haoqiang, Einstein, Physics and Life – An Interview with Mr. Yang Zhenning, Review of Science and Culture, 2005 (Vol. 2), No. 3, 72--89.
[7] See Dyson article on Wikipedia: http://en.wikipedia.org/wiki/Freeman_Dyson.
[8] C. N. Yang 1983.
[9] Dyson 1999." Chen Ning Yang，A Conservative Revolutionary”. There is a Chinese translation, "Yang Zhenning - Conservative Revolutionary", included in Yang Zhenning in 2008. Reprinted in China Reading Daily on April 29, 2015.
[10] Dyson 1982.
[11] It can be added that, according to Feynman's book You're Funny, Mr. Feynman! According to the self-report of Surely You re Joking, Mr. Feynman!, the senator of the Institute for Advanced Study did have such expectations of Feynman and sent a letter of appointment to Feynman, but Wasenmann refused. This is understandable: Feynmann was not only a physicist, he was also an actor, and the podium was an indispensable stage for him. More importantly, Feynman made it clear: "I have no responsibility to be like they expect me to be. It’s their mistake, not my failing.”
<h2 class = "pgc-h-arrow-right" > Four Cornell's Lessons and Princeton's Redemption</h2>
From 1949 to 1951, Dyson returned to England as a researcher at the University of Birmingham. R. Pyles, Chair of the Department of Physics Peierls) received him. In Birmingham, A. Salaam, who had just completed his PhD, Salam) called his "hero" Dyson and asked for a visit. The meeting inspired Salam to advance Dyson's work on re-normalization and began his illustrious academic career.
In 1950, Dyson and the mathematician V. Robert, who came to Princeton for Advanced Study, visited. Huber) married.
Dyson returned to the United States in 1951. To attract Dyson, Cornell University hired Dyson as a professor of physics without a Ph.D. From 1951 to 1953, Dyson lectured at Cornell while instructing postdocs and graduate students to do theoretical calculations. His lecture notes, Higher Quantum Mechanics, helped many people enter the field, and was officially published as a book more than sixty years later. In terms of mentoring students, he considered it such a failure that he decided not to bring graduate students from now on. [2]
The story goes like this. When Dyson made some progress with his students, he went to the University of Chicago to visit Fermi, an expert in the field. Dyson was proud to present their calculations to Fermi, looking forward to Fermi's approval and excited reaction. To his surprise, Fermi was unmoved, but calmly commented, "There are two methods of calculation: the first, which I prefer, is based on clear physical images; the second is based on a strict mathematical framework." And your calculations, are not. For Fermi's criticism, Dyson was convinced. In fact, their calculations are not particularly consistent with the experimental data. In 1999, at an emeritus dinner for Fermi's student and dyson's old colleague Yang Zhenning, Dyson gratefully recalled the crucial lesson Fermi had taught him.
...... Although I was not a student of Fermi, I had the privilege of talking to Fermi for twenty minutes at a critical moment in my academic career. I have learned more in these twenty minutes than I have learned from Oppenheimer in twenty years. ...... In those twenty minutes, his down-to-earth insights eliminated years of unnecessary calculations.
Back at Cornell, Dyson realized that the student's two years of hard work had been wasted, and he felt very guilty about it. This cast a great shadow on him. In order to avoid the mistake of the children again, he decided not to take graduate students anymore. At Cornell, Dyson also had academic contacts with the young Chinese mathematician Zhong Kailai, who solved a mathematical problem that Zhong Kailai had asked him.
What saved Dyson from frustration and guilt was Oppenheimer's offer. Dyson bids farewell to Cornell for Princeton in 1953, and Dyson is hired as a professor at the Institute for Advanced Study (until his retirement in 1994). It should be said that Dyson found a home here. Mr. Jiang Caijian, author of "Normative Theory and the Beauty of Symmetry: A Biography of Yang Zhenning" and former chief writer of Taiwan's China Times, once asked his views on the Institute for Advanced Study in an interview with Dyson[4]:
Jiang Caijian asked: I remember that before Yang Zhenning came here from the University of Chicago to work at the [Princeton Institute for Advanced Study], his teacher Fermi told him that this place was like a monastery, and that he could stay for a while but not for long. Yang Zhenning has been here for seventeen years and you have been here forty years, what do you think about Fermi's words?
Dyson: It varies from person to person. I think Yang Zhenning is right to leave, because he needs a bigger world and a bigger cause. For me, it's good to stay here because I'm not an empire builder, I'm happy here, I'm happy to spend time doing research and writing books, and I'm satisfied. Although I am getting older, I can always maintain my vitality.
Being able to work in the convent of the Institute for Advanced Study in Princeton was the greatest fortune of Dyson's life. Dyson made many scientific colleagues at the Institute for Advanced Study. For example, among the colleagues and visiting scholars at the Institute are Yang Zhenning, Li Zhengdao, and M. Mehta. L. Mehta), R. Yost Jost), A. Lenard）。 Dyson was also frequently exchanged by E. Dyson, a professor at nearby Princeton University. P. Wigner), V. Bargmann), E. H. Lieb) and others. Much of Dyson's work is shaped by communicating with them.
In 1957, a fortuitous reason— the British government did not recognize Dyson's children born in Switzerland and the United States, and therefore did not issue them passports — led Dyson to eventually become a U.S. citizen. Dyson wrote in "The Guide"[5]: "I was originally British, but I only became an American citizen by mistake. I am proud of both countries. "I asked Dyson about the cultural differences between the United Kingdom and the United States. He replied:
The cultures of the United Kingdom and the United States are different in many ways. Britain has a longer history and a more culture, but is pessimistic about life. The United States, on the other hand, has a more diverse citizenship, is technologically powerful, and offers many opportunities for young people. One of the most obvious differences is in the attitude towards games and competitive sports. Children in england are taught that the most important thing is to be a generous loser, to ensure fairness when competing, and to lose grace when failing. And American children are taught that the most important thing is to be the winner and to win by all means. Both cultures are precious. I'm glad that the world has retained their space at the same time.
[1] Advanced Quantum Mechanics, World Scientific, 2007.Electronic http://arxiv.org/abs/quant-ph/0608140 available online.
[2] Dyson himself did not have a Ph.D., so there is no information about Dyson in the Mathematics Genealogy Project. Bate can be counted as Dyson's mentor, but they are not in a formal mentor-graduate relationship. Dyson's talent is mainly based on self-study.
[3] Dyson 1999.
Jiang Caijian 1998. Dyson: Science is Closer to Art Than Philosophy. Taiwan's China Times, January 30, 1998 (Social Comprehensive Edition).
[5] Dyson 1992.
< h2 class="pgc-h-arrow-right" >5 Subsequent physics and mathematical work</h2>
The American Mathematical Society's 1996 Selected And Commentaries on Dyson Papers includes some of his most important scientific work up to 1990. The book mimics the format of Yang Zhenning's 1983 selected essays, bringing together 49 pages of commentary as an opening. Just as Yang Zhenning's commentary describes the reason why Yang Zhenning became Yang Zhenning, Dyson's commentary also describes the reason why Dyson became Dyson.
The work included in the Dyson Papers Anthology and Commentary is divided into three areas: mathematics, physics, engineering, and biology. We will only introduce his physics and mathematical work here.
Of all dyson's physics work after 1948, two strokes deserve special writing. The first was 1961 work on stochastic matrices, the result of a conversation between Dyson and his founder, Wigner. For Dyson, the work was extremely exciting, and he wrote in the Commentary to Dyson's Selected Papers[1]:
In 1961, I took an academic leave at Brookhaven and finished a series of three papers at breakneck speed. It's as if I'm discovering new questions to answer every day. Each beautiful equation leads to another, more beautiful equation the next day.
In the years that followed, Dyson continued to return to this theme from time to time. Thanks to Wigna, Meta, M. Gordon Through the efforts of Gaudin, Dyson, and others, stochastic matrices have evolved into a systematic science, and they have been popular until now. Often touted as a beautiful talk, a casual conversation between Dyson and Hugh Montgomery, a number theorists at the Institute for Advanced Study, led them to discover a subtle correlation between random matrices and the Riemann hypothesis in number theory.
Dyson's second major job was in statistical physics. In 1965-1966 he collaborated with Lerner to prove the stability of matter for the first time mathematically rigorously. The problem was raised a year ago by M. Fisher. Fisher) and D. Luerre Ruelle) was raised as a bounty (a bottle of champagne). Dyson and Lerner's mathematical skills stemmed from a 1957 improvement in a work by Lee and Yang Zhenning. Dyson and Lerner's nearly 40-page complex proof was discovered 10 years later by Liebu and W. Søring. Thirring) simplified to less than 3 pages. In this regard, Dyson reflected in the "Commentary on the Selected Works of Dyson":
Why are our proofs so bad and their [Lieb and Serling' proofs so beautiful? The reason is simple. Lerner's and I's proof is based on some mathematical technique, in the jungle of inequalities, without any ideas from the physical side to guide. Lieb and Serling, on the other hand, proceeded from the idea that matter is stable because the classical Thomas-Fermi model was stable, seeking the right mathematical language to translate this idea into rigorous proof. When I was a student at Cambridge, the mathematician Littlewood once said in class that the first-rate mathematicians were those who published bad proofs. After the first-rate mathematicians published the bad proofs, the second-rate mathematicians studied the details and gave better proofs. Two proofs of the stability of matter provide a counterexample to Littlewood's maxim. Liebu and Serling found good proofs, and they were both first-rate mathematicians and first-rate physicists. The main value of our bad proof is that it motivates Lieb and Serrin to seek more beautiful proofs.
Although outside of mainstream mathematics, Dyson was also influential in the mathematical community. In general, mathematicians appreciated his view of mathematics more, so Dyson was often invited to give lectures on various occasions. For example, in 1965, he was invited by the American Association for Industrial and Applied Mathematics to give a John von Neumann Lecture entitled "Applications of Group Theory in Particle Physics." In 1972, he was invited by the American Mathematical Society to give a Lecture entitled "The Missed Opportunity"[2]. In Gibbs' speech, Dyson gave many examples that strongly showed that mathematicians, because of their alienation from physicists, missed many important discoveries such as the principle of special relativity implicit in Maxwell's equations. Dyson learned his lesson of missing out on the mathematician I. G. Macdonald) found an opportunity for a wonderful connection between modal forms and affine Lie algebras, "and that's only because number theorists Dyson and physicist Dyson didn't communicate with each other" — a call for mathematicians to talk more to physicists and advance scientific research together.
Dyson's oratorical talent may have been influenced by Martin Luther King Jr. (M. Dyson). L. King's excitation. In his book Cosmic Waves, he mentions Martin Luther King Jr.'s famous "I have a dream" lecture on August 28, 1963.[3]
Martin Luther King Jr. spoke like a prophet in the Old Testament. I was so close to him that I cried when I listened to him, and I wasn't the only one who cried. “I have a dream.” He repeats this phrase over and over again as he describes to us his vision of peace and justice. In a letter I wrote that night, I wrote, "I'm ready to go to jail for him." "I didn't know at the time that I was hearing one of the most famous speeches in human history, only that it was the greatest speech I'd ever heard. I didn't expect Martin Luther King Jr. to be assassinated five years later.
In 1987, the centenary of the birth of the great Indian legendary mathematician Ramanujan, Dyson was invited to participate in an academic commemoration event because of his early research on Ramanuen's work. His lecture was "Strolling through the Gardens of La Manuean". In his speech, he asked mathematicians and physicists to focus on Ramanuen's last remarkable discovery, mock functions. He said with sustenance (reminiscent of Martin Luther King Jr.'s famous speech):
My dream is that in my lifetime I will be able to see that our young physicists realize the correspondence between what is predicted by superstring theory and the facts of nature, extending from the functions to the thermo-theta functions.
Fifteen years later, in 2002, the young Dutch mathematician S. Zwigs Zwegers) mathematician D. Zwegers at the Max Planck Institute of Mathematics in Bonn, Germany. Zagier) completed his doctoral dissertation entitled "Thesista Function" under his direction. On this basis, in 2008, the mathematician K. Breman of the University of Wisconsin in the United States Bringmann) and K. Ono Ono) took another step forward. They responded to Dyson's call and partially fulfilled Dyson's dream. More in line with Dyson's prediction is the "Umbral Moonshine Conjecture" proposed by Chinese mathematician and theoretical physicist Miranda Chih-Ning Cheng and her collaborators in 2012 and proved by Ono et al. in 2015. Professor Cheng Zhining herself agreed with this, and she told me that she did not think of Dyson's words when she first proposed this conjecture. Dyson's mathematical foresight is evident here.
In 2008, Dyson prepared a lecture entitled "Birds and Frogs" for the Einstein Lecture of the American Mathematical Society. The lecture was temporarily cancelled due to Dyson's illness, but the transcript[4] was published. The basic idea of the speech was taken from "Omnipresence of Infinity",[5] but with a higher intention, Dyson mentioned many interesting and philosophical topics. Dyson begins by writing:
Some mathematicians are birds, some are frogs. Birds soar high in the sky, overlooking the vast field of mathematics, up to the distant horizon. They are happy to unify our minds and incorporate a wide variety of problems from different parts of the mathematical landscape. Frogs live in mud and can only see flowers growing nearby. They take pleasure in the details of special objects and solve only one problem at a time. I happen to be a frog, but many of my best friends are birds. The theme of my talk tonight is "Birds and Frogs." Mathematics requires both birds and frogs. Mathematics is rich and beautiful because the bird gives it a broad view and the frog gives it intricate detail. Mathematics is both a great art and an important science because it combines the universality of concepts with the profundity of structure. It would be unwise to assert that a bird is superior to a frog because it sees farther, or to assert that a frog is superior to a bird because the frog sees deeper. The world of mathematics is vast and deep, and we need birds and frogs to work together to explore it.
The metaphor of the bird and the frog is so wonderful that one cannot help but wonder if Dyson is secretly deriving the ancient Greek poet Archilochus's metaphor of the hedgehog and the fox, as the writer I. Berlin used it to comment on L. Tolstoy. Tolstoy) has the same view of history. I once emailed Dyson to ask if his title "Birds and Frogs" was inspired by Achirocus's idea that philosophers divide into "foxes and hedgehogs". He replied: "Yes, the title of the speech comes from the Greek dramatist Aristophanes, who wrote two famous plays, The Bird and the Frog, but whose ideas are similar to Achirocus's fox-hedgehog dichotomy. I have found that for both mathematicians, the frog and the bird are a better metaphor."
Dyson gives many examples of frogs and birds, such as F. Bacon and R. Descartes, Bersikovich and Weyl, von Neumann and Y. Manin, and implicitly compares himself with Yang Zhenning as another pair:
After a few years as a student at Persekovich, I came to Princeton and got to know Weil. Weyl is a typical flying bird, just as Persekovich is a typical frog. I was fortunate enough to have a year-long stint with Weil before he retired from the Institute for Advanced Study in Princeton, from which he returned to his hometown in Zurich. He liked me because that year I published a paper on number theory in the Annals of Mathematics and a paper on the theory of quantum radiation in the Review of Physics. He was one of the few people who were experts in both disciplines at the time. He welcomed me to the Institute for Advanced Study and wanted me to be a bird like him. To his disappointment, I was nothing more than a hopeless frog.
The past fifty years have been difficult times for birds. Even in difficult times, there is work to be done by the birds, and the birds show the courage to overcome the difficulties. Shortly after Weil left Princeton, Yang Zhenning came to Princeton from Chicago and moved into Weil's former home. Among physicists of my generation, Young took weil's place as a leading bird. While Weyl was still alive, Young and Robert Mills discovered the Non-Abelle Gauge Field Yang-Mills Theory (Weyl died in 1955, the Young-Mills paper was published in 1954), a brilliant generalization of Weyer's early normative field ideas.
The first paragraph is similar to dyson's remembrance of Oppenheimer quoted earlier! It is hard to imagine that dyson, who is only 25 years old, can be so favored by both the leader of the mathematical community, Weil, and the head of the physics community, Oppenheimer! You know, as a descendant of Weyl in physics, Yang Zhenning, one of the biggest regrets in his life is that he didn't know that Weyl, who was once close at hand, had always been obsessed with the principle of norms! Yang Zhenning once wrote[6]:
Among physicists, no one knows that his [Weyl]'s interest in normative field ideas is relentless. Neither Oppenheimer nor Pauli ever mentioned this. I suspect they also didn't tell him about my paper and Mills' 1954 paper. If they had told him, or if he had stumbled upon our article, then I can imagine that he would have been very happy and would have been very excited. Because I put together the two things he cherishes most—the normative field and The Li Qun.
Yang Zhenning's regret can really be described as "the most distant distance in the world is not the distance between life and death, but I stand in front of you, but you don't know that I love you". The "you" here is asuka Waiel. The metaphor of the bird and the frog highlights the difference between Yang Zhenning and Dyson, just as Yang Zhenning once borrowed the metaphor of the fox and the hedgehog to highlight the difference between Hua Luogeng and Chen Shengshen, two famous mathematicians in modern China.
Dyson also jokingly suggests a possible way to overcome the Riemann hypothesis (instead considering the enumeration and classification of the Riamann hypothesis). It can be seen that Dyson has not let go of his youthful dreams (to prove the Riemann hypothesis), just like Qu Yuan said, "Yu Yu is good at this strange dress, and he is old but not weak".
Dyson was interested in von Neumann's work ( such as game theory and computer theory ) , and in May 2010 he was invited to give a popular report at Brown University entitled "Walking in von Neumann's Garden".[8] As can be seen from the titles of the two speeches, "Strolling through von Neumann's Garden" and "Strolling through Ramanujan's Garden," Dyson tended to see mathematics as an intellectual pastime. Perhaps, in his eyes, mathematics is not so much an intellectual struggle as it is an adventure hunt.
Dyson still returns to pure mathematical research from time to time. In 2012, dyson, who was nearly ninety years old, also published a paper in the mathematical journal Ramanuen Magazine titled "Spin-offs and The Synthesis of Giant Regularities", and also collaborated with W. Pres. Press) collaborated in publishing a research paper on the "prisoner's dilemma" in game theory in advances in the National Academy of Sciences. But Dyson argues that his mathematical and physical research since 1990 is more interesting than particularly academic. He said in his autobiography for The Face of Science[9]:
Most scientists see science as a skill similar to building a house or cooking, and a few scientists see science as a philosophical exploration. I belong to the former. I never cared if the problem I was trying to solve was important. Irrelevant questions in the field of pure mathematics are just as interesting as important questions in atomic physics and biology.
In May, World Science Press, Singapore, published a new book by Dyson, featuring a selection of representative essays from 1990–2014, titled Birds and Frogs. This can be seen as a sequel to his 1996 Anthology of Essays, but its focus, like From Eros to Gaia, is mostly popular rather than professional.
[1] Dyson 1996. Selected Papers of Freeman Dyson with Commentary. American Mathematical Society.
[2] Dyson 1972, “Missed opportunities”, Bull. Amer. Math. Soc. 78 (1972), 635–652.
[3] Dyson 1982.
[4] See http://www.ams.org/notices/200902/rtx090200212p.pdf%3Fq%3Dbirds-and-frogs. There are at least 4 Chinese translations of this speech. For example, it can be seen: the translation of Zhao Zhenjiang in the first issue of Mathematics translation lin in 2010 (electronic version is available on the Internet); the translation of Zhao Xuexin in the second issue of mathematical humanities in 2014, "Birds and Frogs".
[5] Dyson 1988. Infinite in All Directions. There is a Chinese translation of "All-round Infinity". Li Du Chinese translation. Beijing: Sanlian Bookstore.] 1997
[6] C. N. Yang 1985. Hermann Weyl’s contribution to physics. Income C. N. Yang 2013. Chinese translation, "Weyl's Contribution to Physics", included yang Zhenning 2008.
[7] C.N. Yang 2013. On page 188 of the book, Yang wrote that Isaiah Berlin (1900-1997) popularized two different types of Greek ideas about philosophers: "The fox mastered many skills, while the hedgehog mastered one skill." "I think this is an excellent way to describe the difference between Hua Luogeng and Chen Shengshen: Hua Luogeng has a wide range of interests and has made important contributions to several different branches of mathematics; while Chen Shengshen focused on one branch of differential geometry, but he revolutionized this branch, and this innovation later had a profound impact on the major branches of geometry, algebra, analysis, topology in the 20th century, and even deeply influenced the development of theoretical physics for nearly 40 years.
[8] See http://www.ams.org/notices/201302/rnoti-p154.pdf. There are two Chinese translations: "Walking in the Garden of Johnny von Neumann", translated by Duan Liuliu and Liu Ruiyi, Mathematical Translation Lin, No. 2, 2014; "Walking in Von Norman's Garden: The Fall of Genius", translated by Zhao Xuexin, Mathematical Humanities, No. 3, 2015.
[9] M. Cook 2005.
[10] Dyson 2015a. Birds and Frogs: Selected Papers,1990-2014. World Scientific. An introduction to the book can be seen in Lin Kailiang, the great physicist of the great scientist's pen - Dyson, "Birds and Frogs", China Reading Daily, August 5, 2015, 13th edition.
<h2 class="pgc-h-arrow-right" > six scientific humanities writing</h2>
In 1975, the Sloan Foundation invited Dyson to write an autobiography of science. While thinking about how to reply, Dyson recalled the words of his teacher Hardy: "Young people should prove theorems, and old people should write books." He accepted the invitation and began his writing career. This led to his debut novel, Cosmic Waves, published in 1979. Dyson once said his life began at the age of 55, when he wrote his first work. Since then, Dyson has spent half of his research and writing time. Dyson's fame as a writer soon surpassed his fame as a scientist. In addition to the books mentioned at the beginning of this article that were translated into Chinese, there are also influential ones such as "The Origin of Life", "Weapons and Hope", and "From Eros to Gaia". For his outstanding achievements, Dyson received the Lewis Thomas Prize in 1996, known as the "Poet and Scientist".
Now let's introduce his most important book, Cosmic Waves, which has been translated in seven languages, including two Chinese translations. The title of the book, "Disturbing the Universe," is taken from the poet T. S. Eliot's famous work " Pruflak's Love Song" According to Dyson's reply to the author, the meaning of the title is: our future activities will change the fate of the universe. In 1993, Dyson wrote a wonderful preface to Qiu Xianzheng's translation of Cosmic Waves. In his preface,[2] he writes:
The book takes a romantic view of the world of science, comparing the life of a scientist to the voyage of an individual soul; it deliberately skips the established framework of each scientist's life, the institution in which he works, and the political and economic framework. In the history of science, groups and individuals are on an equal footing, but most historians tend to focus on the activities of institutions and groups. This book places special emphasis on the individual, because I wanted to write something new and different. My romantic view of science, though not the whole truth, is an indispensable focus of truth.
Chinese readers may be more accustomed to seeing science as a collective creative enterprise than American and European readers; therefore, I am also pleased to introduce my personal views to Chinese readers. If you don't think my story is novel and strange, and don't notice that it's different from the way you're used to thinking, then you've wasted the original intent of this book.
This book was published in the United States fourteen years ago, and since then I have written four more books for non-professional readers, but Cosmic Waves is still my favorite. It was my first book, and the words came from the heart, and I put more effort and emotion into it than several other books. If only one of my writings had survived through the ages, and I had the right to choose which one, I would not hesitate to choose this one.
"Cosmic Waves" is bound to be able to pass on through the ages. Because Dyson has a wide range of interests and rich life experience, this book is quite interesting to read. The sixth chapter of the book is devoted to his four-day driving trip to Albuquerque with Feynman in 1948, and repeated discussions with Feynman along the way led Dyson to finally gain a deep understanding of Feynman's method of path integration (also known as "summing history"). Dyson's companionship with Feynman was initially an accidental local event, but it had a profound impact on the lives of both Dyson and Feynman, and eventually profoundly changed the overall face of twentieth-century physics. Dyson thought it was the luckiest occasion of his life. (Inexplicably, Feynman himself seems to have ignored Dyson's influence on him, and he rarely mentions Dyson.) ）
Over the years, Dyson has been working tirelessly. In addition to writing books, he has written many interesting articles. For example, in 1955, when Herman Weil, a great mathematician of the twentieth century and a permanent member of the Princeton Institute for Advanced Study, died, Dyson wrote a short obituary for Nature, Britain's top scientific journal, paraphrasing Weil's values as a great mathematician.[3]
He [Weyl] once said to me half-jokingly, "My job is to try to unite truth and beauty; when I have to make a choice, I often choose beauty." ”[4]
Truth and Beauty
Coat of arms of the Institute for Advanced Study in Princeton[5]
When Feynman died in 1988, Dyson edited a memoir, "Feynman in 1948" (see Dyson 1992), based on his previous letters to his parents.
In recent years, some great physicists born in the early twentieth century have passed away, and the arrival of the new century has come the turn of many great physicists to celebrate their centennials. Many of those who had associated with Dyson, such as Pauli (1900-1958), Fermi (1901-1956), Dirac (1902-1984), Oppenheimer (1904-1967), Bate (1906-2005), Terer (E. Teller, 1908-2003), S. Chandrasekhar Chandrasekhar, 1910-2005), Kemer (1911-1998), Wheeler (J. A. Wheeler, 1911-2008), Salam (1926-1996), etc., he wrote memoirs.
Dyson also wrote for The New Yorker and Scientific American from time to time, and often wrote prefaces and reviews of new scientific works, so his name appeared frequently in the New York Review of Books. In 2013, Zhejiang University Press published a Chinese translation of Dyson's book review, The Scientist as Rebel. Just recently, Dyson published his second book review, the Dreams of Earth and Sky. In recent years, many excellent popular science books have been published in China, in fact, many of them have book reviews written by Dyson, such as the American popular science writer C. Reid's Hilbert,[8] J. Gleick's Biography of Newton,[9] and A Brief History of Information,[10] by theoretical physicist B. Green. Greene' The Structure of the Universe,[11] the Feynman Codex, edited by Feynman's daughter Michelle Feynman,[12] and the French mathematician I. Ekeland's Best Possible World,[13] by The British biographer G. Farmelo) in Quantum of Quantum: The Biography of Paul Dirac. If the translator can translate these beautiful book reviews together and attach them to the Chinese translation, it will surely be very instructive to the reader.
[1] Lewis Thomas, 1913–1993, American medical scientist, biologist, and popular science writer. Many of his books have been translated into Chinese, such as The Celebration of Cell Life and Jellyfish and Snails. The Lewis Thomas Prize can be found on Wikipedia for detailed information. It is worth mentioning that in 2015, two mathematicians took the crown for the first time, Ian Stewart and Steven Strogatz.
[2] Dyson 1998.
[3] Dyson 1956. “Obituary : Hermann Weyl”, Nature 177: 457-458. 戴森在给《自然》投稿时曾注明：“I asked four people in Princeton who are better qualified than I am to write it, all of them excused themselves, and so I ended by writing it myself.” （Records of the Office of the Director / Faculty Files / Box 37 / Weyl, Hermann 1946-1993.）
[4] Coincidentally, the Chinese writer Wang Zengqi (1920-1997) expressed a similar view: I am not seeking profundity, but harmony.
[5] The naked woman on the left represents Truth (presumably because "truth is naked"?). ), the dressed representative on the right represents Beauty. The whole design was inspired by John Keats's famous poem "Ode to the Ancient Urn of Greece" (Afterglow Chinese Translation): Beauty is true, true is beautiful - this is what is known and should be known in the world.
[6] Dyson 2013. The Rebellious Scientist. Xiao Mingbo, Yang Guangsong, trans. Hangzhou: Zhejiang University Press.]
[7] Dyson 2015b. Dreams of Earth and Sky. New York Review Books. The Chinese translation of "Dream of Heaven and Earth" will be published by Zhejiang University Press.
Translated by Yuan Xiangdong and Li Wenlin. Shanghai Science and Technology Press. 2007. Dyson's book review is available at Science 27 November 1970: Vol. 170 no. 3961 pp. 965-966.
Wu Zheng translation. Beijing:Higher Education Press.] 2014. Dyson's book review includes the Chinese translation of Old Newton, New Impressions, by Dyson in 2013.
Gao Bo translation. Beijing:People's Post and Telecommunications Publishing House.] How We Know, The New York Review of Books, March 10, 2011. Income dyson 2015b.
Liu Ming, cited. Changsha:Hunan Science and Technology Press. 2013. Dyson's book review includes the Chinese translation of The World on Strings, included in Dyson in 2013.
Translated by Ye Weiwen. Changsha:Hunan Science and Technology Press. 2008. Dyson's book review included the Chinese translation of The Wise Man in Dyson 2013.
Feng Guoping and Zhang Duanzhi. Beijing:Science Press.] 2012 Dyson's Book Review of Nature s Greatest Book, The New York Review of Books, October 19, 2006. Income dyson 2015b.
Translated by Lan Mei. Chongqing University Press. 2015 Dyson's Book Review Silent Quantum Genius, The New York Review of Books, February 25, 2010. Income dyson 2015b.
< h2 class="pgc-h-arrow-right" > seven conclusions</h2>
As a mathematician, Dyson's mathematical abilities are beyond doubt. But he wasn't particularly proud of his status as a mathematician. In his opinion, some mathematicians are too isolated and impersonal. He later divorced his wife Huber because she was a mathematical lunatic, obsessed with math, even ignoring her children, and never woken up, unlike Dyson when she was awakened by her mother when she was young. In 1958, Dyson married marathon runner Imme Jung. Dyson had six children, five of whom were daughters, and his only son, George Dyson, was a prominent historian of science.
Dyson with his wife and daughter (family portrait of George's absence)
http://www.achievement.org/autodoc/page/dys0int-2
George Dyson
Dyson's mathematical career was closely related to the Cambridge School of Mathematics, especially Hardy, and it was Hardy and Wright's Introduction to Number Theory that sparked Dyson's lifelong interest in number theory. It should be noted that although Dyson's ability to learn and absorb new things is very strong, the mathematics he learned during his two years of college is actually very limited .[2] As Dyson wrote to this writer, his teachers Hardy and Littlewood, as mathematical leaders in Britain, even hindered the progress of British mathematics:
Hardy and Littlewood were old-fashioned mathematicians who lived in the twentieth century but did nineteenth-century mathematics. Although they did a beautiful job, they had no interest in new abstract ideas that originated in France and Germany. As a result, the younger generation of British mathematicians, including me, grew up in an environment far removed from the new mathematics that flourished in France.
In fact, mathematics underwent rapid development in the 1930s and 1940s, but Hardy and Littlewood were busy studying classical mathematics (analytic number theory and classical analysis), which led to the next generation of Mathematicians in Britain not keeping up with the modern mathematical trend of the rise of abstract algebra and geometric topology. In Cambridge at the time, only Hodge was the only exception. Not only did he keep up with modern mathematics, but he also made great achievements around the time Dyson enrolled in Cambridge. But Dyson was not attracted by Hodge's lectures. All of this leads to Dyson's lack of a relatively comprehensive understanding of mathematics. Dyson's mathematical vision and taste were confined to Hardy, Littlewood, and Ramanujan. But the work of these people (analytic number theory and discrete mathematics) is too far away from mainstream mathematics. In particular, Ramanujan's work embodies a strange beauty, which is simply "before the ancients, after the people do not see the comers" . In LaManuean, you don't see history and tradition at all, and Ramanuen is like his fellow poet, R. Tagore. Tagore) in the poem "The sky has not left a trace of me, but I have flown by" in the bird. "There are occasional fingers and claws on the mud, and Hongfei's recounting things", tracing his footprints is a promising future. This kind of mathematics is really unsustainable. (Another historical reason, of course, is that LaManuean's lost Notebook was not yet discovered.) ）
Although Dyson made some valuable achievements in the study of number theory in the early days, he was not satisfied with the cold atmosphere of high and low in pure mathematics, so he decided to leave pure mathematics and turn to applied mathematics. In the introduction to the book Sun, Genome, and the Internet,[3] he writes:
Later in my scientific career, I was not faithful to Hardy's ideals. At first I followed in his footsteps into the field of number theory and solved several number theory problems. These are beautiful questions, but they are irrelevant. Later, after three years of working as an expert in number theory, I decided to become an applied mathematician. I think it is much more exciting to understand the fundamental mysteries of nature than to continue to prove theorems that can only interest a handful of mathematicians.
As a physicist, in the early days, because of Fermi's suggestion, Dyson realized that doing physical research can not only rely on pure mathematical calculus, but also need the guidance of physical intuition. Dyson was well aware that he lacked physical intuition. His success in physics is due to extensive exchanges with physicists, to his mathematical taste and talent: he does physics with the values of mathematicians.
In his 1964 article Mathematics in the Physical Sciences,[4] he wrote in Scientific American: "Mathematics for physics is not only a tool for calculating phenomena, but also a major source of concepts and principles for the creation of new theories. As a resonance, Mr. Yang Zhenning has expressed similar views[5]:
Most of my physics colleagues have taken a utilitarian approach to mathematics, perhaps because I appreciated mathematics more because of my father's influence. I admire the values of mathematicians, the beauty and power of mathematics: its tactical ingenuity and flexibility, and its strategic foresight. And, miraculously, some of its wonderful concepts are the basic structures that govern the physical world!
However, physicists and mathematicians have different values, and Dyson's values are not widely recognized by physicists. This is in stark contrast to what mathematicians think of him: mathematicians do not consider Dyson's mathematical work important, but are willing to listen to his mathematical insights (for example, the famous contemporary mathematician M. F. Atiyah mentioned in the preface to his fifth volume of The Anthology of Papers) that he had benefited from conversations with Dyson), while physicists recognized Dyson's physical achievements (for example, he won the 1981 Wolf Prize in Physics) but rejected his mathematical values.
Dyson positioned himself as a mathematical physicist in his essay "The Unseasonable Pursuit",[6]. He understood the aim of the discipline of mathematical physics as an understanding of physical phenomena in a rigorous style and method of pure mathematics; the goal of mathematical physicists was to clarify the precise mathematical meaning of the concepts that were the cornerstones of physical theory. As a veritable mathematical physicist, Dyson is highly recognized. At the 2012 World Congress of Mathematical Physicists, Dyson received the field's highest prize, the Henri Poincaré Prize from the International Mathematical Physics Association.
However, both as a mathematician and as a physicist, Dyson achieved only partial success. Only Dyson, as a writer, can be regarded as a complete success. If a hundred of the most accomplished mathematicians were to be selected from twentieth-century mathematicians, Dyson would not have been shortlisted. As a result, his young dream of becoming one of the characters in the twentieth-century Mathematical Elite series was bound to fail. As a physicist, although he was famous as early as the age of twenty-five, he never expected himself to become a great figure like his colleague Yang Zhenning.
Physicists have long seemed to have higher expectations of Dyson, such as Philip Anderson, a physics professor at Princeton University and winner of the 1977 Nobel Prize in Physics, who told P. Servi about his work. F. Schewe) wrote in his biography of Dyson,[7] "An iconoclast s career": "Dyson was a man of great ability and great achievements, but what if he had a specialization in his craft?" This is presumably expecting Dyson to become a "hedgehog" or a "flying bird." But it should be pointed out that Dyson's extensive interest and rich imagination make him look like a very comprehensive person, and people expect him to be a person who can oversee the overall situation, but in fact, his primary identity is a mathematician, and he is better at analysis and careful verification.
Perhaps Dyson could not have occupied a particularly high position in the mathematical and physics circles of the twentieth century, but as a writer among scientists, he was absolutely second to none.
Dyson once replied that hardy was hardy in writing because he wrote an excellent book for non-mathematical readers, "A Mathematician's Confessions." Hardy's writing is really fascinating, perhaps because he has experienced the most romantic legend in the history of mathematics and discovered the self-taught Indian mathematician Ramanujan, so the writing is also passionate. However, Hardy's remarks are more extreme, and once absolute, they will create a strange beauty and indestructible force, so that readers often unconsciously believe it. Hardy, for example, wrote in his defense:
Only a small part of mathematics is useful, and even this small part is boring. The "real" mathematics of the "real" mathematicians (whether it is "applied" mathematics or "pure" mathematics), namely the mathematics of Fermat, Euler, Gauss, Abel, and Riemann, is almost all useless. If it can explain the existence of true mathematics, it should be explained as art.
Hardy is a bit like his compatriot Oscar Wilde, another genius who "doesn't say anything to the death." And because Hardy has experienced two world wars, and the genius Ramanujan, who he discerned, died young, he was full of pessimism everywhere when he picked up his pen in his twilight years, which may have invisibly touched some readers. [8] [8] Some of his statements, such as his statement that "the mathematics of Fermat, Euler, Gauss, Abel, and Riemann, are almost all useless".
For writing and mathematical research, Hardy is entirely based on beauty as the supreme law. He wrote in The Confession of a Mathematician: "Beauty is the first touchstone: ugly mathematics is not visible in the day." It can be said that Hardy was a mathematician who was "pure" to the extreme, even purer than Weil. The author once asked Dyson in a correspondence which one he would choose. He replied that unlike Hardy and Weil, he simply prioritized the real when doing research and the wonderful when telling stories.
In contrast, Dyson's writings flashed with wisdom and humor from time to time, and his judgment was more neutral, and he could reconcile bohr's principle of complementarity and Heisenberg's uncertainty principle as philosophical basis for statements that may seem contradictory. Moreover, Dyson's vision is broader than Hardy's. He read about Verne, Tolstoy, and O. Wells in his early years. Wells), Haldane, Huxley Huxley), G. Orwell Orwell's work had a great influence on him. Like his predecessors, Dyson had extraordinary imagination and insight. In addition, Dyson often draws on the sidelines of his writing, especially drama and poetry, which are the result of his parents' influence since childhood and Frank's influence in middle school, which adds a lot to his work. For example, in the index of cosmic waves, you can see the names of many poets and writers, such as W. Auden. H. Auden), W. Black Blake), J. Goethe W. von Goethe), J. Milton Milton), W. Shakespeare Shakespeare) and W. Yeats B. Yeats）。 Dyson says in The Origin of Life that his favorite poet was William Blake, because even if his conjectures or predictions turn out to be wrong, Blake's famous phrase (quoted from A Vision of the Last Judgment) has long since relieved him: To be an Error and to be Cast out is a part of God's design[9].
Hardy and Dyson have in common that perhaps can be summed up in Bacon's famous quote: "If there is no peculiar singularity, there is no beauty that is different." And if we want to point out the difference between Dyson and Hardy, perhaps we can steal Hardy's own words.[10]
If I could really put my statue on a monument in London Square, would I hope that the monument would be so high that people would not be able to see the statue, or would I hope that the monument is so short that people can see the statue at a glance? I would choose the former. As you can imagine, Dyson [originally written by Dr. Snow. Snow)[11]] would choose the latter.
The author once asked Dyson if he agreed with the latter statement? He agreed. In fact, Dyson said in the preface to His book From Eros to Gaia,[12] "The purpose of all my works is to open a window for experts high within the temple of science to look out into the outside world, and for the general public outside the academic ivory tower to look inside." "He succeeded.
In 2013, Dyson took a photo of his 90th birthday and 60th anniversary celebration at IAS
[1] D. J. Albers, “Freeman Dyson: Mathematician, Physicist, and Writer”, The College Mathematics Journal, Vol. 25, No. 1 (1994), pp. 3-21.
[2] A clear proof of Dyson's paper, "The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics"," in journal of mathematical physics, 3, No. 6, pp. 1199-1215, states that the "triplet way" has its roots in the classic Frobenius theorem complex and quaternions), and this is what Princeton University physics professor Bergman pointed out to him. Frobenius' theorem is a fundamental result of abstract algebra, but unfortunately Dyson never heard of it when he was an undergraduate at Cambridge.
[3] There are two Chinese translations of The Sun, genome, and the Internet: Tools of the Scientific Revolution. Translated by Qin Fangming. Beijing: Sanlian Bookstore.] 2000; "Three Events in the 21st Century: A Three-Chapter Dialogue Between Humanities and Science and Technology", translated by Xi Yuping. Taiwan: The Commercial Press, Inc. 1999.
[4] Dyson 2007. Mathematics in the Physical Sciences, in M. Klein, ed., Mathematics in the Modern World, pp. 636-656. Shanghai: Shanghai People's Publishing House.]
[5] C. N. Yang 1983.
[6] Dyson 1981. "Unfashionable pursuits", with the Chinese translation of "Unseasonable Pursuits". Yuan Xiangdong translation. The electronic version can be found in the personal homepage of Professor Zhou Jian of the Department of Mathematics of Tsinghua University http://faculty.math.tsinghua.edu.cn/~jzhou/Buhe.htm
[7] P. F. Schewe 2013. Maverick Genius: The Pioneering Odyssey of Freeman Dyson. Thomas Dunne Books.
[8] In particular, Norman Levinson, Hardy's proud protégé and future chair of MIT's Mathematics Department, wrote a rebuttal in "Coding Theory: A Counterexample to G. H. Hardy's Conception of Applied Mathematics," The American Mathematical Monthly 77 (1970) : 249--258.
[9] Cast in error and discarded, also carefully designed by God.
Hardy 2007.
[11] Snow (C. Snow) P. Snow, 1905-1980), British chemist and author, best known for his 1959 lecture on Two Cultures.
[12] Dyson 1992.
Acknowledgements: The writing of this article was encouraged and supported by Mr. Yang Zhenning of the Institute for Advanced Study of Tsinghua University; Mr. Yang made many valuable comments on the first draft. Dyson went to great lengths to help the author through email, and also provided photos for this article in particular. In the process of writing and revising, the author also received Susan Higgins (S. Higgins). Ms. Higgins), Mr. Jiang Caijian, Professor Chen Guanrong, Professor Tang Tao, Professor Ding Jiu, Professor Ouyang Shunxiang, Professor Ge Molin, Professor Zhou Jian, Professor Xiao Mingbo, Professor Zhang Shu'e, Professor Liu Yunpeng, Professor Zhao Zhenjiang, Professor Fu Xiaoqing, Dr. Cui Jifeng, dr. Zhang Haitao would like to express their gratitude for their great help.
Further reading:
Strange words · Quantum Mechanics Edition – this time I really can't understand | Dr. Lewis
What should China learn from the United States when it revitalizes mathematics? | Ding Jiu
Historical research is not about deceiving oneself: Yau Chengtong's criticism and expectations of Chinese mathematics | Yuan Lanfeng
How fast China's scientific and technological strength is approaching the | of the United States Yuan Lanfeng
Background: The author of this article is Lin Kailiang, a teacher in the School of Science of Northwest A & F University. He holds a bachelor's degree in mathematics from Tianjin University and a doctorate in basic mathematics from Capital Normal University. In addition to teaching, he is keen on the popularization and dissemination of mathematics education and the history of mathematics, and has published many professional or popular articles in journals such as Mathematics Communication, Mathematical Culture, Mathematical Humanities, Mathematical Bulletin, Newsletter of the Chinese Mathematical Society, Mathematical Research and Review, and WeChat public accounts such as "Fun Mathematics", "Mathematics Throughline", "Mathematics Enthusiasts Club", "Harmony Mathematics", "Return to Simplicity", "Intellectuals" and other WeChat public accounts. He co-translated "Mathematicians Explain Mathematics in Primary Schools", "Contemporary Great Mathematicians Painting Biography", "Mathematics and Human Thinking", "Mathematical Giants", "Calculus and Its Applications", etc., and co-edited "Yang Zhenning's Scientific World". One of the masterpieces is the biography of Freeman Dyson, a professor at the Institute for Advanced Study in Princeton, USA, that is, this article. This article was published on February 29, 2020 on the WeChat public account Fun Math (Dyson Legend), and the Voice of the Wind and Cloud is reprinted with permission.
Editor-in-Charge: Xinyue Chen