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Interesting mathematics suitable for primary school students
Hua, a modern mathematician in China. 191010 65438 was born in Jintan, Jiangsu province, and 1985 12 died in Tokyo, Japan. 1924 Jintan middle school graduated from junior high school, but due to poor family circumstances, he had to drop out of school after finishing junior high school and became a shop assistant. /kloc-suffered from typhoid fever at the age of 0/8, resulting in disability of his right leg. 1930, taught in Tsinghua University. 1936 Visiting study at Cambridge University, UK. 1938 became a professor in The National SouthWest Associated University after returning to China. From 65438 to 0946, he went to the United States and served as a researcher at Princeton Institute of Mathematics, a professor at Princeton University and the University of Illinois, and returned to China from 65438 to 0950. He has served as Professor Tsinghua University, director and honorary director of Institute of Mathematics and Institute of Applied Mathematics of China Academy of Sciences, chairman and honorary chairman of Chinese Mathematical Society, director of National Mathematical Competition Committee, foreign academician of American National Academy of Sciences, academician of Third World Academy of Sciences, academician of Bavarian Academy of Sciences of the Federal Republic of Germany, deputy director, vice president and presidium member of physics department, mathematics and chemistry of China Academy of Sciences, director and vice president of mathematics department of China University of Science and Technology, vice chairman of China Association for Science and Technology, and member of the State Council Academic Degree Committee. He was a member of the first to sixth the NPC Standing Committee and vice-chairman of the sixth China People's Political Consultative Conference. He was awarded honorary doctorates by Nancy University in France, The Chinese University of Hong Kong and the University of Illinois in the United States. Mainly engaged in the research and teaching of analytic number theory, matrix geometry, typical groups, automorphic function theory, multiple complex variable function theory, partial differential equations, high-dimensional numerical integration and other fields, and has made outstanding achievements. In the 1940s, the historical problem of Gaussian complete trigonometric sum estimation was solved, and the best error order estimation was obtained (this result is widely used in number theory). The results of G.H. Hardy and J.E. Littlewood on the Welling problem and E. Wright on the Tully problem have been greatly improved and are still the best records.

Since 1960s, he has applied mathematical methods to practice, screened out optimization methods and overall planning methods aiming at improving work efficiency, and achieved remarkable economic benefits.

Comrade Hua is a contemporary self-taught master of science and a world-famous mathematician. He is the founder and pioneer of China's research on analytic number theory, canonical group, matrix geometry, automorphic function theory and multiple complex variable function theory. It laid the foundation for matrix geometry in the future.

■ Early learning stage

19101012 was born in a small businessman's family in Jintan county, Jiangsu province, with a height of1.65m. My father Hua Ruidong runs a small grocery store, and my mother is a virtuous housewife. /kloc-graduated from renmao primary school in the county town at the age of 0/2 and entered Jintan county junior high school. 1925 after graduating from junior high school, he was unable to enter senior high school because of his poor family, so he had to study accounting in the Chinese vocational school founded by Huang Yanpei in Shanghai. In less than a year, due to the high cost of living, I was forced to drop out of school and go back to Jintan to help my father manage the grocery store.

In the monotonous life of standing at the counter, he began to teach himself mathematics. /kloc-married Wu Xiaozhi in the autumn of 0/927. From 65438 to 0929, Hua was employed as a clerk in Jintan Middle School and began to publish papers in Shanghai Science and other magazines. 1929 In the winter, he suffered from severe typhoid fever. After nearly half a year's treatment, he recovered, but his left leg joint was seriously damaged, leaving him with a lifelong disability. He had to walk on crutches.

In fact, when Hua was in junior high school, his homework was not good once, and sometimes he failed in math. Hua's math teacher, a famous educator and translator in China (1900 was born in Jintan), was teaching in Jintan Middle School at that time. He found Hua playful, but quick-thinking, and his math exercises were often changed, and his method of solving problems was very unique and original. On one occasion, the teacher of Jintan Middle School lamented that there were many "poor students" and no "talents" in the school. Wang Weike said, "Not necessarily. In my opinion, China is one! " "Hua Luogeng?" A teacher smiled and said, "Look at him, this word is like a crab crawling. Can he become a' talent'? " Wang Weike said with some excitement, "Of course, he has little hope of becoming a great calligrapher, but how can you see his talent in mathematics from between his lines?" You know, gold is buried in sand and looks no different from sand. What we need most as teachers' eyes is the ability to find gold in the sand, otherwise we will bury talents! "

1in the spring of 930, his paper "Why can't the solution of Su Jiaju's algebraic quintic equation be established" was published in Shanghai Science Journal. After seeing it, Professor Xiong Qinglai, then head of the Department of Mathematics of Tsinghua University, inquired about it in many ways and recommended him to be a librarian in the Department of Mathematics of Tsinghua University. 193 1 at the turn of autumn and winter, Hua entered the Tsinghua campus.

Hua works and studies in Tsinghua University. It took him two years to complete the road that ordinary people need eight years to complete. 1933 was promoted to teaching assistant, 1935 became a lecturer. 1936 was recommended by Tsinghua University and sent to Cambridge University in England. During his two years in Cambridge, he devoted all his energy to the study of mathematical theoretical problems and was unwilling to waste time applying for a degree. His research results have attracted the attention of the international mathematics community. 1938 returned to China and was employed by Professor The National SouthWest Associated University. From 1939 to 194 1, under extremely difficult conditions, he wrote more than 20 papers and completed his first mathematical monograph, the theory of prime numbers on overlapping bases. 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 from 65438 to 0947, and translated and published in German, English, Hungarian and Chinese in various countries.

1946 was invited to visit the Soviet union from February to May. 1946, the then national government also wanted to build an atomic bomb, so it sent three famous scientists, Hua, Zeng Zhaolun, to visit the United States. In September, Li Zhengdao, Zhu Guangya and others left Shanghai for the United States. They first served as visiting professors at Princeton Institute for Advanced Studies, and later were hired as tenured professors by the University of Illinois.

■ The period of returning to China for construction

1949 After the founding of New China, Hua was very excited and determined to bring his family back to China. The five of them left the United States by boat and arrived in Hong Kong on February 1950. In Hongkong, he published an open letter to students studying in the United States, full of patriotic passion, encouraging them to return to China to serve the new China. On March 1 1, Xinhua News Agency broadcast this letter. On March 1950, Hua, his wife and children arrived in Beijing by train.

Hua returned to Tsinghua campus and served as the head of the Department of Mathematics of Tsinghua University. Then, at the invitation of Guo Moruo, President of China Academy of Sciences, he started to build a mathematical research institute. 1952 In July, the Institute of Mathematics was established with him as its director. He devoted himself to training mathematical talents for New China, and Wang Yuan, Lu Qikeng, Gong Sheng, Chen Jingrun and Wan Zhexian all became famous mathematicians under his training.

In just a few years after returning to China, his research in the field of mathematics has been fruitful. His paper "On Functions of Multiple Complex Variables in Typical Fields" won the first prize of national invention in June 1957, and has been published in Chinese, Russian and English versions. 1957 published Introduction to Number Theory; 1959, Leipzig first published the estimation of exponential sum and its application in number theory in German, and then successively published Russian and Chinese versions. 1963 co-authored the book Typical Groups with student Wan Zhexian. In order to cultivate teenagers' enthusiasm for learning mathematics, he initiated and organized a mathematics competition for middle school students in Beijing. He personally participated in the problem setting, invigilation and marking, and repeatedly went to other places to publicize this activity. He also wrote a series of popular math books, which had a great influence on teenagers. He advocated cultivating academic atmosphere and conducting academic discussions in scientific research. He initiated the establishment of China Institute of Computer Technology, and was also one of the earliest scientists who advocated the development of electronic computers in China.

China participated in various social activities in New China with a high degree of patriotic enthusiasm. 1953, he participated in a delegation of China scientists visiting the Soviet union. As a representative of China mathematicians, he attended the first World Congress of Mathematicians after World War II in Hungary. He also participated in the Asia-Pacific Peace Conference and the World Peace Council. From 65438 to 0958, together with Guo Moruo, he led the China delegation to attend the conference on "Coordination of Science, Technology and Engineering Issues" held in New Delhi.

1958, Hua was appointed vice-president of China University of Science and Technology and head of the Department of Applied Mathematics. While continuing to study mathematical theory, he tried to find a way to combine mathematics with industrial and agricultural practice. After a period of practice, he found that the overall planning method and optimization method in mathematics can be widely used 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 overall planning method in industrial and agricultural practice. At the beginning of 1964, he wrote to Chairman Mao, expressing his determination to take the road of combining workers and peasants. On March 18 of the same year, Chairman Mao wrote back in person: "Poems and letters have been read. Top gun, congratulations. " He wrote "Brief Introduction and Supplement to the Master Planning Law" and "Brief Introduction and Supplement to the Optimal Selection Law", and personally led the teachers and students of China University of Science and Technology to some enterprises and factories to promote and apply the "double methods" to serve industrial and agricultural production. "Go to Jianghan to fight the heat in summer and go to Songliao first frost in winter." This is a portrayal of his life at that time. Chairman Mao wrote to him again on 1965, congratulating and encouraging him to "work hard and serve the people instead of individuals".

■ During the Cultural Revolution.

After the "Cultural Revolution" began, Hua, who promoted the "double law" in other places, was called back to Beijing by express telegram to write an inspection and accept criticism. After learning this situation, Premier Zhou Enlai instructed: "The overall planning method is still necessary." 1in April, 970, the State Council invited the heads of seven industrial departments to attend a lecture on optimization and overall planning in China. Later, relying on his personal reputation, he seconded capable personnel to various places to form a "group to promote the optimal selection method and the overall planning method" and personally led a team to promote the "double methods" throughout the country to serve industrial and agricultural production. Team * * * has been to 26 provinces, autonomous regions and municipalities directly under the central government, and mass activities of scientific experiments and practices have been set off everywhere, which has achieved great economic and social benefits. His work has been concerned and supported by Hu Yaobang, Ye Jianying and other comrades.

During 1975, when he was promoting "double therapy" in Daxinganling, he suffered the first myocardial infarction because of overwork. After the downfall of the Gang of Four, he was appointed vice president of China Academy of Sciences. His research achievements for many years, such as Starting from the Unit Circle, Application of Number Theory in Approximate Analysis (in cooperation with Wang Yuan) and Optimality Theory, have also been published. 1979 In May, after being isolated from the outside world for more than 10 years, he visited Western Europe for seven months, and with the desire of "playing chess, teaching others how to do things", he introduced his mathematics research results to his international counterparts.

■ Old age, everyone's period

1982 1 1 month, his second myocardial infarction.

1983 5438+00 June, at the invitation of California Institute of Technology, went to the United States for a one-year lecture. During his stay in the United States, he attended the inaugural meeting of the Third World Academy of Sciences held in Park Jung-soo, Italy, and was elected as an academician. 1in April, 984, he attended the ceremony of awarding him a foreign academician by the American Academy of Sciences in Washington, D.C., and he was the first China person to receive this honor. 1985 was elected as the vice chairman of the CPPCC at the Third Session of the Sixth CPPCC in April.

Hua has done a lot of social work. He is a member of the first to sixth the NPC Standing Committee; /kloc-0 joined NLD in September, 1952, and/kloc-0 was elected as the vice chairman of NLD Central Committee in September, 1979. 1958 requested to join the China * * * production party, and 1979 was approved to join the China * * * production party in June. In response to Comrade Deng's encouragement, he said: "The horizontal knife does not care about hoary heads, but leaps to young adults and lives up to the name of party member."

June 3 1985 Visited Japan at the invitation of Japan Asian Cultural Exchange Association. On June 12, at 4 pm, he gave a speech to the Japanese mathematics community in the lecture hall of the Department of Mathematics and Physics of the University of Tokyo. The topic is "Pure Mathematics and Its Application". At 5 pm, the speech ended. At the moment he received the flowers, his body suddenly leaned back and fell on the rostrum. At 65: 438+00: 09 pm, he was declared dead of acute myocardial infarction.

Hua's achievements in mathematics in his life are enormous, and he has made outstanding contributions in many fields, such as number theory, matrix geometry, typical groups, automorphic function theory, multiple complex variable function theory, partial differential equations, high-dimensional numerical integration and so on. He has made such great achievements because he has a sincere patriotism and indomitable spirit of innovation. Because of this, he was able to resolutely give up the generous treatment of American tenured professors and welcome the dawn of the motherland; He can resist criticism and attack, work hard, serve the people instead of individuals, and become an outstanding scientist who enjoys a good reputation at home and abroad.

Hua's wife

Hua is a famous mathematician at home and abroad, and his outstanding achievements have always been admired by the world. Whenever people ask about his success, he always praises his wife Wu Xiaozhi and sighs: "She is an unsung hero, and my whole career cannot be separated from her!" " For decades, Wu Xiaozhi has played an important role in China's life and career.

1. 18 years old, Wu Xiaozhi married his fellow villager Hua. Less than a few months after the marriage, the plague spread to Jintan County, Jiangsu Province, killing her mother-in-law. Before long, Hua was also infected with the plague and was in a coma every day. At this time, Wu Xiaozhi gave her nursing daughter to her mother to take care of, and she waited by her husband day and night. Because her mother-in-law has just died, her daughter has just arrived, and her husband is seriously ill, which is even worse for Hua, who is not rich. To this end, Wu Xiaozhi carried her family, took the jewelry she loved when she got married to the pawnshop, and exchanged money for medicine to treat her husband. Perhaps the power of love strengthened Hua's determination and courage to overcome the disease, and he finally struggled out of the brink of death. Unfortunately, illness crippled one of his legs.

Second, after his recovery, Hua was physically disabled, but he was strong-willed. He is determined to devote himself to the scientific research of his motherland and study mathematics harder. In order to provide convenience for her husband, even if there is no food in the pot sometimes, she tries to solve it herself and never lets her husband be distracted. Soon, Hua published the article "Why Su Jiaju's Algebraic quintic Equation Solution Can't Be Established", which was appreciated by Professor Xiong Qinglai of Tsinghua University and invited him to teach in Tsinghua. Wu Xiaozhi naturally wants to live in Beijing, but she thinks her husband's monthly salary is too low to support a family of three. And she is pregnant, giving birth will increase a lot of expenses; Besides, my father-in-law is old and sick and needs to be taken care of. So I canceled my plan to go to Beijing with my husband and provoked a heavy burden of housework.

3.1In the summer of 936, 25-year-old Hua was sent to Cambridge University in England to study. The following year, Japanese imperialism launched the July 7th Incident. After learning the news of Japanese imperialist aggression, China was very indignant. He resolutely gave up the opportunity to study in Britain, returned to the motherland with the enthusiasm of resisting Japan and saving the nation, and went to teach in The National SouthWest Associated University, Kunming. So, a family of four reunited after a long separation and began to reunite again. Because Hua is very busy at work and has no time to give more care and education to his children, this important task falls on Wu Xiaozhi's shoulder again.

4. After the founding of New China, the Hua family moved to Beijing. Although living conditions have improved, Wu Xiaozhi's spirit of diligence, housekeeping and caring for her husband and children has not changed. After the Third Plenary Session of the Eleventh Central Committee of the Communist Party of China, the spirit of China was uplifted and the heart of serving the country was even stronger. Meanwhile, all the work is getting busier and busier. Wu Xiaozhi not only does housework, but also helps him copy papers and letters. Once the guest goes home, Wu Xiaozhi will undertake all kinds of chores for him; He always takes out crutches, cigarettes and hats and hands them to him when he goes out for meetings. In view of this, relatives and friends of Hua once asked Wu Xiaozhi why she was so considerate to her husband. Her answer is: "If I can help him a little, he will care less and do more for the country." They have three sons Hua, Hua Linghe and three daughters Hua Shun, Hua Su and Hua Mi.

Teacher Hua

Xiong Qinglai, Hua's teacher, is a pioneer of modern mathematics in China. 1893 ——1969, word Dizhi, from Yunnan. I studied in Belgium and France, where I received my doctorate. He made great achievements in the research of function theory, and defined an "infinite order function", which was adopted internationally and called bear infinity. Mr. Xiong Qinglai loves education very much and is very enthusiastic about training scientific talents in China. In his early years, when he was a professor at Southeast University, he found that a student named Guang Liu was quite talented, and he often instructed him to study and study. Later, he and another professor who had taught Guang Liu helped him to study abroad, and even sold his clothes to send him money. Later, this Guang Liu became a famous physicist. Later, Mr. Xiong Qinglai came to Tsinghua University as the head of the Department of Mathematics, and read Hua's name in academic magazines. After learning about China's self-study experience and mathematical talent, he resolutely broke the routine and invited Hua, who only had a junior high school education of 19 years old, to Tsinghua University. When he was paraplegic in his seventies, he took care of two graduate students, Yang Le and Zhang Guanghou, who later became very successful young mathematicians.

Major achievements

China is the founder and pioneer in the research of analytic number theory, matrix geometry, canonical group and self-safety function theory. The international achievements in mathematical research include Fahrenheit Theorem, Huai-Hua Inequality, Fahrenheit Inequality, Pu Lawwill-Gardiner Theorem, Fahrenheit Operator, Hua-Wang Method and so on. Comrade Hua left us ten monographs in his life: On the Prime Number, Calculation of Exponential Sum and Its Application in Number Theory, Harmonic Analysis of Typical Fields in the Theory of Functions with 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) and. Optimization Theory and Mathematical Theory for Optimizing the Scope of Planned Economy have been translated and published abroad, and some of them have been included in mathematical classics of this century. In addition, there are more than 200 academic papers such as popular science works "Evaluation and Supplement of Optimization Method" and "Evaluation and Supplement of Overall Planning Method", which are compiled into "Selected Works of Huake Puwen".

In algebra, the basic theorem of one-dimensional projective geometry left over from history for a long time is proved. This paper gives a simple and direct proof that the normal child of an object must be contained in its center, which is Hua theorem. His monograph "On Prime Numbers of Pile Foundations" systematically summarizes, develops and perfects Hardy and Littlewood's circle method, vinogradov's triangle sum estimation method and his own method. After more than 40 years of publication, its main achievements still occupy the leading position in the world, and it has been translated into Russian, Hungarian, Japanese, German and English, becoming one of the classic works of number theory in the 20th century. His monograph "Harmonic Analysis on Typical Fields of Multiple Complex Variables" gives the complete orthogonal system of typical fields with accurate analysis and matrix skills, combined with group representation theory, and thus gives the expressions of Cauchy and Poisson kernel. This work has a wide and deep influence on harmonic analysis, complex analysis and differential equations, and won the first prize of China Natural Science Award. Advocating the development of applied mathematics and computer, he has published many books such as Master Planning Method and Optimization Research, which have been popularized in China. In cooperation with Professor Wang Yuan, he has made important achievements in the application research of modern number theory methods, which is called "Hua Wang Fa". He made great contributions to the development of mathematics education and the popularization of science. He has published more than 200 research papers and dozens of monographs and popular science works.

Huamiaolian

1953, the Academy of Sciences organized a delegation to go abroad, headed by the famous scientist Qian Sanqiang. Members include Hua, Zhao Jiuzhang and Zhu Xian. In his spare time, Hua Lao wrote a couplet: "The top three are Han, Zhao and Wei", asking for a couplet.

This is a difficult category in "comparative example". As early as the Northern Song Dynasty, some people tried to get the correct answer through the couplets of "Three Lights, the Sun, the Moon and the Stars". At that time, Su Dongpo, a great writer, solved this problem with "four poems". In Qing Dynasty, the famous painter Zheng Banqiao gave Zheng Banqiao a pair of couplets. When I opened it, I saw the first couplet with the words "Three Exquisites of Poetry, Calligraphy and Painting" written on it. It was no longer appropriate to describe Zheng Banqiao's contribution, but the second couplet was really difficult. Later, some people in Zheng Banqiao solved this problem with the bottom line of "returning one official to another". The "one official" here has the triple character of "going back", which not only solves the difficulty of combining numbers, but also quotes the allusions in Tao Yuanming's "Returning to Hometown" and praises the outstanding character of Zheng's combination of poetry and calligraphy. Banqiao's friends have been one step ahead of Su Dongpo.

However, the Shanglian proposed by Hua Lao has made new progress. The "top three" here refers to Korea, Zhao and Wei San during the Warring States Period, but it implies the name of the head of the delegation, Comrade Qian Sanqiang, which not only solves the traditional difficulty of the couplet of numbers and numbers, but also requires the name of another scientist to be embedded in the bottom couplet. After a while, when Hua Lao saw that everyone had no bottom line, he revealed his bottom line: nine chapters of hook, stock and string. Nine Chapters is a famous mathematical work in ancient China. However, the "Nine Chapters" here happen to be the name of another member of the delegation-atmospheric physicist Zhao Jiuzhang. The wonderful couple of Hua Lao fascinated the audience because it created a new "example" of digital couplets.

1980 professor Hua wrote the following couplets when guiding the master planning method and optimization method in Suzhou:

Watching chess is not a gentleman, help each other;

Raise your hand to show regret. Be a gentleman and correct your mistakes.

Warning words

Although Jincheng is happy, it is better to go back to your hometown; Although heaven is good, it is not a place to stay for long. Back and forth.

I never forget when others help me, but I don't remember when I help others.

In the long March of seeking truth, only by studying, constantly learning, diligently learning and creatively learning can we cross mountains and mountains.

Over time, I have seen merits and demerits.

Time is accumulated in minutes, and people who are good at using sporadic time will achieve greater success.

A strong man broke his wrist, regardless of any scars, fighting against the Millennium old demon and the hundred generations of new wind. Give yourself generously.

Self-study, not afraid of the low starting point, not afraid of the end.

Scientific achievements are accumulated bit by bit, and only long-term accumulation can merge into the sea.

Scientific inspiration is by no means something that can wait. If there is any accidental opportunity for scientific discovery, then this "accidental opportunity" can only be given to educated people, people who are good at independent thinking, and people who have perseverance, not to lazy people.

Science is honest knowledge, and it is impossible to create inventions by luck. If you don't understand the essence of the problem, it's useless to meet the opportunity. That's why I went to Baoshan and returned empty-handed.

Science is the knowledge of seeking truth from facts, and nothing can be false.

In my opinion, people have two shoulders and should play a role at the same time. I want to shoulder the burden of door-to-door delivery and send scientific knowledge and tools to the workers' masters. The other shoulder can be used as a ladder for young people to climb a higher scientific level.

Genius is unreliable, intelligence is unreliable, and it is unimaginable to pick up great scientific inventions conveniently.

Learning and research are like climbing a ladder. If you want to climb up step by step, try to climb four or five steps with one foot on the ground and reach the sky, you will certainly be able to wrestle.

Everyone must form the habit of self-study, even the students who are in school today, because they will leave school sooner or later! Self-study is the ability to learn and think independently. It's up to the traveler to walk on his own.

Step by step! The road I have taken is a step-by-step road.

Independent thinking ability is very necessary for scientific research or any other work. Any major scientific invention in history is due to the inventor giving full play to this original spirit.

When we meet, we should talk less about greetings and more about art.

Science is honest knowledge, so we should adopt an honest and realistic attitude in scientific research, and there should be no false exaggeration. I just don't know if I don't know. I don't know, I just don't understand. Don't pretend to understand if you don't understand, but pursue it. If you don't know, you don't know where it is Yes, I know where it is. To tell the truth, the first thing is to lay a good foundation. Science is practical knowledge with strong consistency and systematicness. If you don't learn the things in front well, the things behind you won't get on. The foundation is not laid well. It's harder to reach the tip. We often encounter some unsolvable problems in our work, many of which are caused by poor foundation. The speed of a person's progress in scientific research is often related to his foundation.

We'd better regard our life as a continuation of our predecessors' life, a part of our present life and the beginning of our future generations' life. If this goes on, science will be more brilliant and society will be better every day.

Scientific inspiration is by no means something that can wait. If there is any accidental opportunity for scientific discovery, then this "accidental opportunity" can only be given to educated people, people who are good at independent thinking, people who have perseverance, and not to lazy people.

The same is true of "difficult". Facing the cliffs, you can't see a crack in a hundred years, but with an axe, you can advance inch by inch, you must advance inch by inch, and you will continue to accumulate. Leaps will come, and breakthroughs will follow.

Genius is unreliable, intelligence is unreliable, and it is unimaginable to pick up the great invention of learning with your hands.

There is no royal road to science, and there are countless reefs and shoals in the long river of truth. Only herb gatherers who are not afraid of climbing, only herb gatherers who are not afraid of stormy waves, can climb the peak to collect fairy grass and go deep into the water to find pearls.

Learning is not enough, and modesty comes from not being satisfied. False modesty can only win vulgar applause, but can not make real progress.

All successful scientists, without exception, are experts in using time, and are also people who are determined to invest a lot of labor in a lot of time.