The story of a mathematician

Hua Luogeng, a modern Chinese mathematician. Born on November 12, 1910 in Jintan, Jiangsu Province, and died on June 12, 1985 in Tokyo, Japan. He graduated from Jintan Middle School in 1924. However, due to his poor family background, he had to drop out of school and work as a shop assistant after finishing junior high school. When he was 18 years old, he contracted typhoid fever, causing disability in his right leg. After 1930, he taught at Tsinghua University. In 1936, he went to visit and study at Cambridge University in England. After returning to China in 1938, he served as a professor at Southwest Associated University. He went to the United States in 1946 and served as a researcher at the Princeton Institute of Mathematics and a professor at Princeton University and the University of Illinois. He returned to China in 1950. He has successively served as professor of Tsinghua University, director and honorary director of the Institute of Mathematics and the Institute of Applied Mathematics of the Chinese Academy of Sciences, chairman and honorary chairman of the Chinese Mathematical Society, director of the National Mathematics Competition Committee, foreign academician of the National Academy of Sciences of the United States, and academician of the Third World Academy of Sciences. Academician of the Bavarian Academy of Sciences, Federal Republic of Germany, deputy director, vice president, and member of the presidium of the Department of Physics, Mathematics, and Chemistry of the Chinese Academy of Sciences, director and vice president of the Department of Mathematics of the University of Science and Technology of China, vice chairman of the China Association for Science and Technology, and member of the Academic Degrees Committee of the State Council. He served as a member of the Standing Committee of the National People's Congress from the first to the sixth session and vice chairman of the Sixth National Committee of the Chinese People's Political Consultative Conference. He has been awarded honorary doctorates from the University of Nancy in France, the Chinese University of Hong Kong and the University of Illinois in the United States. He is mainly engaged in research and teaching in the fields of analytic number theory, matrix geometry, canonical groups, automorphic function theory, function theory of multiple complex variables, partial differential equations, high-dimensional numerical integration and other fields, and has made outstanding achievements. In the 1940s, the historical problem of estimating the complete trigonometric sum of Gaussian was solved and the best error order estimate was obtained (this result has been widely used in number theory); on G.H. Hardy and J.E. Littlewood's work on Waring's problem and E .Wright's results on the Tower Problem made significant improvements and remain the best record today.

Since the 1960s, he has applied mathematical methods to practice, screened out optimization methods and coordinating methods with the goal of improving work efficiency, and achieved significant economic benefits.

Comrade Hua Luogeng is a contemporary self-taught scientific master and a world-famous mathematician. He is the founder and pioneer of research in many aspects such as analytic number theory, canonical groups, matrix geometry, automorphic function theory and multi-complex variable function theory in China. It laid the foundation for future matrix geometry and so on.

Born on November 12, 1910, in a small businessman family in Jintan County, Jiangsu Province, he was 1.65 meters tall. His father, Hua Ruidong, opened a small grocery store, and his mother was a virtuous housewife. After graduating from Renyuan Primary School in the county at the age of 12, he entered Jintan County Junior High School. After graduating from junior high school in 1925, because his family was too poor to study in high school, he had to study accounting at the China Vocational School founded by Huang Yanpei in Shanghai. Within a year, he was forced to drop out of school due to the high cost of living and returned to Jintan to help his father run the grocery store.

In the monotonous life of standing at the counter, he began to teach himself mathematics. In the autumn of 1927, he married Wu Xiaozhi. In 1929, Hua Luogeng was employed as a clerk at Jintan Middle School and began to publish papers in Shanghai Science and other magazines. In the winter of 1929, he suffered from severe typhoid fever. After nearly half a year of treatment, he recovered. However, the joints of his left leg were severely damaged and he was left with a lifelong disability. He had to use a cane to walk.

In fact, when Hua Luogeng was in junior high school, he was not good at his homework and sometimes failed the math test. Hua Luogeng's mathematics teacher who was teaching at Jintan Middle School at the time and the famous Chinese educator and translator Wang Weike (born in Jintan in 1900) found that although Hua Luogeng was playful, he was quick-thinking and often changed his mathematics problems again and again, and his problem-solving methods Very unique and unique.

Once, when a teacher at Jintan Middle School lamented that the school had many "bad students" and no "talents", Wang Weike said: "Not necessarily, in my opinion, Hua Luogeng is one of them!" "Hua Luogeng?" A teacher said with a smile: "You Look at his two characters that look like crabs. Can he be considered a 'talent'?" Wang Weike said excitedly: "Of course, he has little hope of becoming a great calligrapher, but his talent in mathematics is not something you can count on. How can we tell from his words? We must know that when gold is buried in the sand, it looks no different from the sand. As teachers, we most need to have the ability to dig for gold in the sand, otherwise our talents will be buried. Ah!"

In the spring of 1930, his paper "The Reasons Why Su Jiaju's Algebraic Solution to the Fifth Equation Cannot Be Established" was published in the Shanghai "Science" magazine. After seeing this, Professor Xiong Qinglai, who was the director of the Department of Mathematics at Tsinghua University at the time, made inquiries and recommended him to work as a library assistant in the Department of Mathematics at Tsinghua University. At the turn of autumn and winter in 1931, Hua Luogeng entered Tsinghua Garden.

Hua Luogeng studied and worked at Tsinghua University. It took him two years to complete a path that would normally take eight years for ordinary people to complete. In 1933, he was promoted to an assistant teacher and became a lecturer in 1935. In 1936, he was recommended by Tsinghua University and sent to study at the University of Cambridge in England. During his two years at Cambridge, he devoted all his energy to studying difficult problems in mathematical theory and was unwilling to waste time applying for a degree. His research results attracted the attention of the international mathematical community. He returned to China in 1938 and was employed as a professor at Southwest Associated University. From 1939 to 1941, under extremely difficult conditions, he wrote more than 20 papers and completed his first mathematical monograph, "The Theory of Stacked Prime Numbers." Under the influence of Mr. Wen Yiduo, he also actively participated in the anti-Japanese democratic and patriotic movement that was in full swing at that time. "The Theory of Stacked Prime Numbers" later became a classic in mathematics. It was published in Russian in the Soviet Union in 1947 and has been translated and published in German, English, Hungarian and Chinese in various countries.

From February to May 1946, he was invited to visit the Soviet Union. In 1946, the Nationalist Government at that time also wanted to develop an atomic bomb, so it sent three famous scientists, Hua Luogeng, Wu Dayou, and Zeng Zhaoluan, to the United States for inspection. In September, he left Shanghai for the United States with Li Zhengdao, Zhu Guangya and others, first as a visiting professor at the Institute for Advanced Study in Princeton, and later as a tenured professor at the University of Illinois.

■Returning to China for Construction

When New China was founded in 1949, Hua Luogeng felt extremely excited and determined to return to China with his family. The family of five left the United States by boat and arrived in Hong Kong in February 1950. He published an open letter in Hong Kong to students studying in the United States. The letter was full of patriotic passion and encouraged overseas students to come back and serve New China. Xinhua News Agency broadcast the letter on March 11. On March 16, 1950, Hua Luogeng, his wife, and children arrived in Beijing by train.

Hua Luogeng returned to Tsinghua University and served as the director of the Department of Mathematics at Tsinghua University. Then, he was invited by Guo Moruo, President of the Chinese Academy of Sciences, to start planning for the establishment of an Institute of Mathematics. In July 1952, the Institute of Mathematics was established and he served as the director. He devoted himself to cultivating mathematical talents for New China. Wang Yuan, Lu Qikeng, Gong Sheng, Chen Jingrun, Wan Zhexian, etc. became famous mathematicians under his training.

In just a few years after returning to China, his research in the field of mathematics was fruitful. The paper he wrote, "Theory of Functions of Multiple Complex Variables in Typical Fields," won the first prize of the National Invention Award in January 1957, and he published monographs in Chinese, Russian, and English editions; in 1957, he published "Introduction to Number Theory"; in 1959 Leipzig first published "Estimation of Exponential Sums and Their Application in Number Theory" in German, and successively published the Russian and Chinese versions; in 1963 he and his student Wan Zhexian co-wrote "Typical Groups" Book publishing. In order to cultivate young people's enthusiasm for learning mathematics, he initiated and organized a mathematics competition for middle school students in Beijing. He personally participated in everything from setting questions, invigilating and marking papers, and went to other places many times to promote this event. He also wrote a series of popular mathematics books, which had a great influence on teenagers. He advocated cultivating an academic atmosphere and conducting academic discussions in scientific research. He initiated the establishment of the my country Institute of Computer Technology and was one of the earliest scientists in my country to advocate the development of electronic computers.

Hua Luogeng participated in various social activities of New China with a high degree of patriotic enthusiasm. In 1953, he joined a delegation of Chinese scientists to visit the Soviet Union. As a representative of Chinese mathematicians, he attended the first post-World War II World Congress of Mathematicians held in Hungary. He also attended the Asia-Pacific Peace Conference and the World Peace Council. In 1958, he and Guo Moruo led the Chinese delegation to attend the "Coordination on Science, Technology and Engineering Issues" conference held in New Delhi.

In 1958, Hua Luogeng was appointed vice president and director of the Department of Applied Mathematics at the University of Science and Technology of China. While continuing to engage in mathematical theoretical research, he worked hard to find a path that combined mathematics with industrial and agricultural practice. After a period of practice, he discovered that the coordinating method and the optimization method in mathematics are commonly used methods in industrial and agricultural production, which can improve work efficiency and change the face of work management. Therefore, while giving lectures at the University of Science and Technology, he led students to promote the optimization method and the overall planning method in industrial and agricultural practice. In early 1964, he wrote a letter to Chairman Mao expressing his determination to take the road of integrating workers and peasants. On March 18 of the same year, Chairman Mao wrote a reply in his own hand: "The poems and letters have been read. It is gratifying to have great ambitions." He wrote "Coordinated Methods and Supplements", "Optimized Methods and Supplements", and personally led China's science and technology University teachers and students went to some enterprises and factories to promote and apply the "dual method" to serve industrial and agricultural production. "In summer, we go to Jianghan to fight the scorching heat, and in winter we go to pines and mountains to be proud of the frost." This is a portrayal of his life at that time. In 1965, Chairman Mao wrote to him again, congratulating and encouraging him to "work hard and serve the people not for individuals."

■Cultural Revolution Period

After the beginning of the "Cultural Revolution", Hua Luogeng, who was promoting the "Dual Law" in other places, was urgently called back to Beijing to write an inspection and accept criticism. After learning of this situation, Premier Zhou Enlai instructed: "The overall planning method still needs to be developed." In April 1970, based on Premier Zhou's instructions, the State Council invited the heads of seven industrial ministries to listen to Hua Luogeng's lecture on optimization and overall planning methods. After that, based on his personal reputation, he seconded capable personnel from various places to form a "Team for Promoting the Optimization Method and Coordination Method", and personally led the team to promote the "Double Method" throughout the country to serve industrial and agricultural production. The team *** has been to 26 provinces, autonomous regions and municipalities directly under the Central Government. Wherever they went, mass activities of scientific experiments and practices were launched, and great economic and social benefits were achieved. His work was cared for and supported by comrades such as Hu Yaobang and Ye Jianying.

In 1975, when he was promoting the "dual method" in Daxinganling, he became ill due to overwork and suffered myocardial infarction for the first time. After smashing the "Gang of Four", he was appointed vice president of the Chinese Academy of Sciences. His many years of research results, such as "Starting from the Unit Circle", "Application of Number Theory in Approximate Analysis" (cooperated with Wang Yuan), "Optimization" and other monographs, have also been officially published. In May 1979, after being isolated from the world for more than 10 years, he visited Western Europe for seven months. With the wish of "playing chess to find masters and using axes to reach the class", he introduced his mathematical research results to the international community. Peers.

■In his later years

In November 1982, he suffered from myocardial infarction for the second time.

In October 1983, he was invited by the California Institute of Technology to go to the United States for a one-year lecture. While in the United States, he went to Rialite, Italy, to attend the founding meeting of the Third World Academy of Sciences, and was elected as an academician; in April 1984, he attended the ceremony in Washington, D.C., to award him a foreign academician by the American Academy of Sciences. He was the first foreign academician. Chinese people who have won this honor. In April 1985, he was elected vice chairman of the National Committee of the Chinese People's Political Consultative Conference at the third session of the Sixth National Committee of the Chinese People's Political Consultative Conference.

Hua Luogeng holds many social jobs. He was a member of the Standing Committee of the First to Sixth National People's Congress; he joined the Democratic League in September 1952 and was elected vice chairman of the Central Committee of the Democratic League in 1979. He made a request to join the Communist Party of China in 1958, and was approved to join the Communist Party of China in June 1979. In response to Comrade Deng Yingchao's encouragement, he said: "The sword does not care about the gray head, but the leap forward is urgent." A young and strong man who lives up to his reputation as a party member."

On June 3, 1985, he visited Japan at the invitation of the Japan Asia Cultural Exchange Association.

At 4 pm on June 12, he gave a lecture to the Japanese mathematics community in the lecture hall of the Department of Mathematics and Science of the University of Tokyo. The topic of his lecture was "Theoretical Mathematics and Its Applications." The speech ended at 5:15 pm. The moment he accepted the flowers, his body suddenly leaned back and fell on the podium. At 10:9 pm, it was announced that he had died of acute myocardial infarction.

Hua Luogeng's achievements in mathematics throughout his life were huge. His number theory, matrix geometry, typical groups, automorphic function theory, multiple complex variable function theory, partial differential equations and high-dimensional numerical integration, etc. He has made outstanding contributions in many fields. The main reason why he has such great achievements lies in his sincere heart of patriotism and perseverance and innovative spirit. Because of this, he was able to resolutely give up the generous treatment of a tenured professor in the United States and welcome the dawn of his motherland; he was able to withstand criticism and blows, work hard, serve the people instead of himself, and became an outstanding scientist renowned at home and abroad.

Hua Luogeng’s wife

Hua Luogeng is a well-known mathematician at home and abroad, and his outstanding achievements have long been praised by the world. Whenever people ask him about his success, he always praises his wife Wu Xiaozhi and sighs: "She is an unsung hero. My entire career is inseparable from her!" For decades, Wu Xiaozhi played an important role in Hua Luogeng's life and career.

1. When Wu Xiaozhi was 18 years old, she was arranged to marry Hua Luogeng, a man of the same age from the same hometown. Less than a few months after the marriage, the plague spread to Jintan County, Jiangsu Province, killing her mother-in-law. Not long after, Hua Luogeng also contracted the plague and was in a coma every day. At this time, Wu Xiaozhi left the nursing daughter to her mother to take care of, and she stayed by her husband's side day and night. Since her mother-in-law had just passed away, her daughter had come to the world, and her husband was seriously ill, Hua Luogeng's family, which was not already wealthy, was even more difficult. For this reason, Wu Xiaozhi went behind the back of her family and took her beloved wedding accessories to a pawn shop to exchange money for her husband's medical treatment and medicine. Perhaps it was the power of love that strengthened Hua Luogeng's determination and courage to defeat the disease, and he finally struggled out of death. Unfortunately, the disease left one of his legs disabled.

2. After Hua Luogeng recovered from his illness, although his body was disabled, his will became stronger. He was determined to devote himself to the scientific research of his motherland and studied mathematics even harder. In order to provide convenience to her husband, even if there was sometimes a situation where there was no rice to cook, she would try to solve it alone and never let her husband be distracted. Soon, Hua Luogeng published a paper "The Reasons Why Su Jiaju's Algebraic Quintic Equation Solution Cannot Be Established", which was appreciated by Professor Xiong Qinglai of Tsinghua University and invited him to teach at Tsinghua University. Wu Xiaozhi naturally wanted to live in Beijing, but she thought that her husband's monthly salary was too low to support a family of three. Moreover, she was pregnant, so having a child would increase the expenses a lot. Moreover, her father-in-law was old and sick and needed care. As a result, she canceled her plan to go to Beijing with her husband and shouldered the heavy burden of housework.

3. In the summer of 1936, 25-year-old Hua Luogeng was recommended to study at Cambridge University in England. The next year, Japanese imperialism launched the "July 7th Incident". Hua Luogeng was filled with righteous indignation after learning about the aggressive acts of Japanese imperialism. He resolutely gave up the opportunity to further his studies in the UK, returned to his motherland with enthusiasm for resisting Japan and saving the nation, and went to teach at Southwest Associated University in Kunming. As a result, a family of four reunited after a long absence and began to reunite again. Because Hua Luogeng was extremely busy with work and had no time to give more care and education to his children, this important task fell on Wu Xiaozhi's shoulders.

4. After the founding of New China, Hua Luogeng and his family moved to Beijing. Although living conditions have improved, Wu Xiaozhi's diligence and frugality in managing the family and caring for her husband and children have not changed. After the Third Plenary Session of the 11th Central Committee of the Communist Party of China, Hua Luogeng was in high spirits and his desire to serve the country became stronger. At the same time, various tasks have become busier. Wu Xiaozhi not only took care of the housework, but also helped him copy papers and letters. Once a guest came to his home, Wu Xiaozhi would take care of all the chores for him; and when he went out for meetings or work, he would always take out his crutches, cigarettes and hat and hand them to him. In view of this, Hua Luogeng's relatives and friends once asked Wu Xiaozhi why she cared so thoughtfully about her husband. Her answer was: "If I can help him a little, he will worry less and contribute more to the country."

" They have three sons, Hua Jundong, Hua Ling, and Hua Guang, and three daughters, Hua Shun, Hua Su, and Hua Mi.

Hua Luogeng's teacher

Xiong Qinglai is Hua Luogeng's teacher , a pioneer of modern mathematics in China. 1893-1969, courtesy name Dizhi, a native of Yunnan. He studied in Belgium and France, and obtained a doctorate in France. He achieved great results in his research on function theory and defined an "infinity". "Grade function" has been adopted internationally and is called Xiong's infinite number. Mr. Xiong Qinglai loves education very much and is very enthusiastic about cultivating scientific talents in China. In his early years, when he was a professor at Southeast University, he discovered a student named Liu Guang Quite talented, Chang often guided him in his reading and research. Later, he and another professor who taught Liu Guang sponsored him to study abroad, and even sold his own clothes to send him money. Later, Liu Guang became Liu Guang. A famous physicist. Later, Mr. Xiong Qinglai came to Tsinghua University to serve as the director of the Department of Mathematics. After seeing Hua Luogeng’s name in an academic magazine and learning about Hua Luogeng’s self-study experience and mathematical talent, he decided to break the rules and asked that he only have a junior high school education of 19. Hua Luogeng arrived at Tsinghua University at the age of 70. When he was suffering from hemiplegia, he was ill and mentored two graduate students, Yang Le and Zhang Guanghou, who later became very accomplished young mathematicians.

Main Achievements

The founder and pioneer of Chinese research in analytic number theory, matrix geometry, typical groups, and self-sustaining function theory. Among the international mathematical research achievements named after Fahrenheit are "Fahrenheit's Theorem" and "Waiyi - "Wah's Inequality", "Wah's Inequality", "Prouwer-Garden Theorem", "Wah's Operator", "Wah's-Wang's Method", etc. Comrade Hua Luogeng left us ten monographs in his life: "Stacking Barriers" Theory of Prime Numbers", "Evaluation of Sums of Exponents and Their Application in Number Theory", "Harmonic Analysis of Typical Fields in Function Theory of Multiple Complex Variables", "Introduction to Number Theory", "Typical Groups" (co-authored with Wan Zhexian ), "Starting from the Unit Circle", "Application of Number Theory in Approximate Analysis" (co-authored with Wang Yuan), "Second-order System of Constant Coefficient Linear Partial Differential Equations with Two Independent Variables and Two Unknown Functions" (co-authored with others ), "Optimization" and "Mathematical Theory of Optimization of the Planned Economy Scope", eight of which have been translated and published abroad, some of which have been included in the classic works of mathematics of this century. In addition, there are more than 200 academic papers and popular science papers. His works "Preferred Fa Commentary and Its Supplement", "Coordinated Fa Commentary and its Supplement", etc., were compiled into "Selected Popular Science Works of Hua Luogeng".

In terms of algebra, it proves the basics of one-dimensional projective geometry left over from history. Theorem; gives a simple and direct proof of the result that the normal subbody of a body must be contained in its center, which is called the Cartan-Breuer-Hua theorem. His monograph "The Theory of Stacked Prime Numbers" system. He has comprehensively summarized, developed and improved Hardy and Littlewood's circle method, Vinogradov's triangular sum estimation method and his own method. His main results are still among the world's leaders after more than 40 years of publication, and have been translated into Russian, Published in Hungarian, Japanese, German and English, it became one of the classic number theory works of the 20th century. His monograph "Harmonic Analysis on Multiple Typical Domains of Complex Variables" uses sophisticated analysis and matrix techniques, combined with group representation theory, to specifically give the complete orthogonal system of typical fields, thus giving the relationship between Cauchy and Poisson kernels. expression. This work has had a broad and profound impact on harmonic analysis, complex analysis, differential equations and other research, and has won the first prize of the China Natural Science Award. He advocates the development of applied mathematics and computers. He has published many books such as "Pinghua on Coordination Methods" and "Optimization" and promoted their application in China. Collaborating with Professor Wang Yuan, he achieved important results in the application research of modern number theory methods, which is called the "Hua-Wang method". He has made important contributions to the development of mathematics education and science popularization. He has published more than 200 research papers and dozens of monographs and popular science works.

Hua Luogeng's Wonderful Couplet

In 1953, the Academy of Sciences organized an overseas study tour, headed by the famous scientist Qian Sanqiang. The members include Hua Luogeng, Zhang Yuzhe, Zhao Jiuzhang, Zhu Xian and many others. When he had nothing to do on the way, Hua Lao wrote the first line of the first couplet: "The three strong ones are Han, Zhao and Wei," asking for a counterpoint to the second line.

In "Contrast Examples", this is a difficult category.

As far back as the Northern Song Dynasty, some people used the first couplet of "Three Lights, Sun, Moon and Stars" to find a solution. At that time, the great writer Su Dongpo solved this problem with "Four Poems on Elegance". In the Qing Dynasty, someone from the famous calligrapher and painter Zheng Banqiao presented a couplet to Zheng Banqiao. When he opened it, he saw only the first couplet, which wrote the words "Three Unique Poems, Calligraphy and Painting". This could not be more appropriate to describe Zheng Banqiao's contribution. But the second line is really difficult to correct. Later, someone in Zheng Banqiao solved this problem with the second line of "An official returns home". The "yiguan" here has the triple character of "return to come", which not only solves the difficulty of number connection, but also quotes the allusion of Tao Yuanming's "Return to the Word", and praises Zheng's reclusiveness with poetry, calligraphy and painting. With his outstanding character, Banqiao friends have taken another step forward than Su Dongpo.

But the first couplet proposed by Hua Lao has developed new developments. The "Three Strong" here refers to the three Warring States periods of Han, Zhao and Wei during the Warring States Period, but it also implies the name of Comrade Qian Sanqiang, the head of the delegation. This not only requires solving the traditional difficulty of numerical linking, but also requires that the second line be included in the second line. Embed the name of another scientist. After a while, Mr. Hua saw that everyone still had no second line, so he revealed his own line: nine chapters of hooks, strands, and strings. "Nine Chapters" is a famous mathematical work in ancient my country. However, the "Jiuzhang" here happens to be the name of another member of the delegation, atmospheric physicist Zhao Jiuzhang. Hua Lao's wonderful pairing made the whole house fall in love, because it opened up a new "contrast" of digital couplets.

In 1980, Professor Hua Luogeng wrote the following couplet when he was instructing the coordination method and optimization method in Suzhou:

Watching chess without speaking is not a gentleman, but helping each other;

Raise your hands A man who regrets and corrects his mistakes.

Warning

Although Jincheng is happy, it is better to return to your hometown; although Paradise is good, it is not a place to stay for a long time. Come back.

When people help me, I will never forget it. When I help others, I won’t forget it.

In the long march to seek the truth, only by learning, constantly learning, diligently learning, and creative learning can we cross mountains and ridges.

As time goes by, we accumulate meritorious deeds, and we make every effort to make every effort possible.

Time is accumulated in minutes and seconds. Only those who are good at using sporadic time will achieve greater results.

A strong man fights to the death, regardless of a few scars, fighting against a thousand-year-old demon and fighting for the new style of EMI. Be generous with yourself.

In self-study, you are not afraid of a low starting point, but you are afraid of not reaching the end.

Scientific achievements are accumulated bit by bit. Only long-term accumulation can the bits and pieces merge into a sea.

Scientific inspiration cannot come by just waiting. If there is any accidental opportunity in scientific discovery, then this kind of "accidental opportunity" can only be given to those who are well-educated, to those who are good at independent thinking, and to those who have a perseverance spirit. Not for lazy people.

Science is an honest knowledge. It is impossible to create inventions by luck. If you don’t understand the essence of a problem, even chances will be in vain. This is the reason for entering Baoshan and returning empty-handed.

Science is a science that seeks truth from facts and cannot be false in any way.

I think that people have two shoulders, and they should play a role at the same time. I want to use one shoulder to carry the burden of door-to-door delivery, and deliver scientific knowledge and scientific tools to the hands of master workers; the other shoulder It can be used as a human ladder for young people to climb to a higher level of science.

Genius is not trustworthy, intelligence is unreliable, and it is unimaginable to pick up great scientific inventions by chance.

Learning and research are like climbing a ladder. If you want to climb up step by step, if you try to take four or five steps at a time and reach the sky from the ground, you must be able to fall.

Everyone must develop the habit of self-study. Even students in school today must develop the habit of self-study, because sooner or later they will leave school! Self-study is the ability to learn independently and think independently. Traveling still depends on the traveler himself.

Go step by step! The path I have taken is a step-by-step path.

The ability to think independently is very necessary for engaging in scientific research or any other work.

In history, any major scientific invention is due to the inventor giving full play to this original spirit.

When you meet, talk less about pleasantries and more about art.

Science is an honest knowledge. When conducting scientific research, we must adopt an honest and realistic attitude, without any falsehood or exaggeration. If you don’t know, you don’t know. If you don’t understand, you don’t understand. If you don’t understand, don’t pretend to understand, and you have to pursue it. If you don’t understand, you don’t understand where you are; if you understand, you understand where you are. The first thing to do with an honest attitude is to lay a solid foundation. Science is a solid knowledge with strong coherence and systematization. If you don’t learn the first things well, you won’t be able to master the later ones; the foundation is not laid well. It's more difficult to get cutting-edge. We often encounter some problems at work that cannot be solved, many of which are due to the lack of a good foundation. The speed of a person's progress in scientific research and other work is often related to his foundation.

It is best for us to regard our own life as the continuation of the life of our predecessors, a part of the same life today, and the beginning of the life of future generations. If this continues, science will become more brilliant day by day, and society will become more beautiful day by day.

Scientific inspiration cannot come by just waiting. If there is any accidental opportunity in scientific discovery, then this kind of "accidental opportunity" can only be given to those who are well-educated, to those who are good at independent thinking, and to those who have a perseverance spirit. Not for lazy people.

The same is true for "difficulty". Facing the cliffs, you can't see a crack in a hundred years, but with an axe, you can advance inch by inch, you have to advance foot by foot, and keep accumulating. The leap will come, and the breakthrough will follow.

Genius is not trustworthy, intelligence is unreliable, and it is unimaginable to pick up great scientific inventions by chance.

There is no smooth road in science, and there are countless rocks and shoals in the long river of truth. Only herb collectors who are not afraid of climbing, and tide-drifters who are not afraid of huge waves, can climb to the top to collect fairy grass and go deep into the water to find Li pearls.

Studying but not knowing enough, humility comes from not knowing enough. False modesty can only win mediocre applause, but cannot achieve real progress.

All the more accomplished scientific workers are, without exception, experts at utilizing time, and they are also people who are determined to invest a lot of time in a lot of work.