The history of geometry was written in ancient Greece, but it has never been handed down.

(2) In the 5th century, Proclus kept some data in the annotation of Euclid's Elements of Geometry.

(3) Some biographies and mathematical works in medieval Arab countries tell the lives of some mathematicians and other materials about the history of mathematics.

(4)12 century, ancient Greek and medieval Arabic mathematics books were introduced into western Europe. The translation of these works is not only a mathematical study, but also the collation and preservation of classical mathematical works.

The history of mathematics in modern western European countries;

From the18th century, J. Montucla, C. Bo Xue and A. C. K started at the same time, represented by the History of Mathematics published by Montucla in 1758 (1799 ~ 1802 by J. De. Since the end of 19, the number of people studying the history of mathematics has gradually increased, and the study of chronology and subject history has gradually begun. After 1945, there has been a new development. The research on the history of mathematics after 19 can be divided into the following aspects.

(1) The representative works of general history research can be quoted from M.B. Cantor's Lecture Notes on the History of Mathematics (4 volumes, 1880 ~ 1908) and C.B. Boyer (1894,19). The Bourbaki school in France wrote the history of mathematics into Principles of Mathematics. Soviet scholars represented by Jozkiewicz and Japanese scholars represented by Mi Yongchang Ji Kazutaro also published several volumes of General History of Mathematics. 1972 American m Klein's book ancient and modern mathematical thoughts is a masterpiece since 1970s.

(2) History of Ancient Greek Mathematics Many works of ancient Greek mathematicians have been translated into modern languages, among which J.L. Heiberg, hultsch, T.L. Heath and others have all made achievements. Loria and Heath also wrote a general history of ancient Greek mathematics. Since 1930s, the famous mathematician Van de Walden has also made achievements in the history of ancient Greek mathematics. Since the 1960s, the work of A. Saab in Hungary has been more prominent. He discussed the origin of Euclid's axiomatic system from the perspective of philosophy history.

(3) Mathematical History of Ancient Egypt and Babylon It is a difficult task to translate Babylonian cuneiform clay tablets and ancient Egyptian papyrus books into modern characters. Chase, archibald and others have translated papyrus arithmetic books, while New Gebauer is more famous for his persistent research on cuneiform blackboard arithmetic books for decades. His Studies on the Historical Materials of Cuneiform Mathematics (1935, 1937) and Cuneiform Mathematics Book (co-authored with saxophone, 1945) are authoritative works in this field. His book "Ancient Precision Science" (195 1) is a collection of research results on the history of mathematics in ancient Egypt and Babylon for half a century. Van de Walden's The Awakening of Science (1954) was added to the history of ancient Greek mathematics and became one of the authoritative works in the history of ancient world mathematics.

(4) Historical Research on Chronology and Branch History (3) The book1Notes on the Development of Mathematics in the 9th Century (1926 ~ 1927) written by German mathematician F klein is the beginning of chronology research on modern mathematics history. It was written in the 20th century, but most of its views on mathematics are 65438. Until 1978, the introduction to the history of mathematics from 1700 to 1900 written by French mathematician J. Dieudon was published, there were not many monographs on the history of chronology mathematics, but there were famous papers such as "Mathematics for Half a Century" written by (C.H.) H. Weil. There are many monographs on the history of various branches of mathematics, from number theory and probability theory to the concept of manifold and the history of Hilbert's 23 mathematical problems, and there are many famous writers. Many famous mathematicians have participated in the study of the history of mathematics, which may be based on (J.-) H. Poincare's belief that "if we want to foresee the future of mathematics, the appropriate way is to study the history and present situation of this science", or as H. Weil said: "If we don't know the concepts, methods and results established and developed by the predecessors of ancient Greece, we can't understand the goal of mathematics in the past 50 years, and we can't understand it.

⑤ The compilation and publication of biographies of mathematicians in past dynasties and their complete works and anthologies is one of the masterpieces in the study of the history of mathematics. In addition, a variety of selected readings of mathematical classics have appeared, bringing together precious fragments of famous mathematicians of all ages.

⑥ Professional academic journals first appeared at the end of 19, including M.B. Cantor (1877 ~1913,30 volumes) and Loria (1898 ~1920 volumes). In modern times, there was the International Journal of Mathematical History edited by the Mathematical History Branch of the International Association for the History of Science.

History of Chinese mathematics:

China is famous for its long history and tradition. The "preparation" section of the official history of past dynasties often discusses the role and history of mathematics. For example, the earlier calendar of the Han Dynasty said that mathematics was "deducing calendars, creating laws, making tools, standardizing roundness, squareness, weight, flatness, balance, balance and quantity, seeking stability, grasping profoundness and doing everything possible". Sui Shu and Li Zhi recorded the history of pi calculation and Zu Chongzhi's brilliant achievements. There are sometimes biographies of mathematicians in the official history of past dynasties. The classic official yearbook records a mathematical bibliography.

The content of the history of mathematics often appears in the preface and postscript of China's ancient books.

For example, Liu Hui's Preface to Nine Chapters of Arithmetic (263) tells the history of the formation of Nine Chapters of Arithmetic; Wang Xiaotong once evaluated the mathematical work of Liu Hui, Zu Chongzhi and others in "Counting Tables in Upper Jicoo"; Zu Ti's preface to the meeting of Siyuan tells the development history from Tianyuan to Siyuan. There is the Origin of Arithmetic in the appendix after Arithmetic Note in Song Dynasty, which is the earliest printed and preserved mathematical historical materials in China and even in the world. At the end of Cheng Dawei's Algorithmic Tongzong (1592), there is a paragraph "The Origin of Calculating Classics", which records the mathematical bibliography between Song and Ming Dynasties.

The above materials are scattered fragments, and the systematic arrangement and research on the history of ancient mathematics in China was carried out in the middle and late Qing Dynasty under the influence of Ganjia School. It mainly includes: ① the collation and research of ancient arithmetic books, the revision, annotation and publication of classic ten calculations (calculations between Han and Tang Dynasties) and Song and Yuan Dynasties, and the discussion with Dai Zhen (1724 ~ 1777) and Li Huang (? ~ 18 1 1), Ruan Yuan (1764 ~ 1849), Shen (1829), Roslin (1789 ~) With a large number of income figures, rich information and appropriate comments, it can be comparable to Montukla's mathematical history.

Li Yan and Qian Baoyu were the founders who used modern mathematical concepts to study and sort out the subject of Chinese mathematical history, which made the study of Chinese mathematical history based on modern scientific methods. They all started to collect ancient arithmetic books around the May 4th Movement. After more than half a century of textual research, collation and research, Li Yan's papers were compiled into a series of Arithmetic History (1 ~ 5 episodes, 1954 ~ 1955), and Qian Baodi owned it. Since 1930s, both of them have published monographs on the history of Chinese mathematics. Li Yan has a history of Chinese mathematics (1937) and a mathematical outline of China (1958). Qian Baoyu has History of Chinese Mathematics (I, 1932) and edited History of Chinese Mathematics (1964). Qian Baoyu's Ten Books of Calculating Classics (1963) is an authoritative work, plus the above monographs.

From the end of 19, someone (,he,) and so on. ) has published articles on the history of Chinese mathematics in foreign languages. At the beginning of 20th century, Japanese Kazuo Sanshi wrote The Development of Mathematics between China and China. In 1950s, Needham made a comprehensive introduction to the history of Chinese mathematics in his magnum opus History of Science and Technology in (Volume III). Some classic mathematics books in China have been translated into Japanese, English, French, Russian and German. In Britain, the United States, Japan, Russia, France, Belgium and other countries, some people directly use China's classical literature to study the history of Chinese mathematics and compare it with other countries and regions.