Wang Fan, a native of Wu Lujiang in the Three Kingdoms, is both an astronomer and a mathematician. He recalculated the length of Sunday according to Pythagorean theorem, and made a new astrolabe with reference to Zhang Heng's theory of astrolabe and his own practical experience in observing astronomy. At that time, the armillary sphere was very small, and the planets on it were too dense to use. The circumference of Zhang Heng's armillary sphere is 10 ft 4 ft 6 in, which is too big to operate. Wang Fan's new armillary sphere, with a circumference of 10 feet, 9 inches and 5 minutes, is smart and practical. Wang Fan also wrote "Hun Tian Tu Ji" to explain the principle of Hun Tian Yi. He calculated that the intersection angle between the ecliptic and the equator is 24 degrees, which is close to 23.27 degrees measured by astronomers with precision instruments. Mathematically, dorri took the accuracy of pi a step further. In ancient China, there has always been a saying that "diameter is one on Wednesday", that is, pi is one third. Zhang Heng further calculated that the square root of pi is 10, which is equivalent to 3. 16. The pi calculated by dorri is 3. 1555, which is also close to the pi calculated by modern times of 3. 14 16. Unfortunately, Wang Fan was born under the tyrant Sun Hao, and he was honest. He was beheaded at the age of 39.

Geng Xun of Sui Dynasty also made great contributions to the making of astronomical instruments. He is a pawn. He once opposed the official government with the Li people in Lingnan. He fell into failure, was punished as a domestic slave, and later became an official slave. When he was a slave, he began to study astronomy, mathematics and mechanical production, and achieved remarkable results. Later, he was promoted to a surname. He created a water elephant without manpower. After practical application, it completely conforms to astrology. According to the ancient Song instrument presented by Tai Shicheng, and absorbing the leakage principle of Li Lan, a Taoist priest in the late Wei Dynasty, he cooperated with Yuwen Kai to make a water leakage device which is easy to carry and use immediately and fixed in front of Ganyang Temple. As long as there is enough water in the leaky kettle, it is an instant, so the time of leaking one or two water is one sixteenth of a quarter, which is much more sensitive than using the floating arrow method to see the score. This kind of timing instrument was widely used in Sui and Tang Dynasties.

Wei Pu, a native of Huainan in Song Dynasty, was a famous folk calendar operator and was deeply appreciated by Shen Kuo, the author of Meng Qian Bi Tan. Shen Kuo recommended him to revise the calendar. He shortened the date of tomorrow's operation by two quarters and revised it into a new Fengyuan Calendar, which was promulgated and used.

Abacus is an outstanding creation of ancient computing tools and algorithms in China, which appeared in the Song Dynasty. Cheng Dawei, a native of Xiuning in the Ming Dynasty, wrote the book Zhi Shu Tong Zong, which is the most complete and influential mathematical work systematically discussing abacus calculation. Cheng Dawei loved mathematics since childhood, then engaged in business, extensively searched ancient and modern mathematics books and visited world famous mathematicians. After decades of work, he wrote this book. This book, with seventeen volumes, was a relatively complete elementary mathematics book at that time. The contents include: Volume I and Volume II, explanations of mathematical terms and expressions, large and decimal systems, measurement systems and fields, 99 formulas, abacus formulas and examples of their usage in abacus calculation, basic operations of integers and fractions, square roots and square roots, etc. Volumes 3 to 12 are divided into ten chapters according to the arithmetic style of nine chapters, which is a compilation of application problems. 13 to 16 volumes are still classified according to the style of nine chapters, and the problem of income mathematics expressed in the form of poetry is called "difficult problem" because of its obscure name; Volume 17 is a miscellaneous method, which consists of a golden cicada peeling off its shell, writing and calculating, a palm of gold, a vertical and horizontal diagram, and a combination of rhythm and Lu. At the end of the book, there is The Origin of Calculations, which records 5 1 kinds of mathematics books from the Yuanfeng period of the Northern Song Dynasty to that time, of which only 15 kinds have biographies, so his description has become a precious historical material for studying the development of mathematics in this period. Arithmetic Unity is a masterpiece of abacus calculation, which not only records all the formulas used in traditional abacus calculation, but also pioneered the method of dividing abacus into cubes and solving quadratic equations, and used abacus calculation to solve quartic and cubic equations at the earliest. This book has had a great influence on later generations. Since its publication, it has been constantly reprinted and adapted, and has become a model for various abacus books in later generations. Soon after its publication, this book spread to Japan. For example, in 1627 "Dust Robbery" published in Japan, more than half of the calculation problems are in the book "Unified Algorithm".

In the late Ming Dynasty, with the arrival of western missionaries in China, the western astronomical system was introduced into China and used for calendar making. Under the auspices of Xu Guangqi, it was compiled into the Calendar of Chongzhen, but before it was put into use, the Ming Dynasty perished. Tang Ruowang, a missionary, was honored after he entered the customs in Qing Dynasty. He cut and condensed the almanac of Chongzhen into the almanac of Western New Law, which attracted the attention of the Qing court. The Qing court named the calendar compiled according to the new law "Li Shixian" and promulgated it to replace the calendar of the Ming Dynasty. Yang Guangxian, a native of Shexian County, is a calendar mathematician. He criticized the western new law and impeached many times, which led to his imprisonment and his death in depression. Yang Guangxian succeeded Qin. Due to the defects in the calculation of China's traditional calendar, Yang Guangxian "knows the principle of pushing steps, but doesn't know the number of pushing steps", and the almanac issued by him is inconsistent with the astronomical phenomena. Later, he was impeached and dismissed by the missionary Ferdinand ferdinand verbiest and others, and planned to be beheaded, so he survived death and died on his way home. Until now, Yang Guangxian has been regarded as a representative of the old school who opposes modern science and technology. But it should be admitted that he studied the traditional astronomical system in China. Although his attack on western France was wrong, it also promoted the missionaries to calculate the calendar more accurately.

The most influential mathematician in the early Qing Dynasty was Mei Wending, a native of Xuancheng, who was known as the first mathematician in the Qing Dynasty. In his attitude towards western science and technology, Mei Wending did not blindly oppose it like Yang Guangxian, but adopted a more rational attitude, advocating both learning and introduction, and opposing wholesale copying. He advocated that regardless of ancient and modern Chinese and western, "learn from others' strengths and be well-founded", and put forward that "scholars who can learn from the law should learn from ancient and modern times". Under the guidance of this thought, he made a comprehensive arrangement and research on Chinese and western astronomy and mathematics known at that time, and formed his own set of mathematical views. Mei Wending enjoyed high prestige in academic circles, when almost all mathematicians had direct or indirect contact and communication with him. Emperor Kangxi appreciated his knowledge very much, summoned him and gave him the amount of "accumulating knowledge and participating in micro-research" as a compliment. Mei Wending persisted in writing all his life and wrote more than 80 books on astronomy and mathematics. Later generations carved them into twenty-nine kinds, and his grandson did not sort them. They are collectively called "Mei Buan Li Shuquan Book" and also called "Shi Mei Series". In mathematics, he compared and combined China's original mathematical heritage with the mathematical knowledge introduced from the west, and he had profound attainments in arithmetic, algebra, geometry, trigonometry, differentiation and integration. In astronomy, he combined with scientific principles introduced from the west, extensively revised and explained more than 70 kinds of calendars in ancient China, and scientifically summarized the calendars in China for thousands of years.

Under the influence and education, several generations of Mei family have studied calendars, such as younger brother, son, grandson Cheng Cheng, Cheng Cheng and great-grandson. 、 ? Hey hey hey? And so on all have expertise in astronomy and mathematics. Mei Yacheng is the most famous among them. He studied arithmetic with his grandfather since childhood and was recommended to the palace to edit and edit the almanac. Mei Ai, the author of The Legacy of Chishui and The Algorithm of Addition and Subtraction, discovered the metonymy method introduced from the west to China, namely the ancient fairy magic of China, which was highly respected. He also co-edited the Origin of Fa Li with He Guozong, including the Essentials of Mathematics edited by him, Chen Houyao and Ming Jiatu. The essence of mathematics basically absorbed all the known mathematical achievements at that time, and it was a comprehensive summary of Chinese and western elementary mathematics. This book discusses and introduces the origin of numbers, various arithmetic problems, the properties of integers, prime numbers and prime number tables, decimal points, stacked products, the solution of linear equations, the solution of higher-order equations, the borrowing ratio, equation theory, logarithmic theory, trigonometry, elementary geometry, slide rule and proportional rule. Some of them are completely new in China's arithmetic history.

Fang Zhongtong, the son of Fang Yizhi, a famous scholar in the early Qing Dynasty and a native of Tongcheng, also summarized the knowledge of mathematics. It took him ten years to write 24 volumes of Sudoku, which roughly covered the Chinese and western arithmetic knowledge that could be seen at that time, including the logarithm that had just come out in the West. It is an encyclopedic work.

During the Ganjia period, mathematicians' main energy shifted to the study of traditional mathematics. Xiuning Dai Zhen is a scholar with many achievements, and he has also made great contributions to the collation of traditional mathematics. He compiled a large number of mathematics books from Yongle Dadian, sorted them out, and worked hard to calculate the ten classic books to clear up the gaps. In addition, he also wrote Pythagoras Che and Strategy. Ling Tingkan of Shexian County has a wide range of academic interests. In astronomy, he discussed the ecliptic orbit and the causes of the four seasons. In mathematics, he was good at spherical triangles and was going to write a book "A Guide to Circular Triangle", but unfortunately he died before he finished the manuscript. Yi Tong's Wang Lai is also knowledgeable, proficient in astronomy and mathematics, and has written the book "Arithmetic of Constant Zhai". Wang Lai has rich knowledge of physics. In books 1 and 4 of Hengzhai Arithmetic, he systematically studied the existence and uniqueness of spherical triangle solutions. The first volume discusses the existence and uniqueness of solutions one by one according to the known conditions of right triangle and non-right triangle. In the fourth book, forty theorems are given to discuss the existence and uniqueness of solutions. In terms of equation theory, although ancient mathematicians in China have been engaged in this research for a long time, they only know that there is a positive root when solving equations. Until the essence of mathematics, quadratic equation can have two positive roots. On this basis, Wang Lai made an in-depth study and realized that cubic equations can have multiple positive roots. The fifth and seventh volumes of Hengzhai Arithmetic specifically discuss that quadratic and cubic equations can only have one positive root. The second half of the fourth volume of Constant House Arithmetic is the theory of recursive mathematics, which specifically discusses the combination problem, defines the combination number, obtains some important formulas, and discusses the discrimination method of each item in the combination and the relationship between combination and stacking. Wang Lai's contribution not only occupies an important position in the history of Chinese mathematics, but also has world significance. Luo Shilin, a native of Shexian County who lives in Yangzhou, carefully studied Siyuan Jade Sword written by Zhu Shijie in Yuan Dynasty and wrote Siyuan Jade Sword and Fine Grass, which made Siyuan Book, an outstanding achievement of ancient arithmetic, known to the world again. He also revised another work of Zhu Shijie, Arithmetic Enlightenment, and sent it back from North Korea for printing and circulation. In addition, he is the author of some mathematical works, such as Composite Skills, Modified Secant Circle Density and Three Stories of Pythagoras.

Women were despised in the society at that time, but some women were positive and even made important contributions to scientific research. Tianchang Wang is one of the best. Her works are said to be as many as sixty-four volumes. The works we can see today include Debate on Profit and Loss, Debate on Respect for Action, Two Explanations of Huangchi, Theory that the Earth is More Important than Nine Days, Theory that the annual rings are fixed in the center of the earth, Pythagoras Triangle Solution, Debate on Precession to Doubt, Theory of the Circle of the Earth, Eclipse Solution and so on. In astronomy, mathematics, geography, meteorology, medicine, history and so on. In order to acquire correct knowledge of astronomy and meteorology, she insisted on observation. The eclipse plan was written on the basis of actual observation, which clearly stated that the earth was a sphere and the backlight became a shadow cone. In The Circle on the Earth, she realized that the space around the earth is not divided up and down, and the sky is everywhere above people's heads, which helps people to establish a correct view of the universe. She is good at thinking. She can not only distinguish between astronomical historical materials and concepts, but also study Mei Wending's works and get the result that the earth is thousands of miles away and the sky is five degrees away.

Lin Tai in Jiaojiang also has a good knowledge of mathematics and astronomy. Mathematically, he has a lot of research on spherical triangles, and he has a book "Examples of Arc Triangles". In astronomy, he is good at measuring the height of the sun from the ground and the radius of the sun by using the triangle principle, and wrote a book "High Arc Fine Grass". He is also good at making various instruments, including simple instruments, astrolabes, proportional gauges, armillary sphere and so on. Hu Yong in Shexian county also made an armillary sphere to observe the sky, the degree and the time. Liu Jingdemaoji is also good at astronomy, and he has written Arctic Altimeter, A Brief Introduction to the Images of Heaven and Earth, and Kun Yu Tu's Theory. And his armillary sphere and celestial ruler are precise and accurate. Ye Shang of Tongcheng also likes astronomy and mathematics, and has written books such as Huntian Shuo, Panorama of the Stars and Equator, Tianyuan Yi Shu Graph Theory, Mathematical Analysis Theory and Pythagoras Theory.