Li, whose original name is Li, whose real name is Fang, whose first name is Qiu Xian, and whose nickname is Ren Shu. Born in 18 1 1, 65438+122, and died in 1882, 65438+9, Haining, Zhejiang Province, he was a famous mathematician, astronomer and mechanic in modern China. He founded the power series expansion of quadratic square root and studied various trigonometric functions.

Chinese name: Li.

Alias: Li (original name)

Nationality: China.

Ethnic group: Han nationality

Place of birth: Haining, Zhejiang

Date of birth: 18 1 1 year 65438+1October 22nd (Xin Weinian).

Date of death:1882 65438+February 9.

Occupation: mathematician, astronomer, mechanic, etc.

Main achievements: pointed cone technology, stacking technology and prime number theory.

Representative Works: Gu Zexi's Arithmetic

The life of the character

Li (181165438+1October 22nd-1882 65438+February 9th) was born in a family of literati, and his ancestors can be traced back to Li Boyi, the capital of song dynasty (. Boyi has been studying and talking about Taoism all his life, and he is not willing to make progress. At the beginning of the Yuan Dynasty, his son Li Yanju was virtuous and upright, so he asked the doctor Jiaxing Road to get acquainted with him, and his family settled in Shixia Town, Haining County. For 500 years, the family line has been passed down to 17' s grandson, named Li Zulie, Mr. Xu Gu, who studies Confucian classics. Zu Liechu married the granddaughter of Wanghai county magistrate Xu Jixi, but unfortunately Xu died young; Married his wife and sister, filled the house, and then died. The second wife, Cui Shi, is the daughter of Cui Jingyuan, a famous Confucian. Cui Shi gave birth to three sons: Lan Xin (Shan Lan), Messing and Xin Rui, and a daughter. Mei Xin knows math, too. Li married his wife Xu Shi in his hometown in his early years and had no children; In his later years, he married a concubine, Mi Shi, in Beijing, but he still didn't have a son. Is the adopted nephew Cui Jingchang as the heir. Jing Chang, who sang Mei, used to be a document of Jiang Customs.

Li studied in a private school since childhood and received a good family education. He is intelligent and studious, and he can recite the poems he has read at a glance.

At the age of 9, Li found a China ancient mathematical masterpiece "Nine Chapters Arithmetic" on his father's bookshelf, which was very novel and interesting, and he became fascinated with mathematics from then on.

14 years old, Li learned the first six volumes of Euclid's Elements of Geometry, namely Xu Guangqi (1562- 1633) and Matteo Ricci (M. Ricci,1522-1663) in the late Ming Dynasty. Euclid's strict logical system and clear mathematical reasoning are quite different from the traditional mathematical thinking in ancient China, which emphasized practical solutions and calculation skills, and each has its own characteristics and advantages. On the basis of Nine Chapters Arithmetic, Li absorbed the new ideas of Geometry Elements, which made his mathematical attainments deeper and deeper.

A few years later, as a student of a county, Li went to Hangzhou, the provincial capital, to take the provincial examination. Because he "dabbled in exegetics, but he was not as good as arithmetic, so he was deeply involved in arithmetic" (Li Xizhai's Arithmetic Preface), and as a result, the eight-part essay was not well done and fell behind. But he doesn't mind at all. Instead, I took advantage of the opportunity in Hangzhou to collect all kinds of math books, bought back Ye Li's circle-measuring goggles and Dai Zhen's Pythagoras circle, and studied them carefully, which greatly improved my math level.

Wu, a native of Haiyan, wrote in the poem "Reading the Book of Domains, Showing Uncle Li": "Many streams converge into one valley, and elegant words count. There are factions in China and the West, and the diameter of the circle is poor. " "Three series to explore China method, the rest is difficult to understand. The rest are eager to learn, and their minds are poor and single-minded. " Xu Xiang's Notes to Xia Chuan's Poems: "Qiu Yong (Wu) inherited Mr. Siting's family studies, and was especially stubborn and earnest. Uncle Li in Tongli is good at being a teacher in Lanzhou. " It seems that Li once studied mathematics with his teacher.

In his hometown, Li and Jiang, Cui Dehua and other relatives and friends organized the Huyin Society, and often went to Dongshan Villa to sing with different rhymes. At that time, the height of Dongshan Mountain was calculated by using the principle that the corresponding sides of Pythagoras were proportional. Chen Huan, his teacher of Confucian classics, said in The Origin of Teachers and Friends that he "always set a table line when learning the technique of nine numbers, and used the length formula to measure the sun scenery according to the seasonal climate, so it was easy to miss the exam". Yu _ said in Vernacular that he "sat on the top of the mountain at night and measured the latitude of the image". There is still a story in Li's hometown: on his wedding night, he poked his head out of the attic window to see the stars.

1840, the Opium War broke out and imperialist powers invaded China, which inspired Li's thought of saving the country through science. He said, "Wow! Today, European countries are becoming more and more powerful, which is a border issue for China. Pushing the original reason, the machine is fine, and pushing the original machine is fine, which is clear. " "In China, everyone learns to calculate on different days and makes beautiful instruments. In other countries outside Weihai, he was shocked and paid tribute. " Since then, he has been engaged in mathematical research in his hometown.

Around 1845, Li set up a library in Jiaxing to teach students, and was able to meet scholars (mainly mathematicians) in Jiangsu and Zhejiang provinces (1799- 1862), Zhang (1808- 1885) and Zhang. During this period, Li's works on "Pointed Cone Technique" such as Interpretation, Revealing Arrow's Secret and Logarithmic Exploration came out one after another. Later, he wrote Four Yuan Festival and Linde Shu Jie.

185 1 year, Li met the famous mathematician Dai Xu (1805- 1860). Dai Xu said in 1852: "Last year, I gave it to Haichang's uncle, and he gave me the unfinished manuscript for revision, and my uncle rewarded me with the arc and the second line cutting. Is it rare to have the help of friends and friends? " (Preface to Dai Xu's Confidentiality Rate) Li and his friends learn from each other academically and learn from each other's strengths. He and mathematicians Luo Shilin (1774- 1853) and Xu Youren (1800- 1860) also "post questions and reply frequently."

In the summer of 1852, Li went to Shanghai Mohai Library to show his mathematical works to foreign missionaries in China, which was appreciated by (A. Wylie, 18 15- 1887) and others. From then on, he began to cooperate with foreigners to translate western scientific works.

The first work translated by Li was the last nine volumes of Euclid's Elements of Geometry. At the same time, he translated twenty volumes of Re-learning with J. Edkins (1823-1905). Later, he also translated Tan Tian (Volume 18), Algebra (Volume 13) and Grading in Differential Calculus (Volume 18) together with Wei (Volume13). The above books were published by Shanghai Mohai Library 1857 to 1859. In addition, he co-translated Naiduan Mathematics with Alexander Wylie and John J. Flair (that is, Newton's Mathematical Principles of Natural Philosophy), but it was not completed and could not be published.

1860, Li was a guest in the shogunate of Jiangsu Governor Xu Youren. After the Taiping Army occupied Suzhou, all his articles, including all kinds of manuscripts, were lost. From then on, he "refused to care about current affairs", avoided Shanghai, immersed himself in mathematical research and wrote a new book. At the same time, he had academic contacts with mathematicians such as Wu Jiashan and Liu Yicheng.

186 1 autumn, Zeng Guofan (181-1872), the leader of the westernization movement and governor of the two rivers, founded Anqing Inner Ordnance Institute in Anhui, and invited the famous chemist Xu Shou (1872). 1862, Li was also hired as a bookstore owner. As soon as he arrived in Anqing, he took out mathematics books such as Geometry Elements destroyed by the war, requested Zeng Guofan to reprint them, and recommended Zhang, Zhang Sigui and others to enter the curtain. They live in the same place, often have academic discussions and actively participate in activities related to science and technology in the new westernization policy.

1In the summer of 864, Zeng Guofan captured Tianjing (now Nanjing), the capital of the Taiping Heavenly Kingdom, and Li and others followed him to Nanjing. He once again proposed to Zeng Guofan to engrave his translated math books into words, which was supported and funded by Zeng Guofan. Therefore, 1865 Jinling Edition Geometry Elements 15 Volume and 1867 Jinling Edition Gu Ze Xi Zhai Arithmetic 24 Volume were published one after another. At the same time (1866), Li Hongzhang (1823-6544), who founded Jinling Machinery Bureau in Nanjing,

1866, Astronomical Arithmetic Museum was merged into Shi Jing Wentong Museum. Li was recommended by Guangdong Governor Guo Songtao (1817-1891) as the head teacher of astronomical arithmetic, while Li was busy publishing books in Nanjing until 188. From then on, he turned to mathematics education and research completely until 1882 died. During this period, there were about 100 students. Oral instruction and finger painting have been going on for more than ten years. Students are all successful in their studies, or are officials from other provinces, or travel abroad "("Cui Jingchang's Uncle Li Junchuan "), and celebrities include Gan, Xiong Fangbai, Chen Shoutian, etc. In his later years, two of his favorite students, Jiang Huaiting and Cai Xiyong, wrote to China and said, "There is nothing more gratifying than this, and I am anxious to tell you." These people have played an important role in spreading modern science, especially mathematics knowledge.

After Li arrived at the museum, he was awarded the title of "Zhongshu in the branch library of Zhongshu" the following year (1869), 187 1 year, 1874 was promoted to the position of the Minister of Foreign Affairs, and 1877 was awarded the title of Minister of Foreign Affairs. For a time, all the "famous officials and great scholars" in the capital made friends with them, and their reputation was greatly improved (Jiang's Poems of Huaiting). However, he still tirelessly engaged in the teaching work of Wentong Library, immersed in academic works. 1872, he published the method of testing numbers, 1877, he solved algebra problems. A few months before his death, he was "still working on the second volume of Pythagoras series, so old and diligent" (Cui Jingchang

Li's research achievements in mathematics are mainly found in his book Xizhai Arithmetic 13, 24 volumes, and the Chagen Law entitled Xizhai Arithmetic 14. Gu Zexi's Arithmetic was published in 1867, which contains his various works on celestial arithmetic in recent 20 years. There are Fiona Fang 1 volume (1845), Revealing Arrow 2 volumes (1845), Logarithmic Exploration 2 volumes (1845), Superimposed Correlation 4 volumes and Quaternary Solution 2 volumes. Elliptic Addendum 3, 1 true tactics of rolling firearms (1858), 1 explanation of the change of logarithmic cone, 1 regression of rolling sequence, 1 rolling field or text, 1 rolling number method. Li's other mathematical works include Interpretation of the Round Sea Mirror, Diagram of the Round Sea Mirror, Nine-volume Diagram, Arithmetic Course in the Museum, Zhu Fuzhen and so on.

Li's mathematical achievements mainly include three aspects: sharp cone skills, stacking skills and prime number theory.

Education business

From 1868, Li was recommended as the chief teacher of astronomical arithmetic in the museum. Until 1882 died, he had been engaged in mathematics education for more than ten years. During this period, he examined and approved mathematics textbooks such as Arithmetic Collected in Wentong Museum and Zhu Jinshu Ju Zhen, and trained a large number of mathematics talents. He is the founder of modern mathematics education in China.

school achievement

Li's achievements in mathematical research mainly include three aspects: sharp cone, piling up and prime number theory. Before analytic geometry and calculus were introduced to China, the theory of cone-tip technology was mainly written in three works, namely, Fiona Fang's Interpretation, Revealing the Secret of Arrow and Logarithmic Exploration, about 1845. The concept of "sharp cone" founded by Li is a geometric model to deal with algebraic problems. His description of "sharp cone curve" is essentially equivalent to giving equations such as straight line, parabola and cubic parabola.

He created the quadrature of a cone. It is equivalent to the formula of definite integral and the law of item-by-item integration of power function. He independently obtained the power series expansion of binomial square root by "element separation" and obtained the infinite series expression of π by combining with "quadrature of sharp cone". The expansions of various trigonometric functions and inverse trigonometric functions, and the expansions of logarithmic functions.

Using calculus to deal with mathematical problems has achieved creative results. The superposition theory is mainly found in the superposition ratio class, which was written in the period of 1859 ~ 1867. This is a work about high-order arithmetic progression. Li started with the study of China's traditional accumulation problem, and made some achievements equivalent to modern combinatorial mathematics. For example, "Triangular Stack Product Finding High Square Inexpensive Angular Table" and "Square Stack Inexpensive Table" are essentially the first famous Stirling numbers and Euler numbers in combinatorial mathematics. This is the famous "Li Identity" at home and abroad.

Since the 1930s, it has been widely concerned and appreciated by the international mathematics community. It can be considered that "stack-than-class" is the representative work of early combinatorial theory. The theory of prime numbers is mainly found in "Looking Up Numbers" published by 1872, which is the earliest work of prime number theory in China. When judging whether a natural number is a prime number, Li proved the famous Fermat prime number theorem and pointed out that its inverse theorem was not valid.

Li made outstanding contributions to the spread of classical mechanics in China. He translated the Course of Elementary Mechanics (second edition, 1833) written by the Englishman W. William Huiwell into Chinese (dictated by Ai), and published it in 20 volumes by Shanghai Mohai Library on 1859. This is the first Chinese translation that systematically introduces mechanics.

In the preface written by Li for the book Re-learning. Special emphasis is placed on the content of dynamics: "Push for a while and learn from it like shelling the enemy; Pushing for a long time is like five stars circling the sun, the moon circling the ground, and then learning. " "There are three rates of dynamic relearning: strength, quality and speed. If the strength is the same, the speed of people with small mass is high, and the speed of people with too large mass is low; If the quality is the same, the strength is small and the mystery is small, and the strength is high and the speed is fast. " "Dynamic relearning is pushing speed. Everything cannot move automatically, but it has the power to move. If it does not apply force after moving, it will move at a uniform speed. If you apply a constant force after moving, you will gradually accelerate. " "When everything rotates, it will ring the center of gravity and move. When two things are connected and intertwined, they will encircle the center of gravity and the moon and the earth will move together. "Li and william alexander jointly translated the book Outline of Astronomy written by the British astronomer Herschel (1792 ~ 187 1). The Chinese translation is called "Talking about Heaven" and published in 1859. Li made some omissions in his writing. This book not only systematically introduces modern astronomy to China for the first time. The theory of universal gravitation and celestial mechanics are also introduced. Chinese translation of some mechanical terms, such as perturbation and nutation. It was first seen in Chatting with Heaven. Since then, Li has been translating Newton's Mathematical Principles of Natural Philosophy. Although this book has not been completely translated, it has been lost after translation. However, since Li introduced Newtonian mechanics to China, the ideological system, viewpoints and methods of western modern science and some achievements in the history of modern science have brought new knowledge to China scholars, and at the same time aroused the enthusiasm of China scholars to learn natural science.

In "Real Gun and Live Gun Tactics", Li put forward a method of trajectory diagram according to the range formula of projectile on plane or inclined plane without considering air resistance. Although these achievements were lower than the ballistics level in Europe at that time, they reflected the process of natural science from introduction to digestion.

Personal work

Li works

Between Daoguang and Daoguang, four Yuan Jie, Linde Shu Jie, arrows reveal secrets, square gardens reveal mysteries, logarithmic exploration, etc. , thus gaining great fame. Xianfeng completed the unfinished business of Xu Guangqi and Matteo Ricci in the late Ming Dynasty. He has also translated many books on western mathematics and natural sciences, such as Generation Generation Generation, Re-learning and Tian Lun, etc.

At the same time, he took "Measuring the Round Sea Mirror" as the basic teaching material and trained many talents. He studied ancient and modern times and integrated Chinese and western mathematics. From 65438 to 0860, he participated in scientific and technological activities in the Westernization Movement.

The main works are collected in Gu Zexi Zhai Arithmetic, 13 kinds, 24 volumes. Among them, the discussion on the quadrature of a sharp cone has begun to take the form of integral, and the research on the solution methods of trigonometric function (Lee's trigonometric identity), logarithmic power series expansion and higher-order arithmetic progression summation (natural number power summation formula) has reached a very high level in traditional mathematics in China.

Translate and publish works

In the ninth year of Xianfeng, the last seven volumes of Geometry Elements were published together. Because of the war, the original was destroyed. Reprinted by Li Hongzhang in the fifth year of Tongzhi, published by Shanghai Liuhe Bookstore in the fourteenth year of Guangxu. The translation and publication of Re-learning systematically introduced classical mechanics knowledge such as Newton's laws of motion to China. Together with William Alec, Li translated Hou's Talk about Heaven (now translated by J Herschel), and introduced the law of gravity and celestial mechanics to China for the first time. Soon, Li translated the first three volumes of Naiduan's Mathematical Theory (Newton's Mathematical Principles of Natural Philosophy), which was interrupted for some reason.

1867, he published Gu Zexi Zhai Arithmetic in Nanjing, and collected works on mathematics, astronomy and ballistics for more than 20 years, including Fiona Fang's Interpretation, Revealing the Secret of Arrow, Logarithmic Exploration, Overlapping Comparison, Quadruple Solution, Linde's Technical Solution, and Ellipse Orthography. In addition to Gu Zexi's Arithmetic, his mathematical works include Kaushugen's Method, Subu Cao Yan, Bi Yuan Hai Jing Jie and Jiu Rong Tu, but the unpublished works include The Method of Making Pythagoras Integer Series, The Ancient Meaning of Fang Zi, The Study of Group Arithmetic, The Solution of Algebraic Difficult Problems, etc.

Engineering schedule

1840, he wrote Tian or Wen, which is his earliest mathematical work.

1845 published The Mystery of Fiona Fang, Revealed by Arrows and Logarithmic Exploration.

1846 published two volumes of "four-yuan solution", with Gu Guangguang as the order.

In 1848, published by Linde and Li Jie in three volumes.

/kloc-went to Shanghai in 0/852, cooperated with British missionary Alexander Wylie and others, and began to translate western mathematics books, and occasionally translated some books on mechanics, astronomy and other disciplines. Collaborated with Valerie Yali, an Englishman, to translate the last nine volumes of Elements of Geometry, which was completed at 1856.

After 1856, he successively wrote two volumes of Elliptic Orthodoxy, three volumes of New Ellipsis 1, Ellipsis Supplement, Historians' True Judgment 1, Cone Transformation Method 1 and Series of Four Techniques.

1859, Mohai Library published Algebra 13, Grading in the Generation of Micro-products 18 and Chat 18. At the same time, he and Ai translated 20 volumes of Fu Xue and 3 volumes of Theory of Conic Curves. During this period, he also cooperated with Alexander Wylie and John Flair to translate several volumes of Newton's masterpiece Mathematical Principles of Natural Philosophy.

His work, together with valuable research on western mathematics by Hua, Xia Luanxiang and others, constituted the second introduction of western mathematics in China after Xu Guangqi, which played a positive role in the development of modern mathematics in China.

In his translation, he created many mathematical terms and terms, such as differentiation and function, which were translated appropriately, and quite a few terms are still in use today.

From 65438 to 0860, he served as an adjutant in Xu Youren and Zeng Guofan's army, and actively participated in scientific and technological academic activities in the Westernization Movement with chemist Xu Shou and mathematician Hua.

Personality influence

Li made great contributions to the Chinese translation of modern western physics knowledge in the19th century. His translation also played an enlightening role in the development of modern physics in China. In the seventh year of Tongzhi, Li went to Beijing, where he served as the director of astronomy and mathematics department of the museum, teaching for 13 years, and contributed the first generation of scientific talents to modern China. Li made a pioneering contribution to the spread and development of modern science in China.

Li became another outstanding representative in the history of mathematics in Qing Dynasty. He translated many books on western science and technology in his life, and introduced the latest achievements of modern science from astronomy to plant cytology to China, making outstanding contributions to the development of modern science.

Since the 1930s, Li has been widely concerned and appreciated by the international mathematics community.