Historians' duty is to tell history according to historical materials, and seeking truth from facts is the basic principle of historiography. Textual research has been formed in western history since17th century. It appeared earlier in China, especially in the Ganjia period of the Qing Dynasty, and it is still the main method of historical research. However, with the progress of the times, textual research methods are constantly improving and its application scope is expanding. Of course, it is necessary to realize that the historical materials are true or false, and the psychological state of the researchers involved in the research process will inevitably affect the choice of research materials and the results of the research. In other words, the authenticity of the conclusions of historical textual research is relative. At the same time, we should realize that textual research is not the ultimate goal of historical research, and the study of mathematical history cannot be textual research for textual research's sake.
If you can't compare, you can't think. All scientific thinking and investigation are inseparable from comparison, or comparison is the beginning of understanding. The development of today's world is multipolar, and different countries, regions and nationalities develop together in cultural exchanges. Therefore, with the development of the research on the history of multi-world civilization and the weakening of western centralism, heterogeneous regional civilization has been paid more and more attention, and the comparison of mathematical cultures in different regions and the research on the history of mathematical communication have become increasingly active. The comparative study of the history of mathematics often revolves around three aspects: mathematical achievements, mathematical scientific paradigm and the social background of mathematical development.
The history of mathematics belongs to both the field of historiography and the field of mathematical science. Therefore, the study of the history of mathematics should follow the laws of both history and mathematics science. According to this feature, mathematical analysis can be used as a special auxiliary means in the study of mathematical history. In the absence or lack of historical data, we can analyze the contents and methods of ancient mathematics from the height of modern mathematics, so as to trace the source, summarize the theory and put forward historical hypothesis. Mathematical analysis is actually a connection between "ancient" and "present". 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. Since18th century, J Montukra, C. Xu Bo Ai and A. C. K started at the same time, and the History of Mathematics published by Montukra in1758 (1799 ~1802, supplemented by Lalander) is as follows. 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, general history research
Representative works can be quoted from M.B. Cantor's Lecture Notes on the History of Mathematics (4 volumes, 1880 ~ 1908) and C.B. Boyer (1894,1919d.e.). 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. Ancient Greek history
Many works of ancient Greek mathematicians have been translated into modern languages, among which J.L. Heiberg, hultsch, T.L. Heath and others have 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. History of ancient Egypt
It is difficult to translate Babylonian cuneiform clay tablets and ancient Egyptian papyrus 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, dynastic history
The book "19th century (1926 ~ 1927)" written by German mathematician C. is the beginning of the study of chronology of modern mathematical history. It was written in the 20th century, but most of the mathematical viewpoints reflected in it are19th century. Until 1978, the introduction to the history of mathematics written by French mathematician Jean Alexandre Eugène Dieudonné 1700 ~ 1900 was published, there were not many monographs on the history of chronology mathematics, but there were some 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 mathematical problems, and there are many famous writers. Many famous mathematicians are involved in the study of the history of mathematics, which may be based on the belief of (J.-) H. Poincare 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. Will 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. Biography of mathematicians
As well as the arrangement and publication of 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. Journal of Mathematics
It first appeared at the end of 19, M.B. Cantor (volume1877 ~1913,30) and Loria (volume 1898 ~ 1922). 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. 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 History of Han Law said that mathematics is "deducing calendars, generating laws, making tools, planning circles, measuring squares, measuring weights and measures, discovering hidden meanings, grasping abstruse things 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.