The subject of studying the history of mathematics development is a branch of mathematics and an important branch of the study of the history of natural science. Like all natural history, the history of mathematics is an interdisciplinary subject between natural science and historical science. The methods used in the study of mathematical history are mainly historical scientific methods, which are different from the usual mathematical research methods in this respect. Its research object is the history of mathematical development, so it is different from the usual historical science research object. Specifically, it studies:
(1) research methods of mathematical history; (2) General history of discipline development-general history of mathematics; (3) Branch history of each branch of mathematics (including small branch history); ④ History and comparison of mathematics in different countries, nationalities and regions; ⑤ Mathematical chronology in different periods; 6 biographies of mathematicians; ⑦ The development history of mathematical ideas, concepts and methods; The relationship between the development of mathematics and other scientific and social phenomena; Pet-name ruby history of mathematics education; Attending the philology of mathematical history; Wait a minute. According to its research scope, it can be divided into internal history and external history.
Internal history studies the history of mathematical development from the internal reasons of mathematics (including its relationship with other natural sciences);
Waishi studies the relationship between mathematical development and other social factors from external social reasons (including political, economic, philosophical and other reasons).
The history of mathematics and all branches of mathematics research are closely related to all aspects of social history and cultural history, which shows that the history of mathematics is interdisciplinary and comprehensive.
People have been studying the history of mathematics for a long time. In ancient Greece, someone once wrote a history of geometry, but unfortunately it failed to pass down. However, in the 5th century, Proclus still kept some information in the annotation of Euclid's Elements of Geometry. In some biographies and mathematical works in medieval Arab countries, the lives of some mathematicians and other materials about the history of mathematics have been told. /kloc-in the 0/2 century, a large number of ancient Greek and medieval Arabic mathematics books were introduced to western Europe. The translation of these works is not only the mathematical research at that time, but also the collation and preservation of classical mathematical works.
The history of mathematics in modern western European countries was studied from18th century by J.? Montucla, C. Bossuet and A.C. K started at the same time, represented by the History of Mathematics published by Montucla in 1758 (1799 ~ 1802 supplemented by J. de Lalander). 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 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 also wrote a history of mathematics, which was included in the series of Mathematical Principles. Soviet scholars represented by Jozkiewicz and Japanese scholars represented by Mi Yongchang Ji Kazutaro also published several volumes of General History of Mathematics. 1972 The book "Ancient and Modern Mathematical Thoughts" written by American M. Klein is considered to be a masterpiece since the 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 the 1930 s, the famous algebra scientist Fan? De? Walden Lake 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. Fan? De? Walden's The Awakening of Science (1954) was added to the history of mathematics in ancient Greece and became one of the authoritative works in the history of mathematics in the ancient world.
(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 Biographies of mathematicians in past dynasties, as well as the arrangement and publication of their complete works and anthologies, are one of the great works 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.
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 Hanshu? According to the Annals of Fa Li, mathematics is "deducing calendars, creating laws, making devices, planning circles, squares, weights, balances, scales, quantities, exploring stability, exploring depth and reaching far, without exception". Sui Shu? Fahuazhi records 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 ~) It "began in the Yellow Emperor and ended in the Zhao (Qing) Dynasty. All scholars for this purpose have passed it down artificially ",and edited by Ruan Yuan and Li Rui (1795 ~ 1799). Later, Luo Shilin wrote an addendum (1840), Zhu Kebao wrote three biographies of local people (1886) and Huang wrote four biographies of local people (1898). Biography of the Domain People is actually a biographical history of mathematics. 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 began to collect ancient books, conduct textual research, sort out and carry out research work around the May 4th Movement. After more than half a century, Li Yan's thesis has been compiled into Essays on the History of Arithmetic (1 ~ 5, 1954 ~ 1955), and Qian Baocong's Essays on the History of Science (1984) has been published. 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.
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History of mathematics
Since the founding of New China, due to the advocacy of Professor Li Yan, Professor Qian Baoyu and Professor Yan Dunjie, many spontaneous people in our country have been engaged in the study of the history of mathematics. These people do research independently and seldom consult each other academically. However, there are indeed many difficult problems to be solved in the history of Chinese mathematics and foreign mathematics. It is because of the needs of the situation at that time that these "self-employed" are urgently needed.
1977 "mutual aid group" has been established for fifteen years. During this period, we learned from each other, supported each other and helped each other, and did a lot of gratifying work for the history of science and technology in China. For example, 1984, entrusted by the State Education Commission, held a seminar on the history of Chinese and foreign mathematics in Beijing Normal University. In addition to more than 100 institutions of higher learning, there are also famous contemporary mathematicians Professor Jiang Zehan, Professor Wu Wenjun and Professor Wang Zikun who come to the "lecture hall" for guidance and lectures, and more than 10 famous mathematical historians from all over the country are invited to give lectures or give special lectures. During the "Workshop", not only the slides of ancient mathematics books in China and the slides of scientific and technological cultural relics collected by the Palace Museum were displayed, but also hundreds of scientific and technological cultural relics collected by the Palace Museum were visited. The activities of this "seminar" have received very fruitful results. After that, many people became interested in the history of mathematics and joined the ranks of the history of mathematics, so as to learn, discuss and study the history of mathematics. Some people are actively preparing to offer courses in the history of mathematics, thus changing the extremely disproportionate situation that only eleven universities in China offer courses in the history of mathematics.
In China's classical mathematics, Nine Chapters Arithmetic and Nine Chapters Shu are two famous academic works, among which there are many unsolved mysteries and problems. In order to solve these problems in scientific research and teaching, entrusted by the State Education Commission, a summer seminar on "Nine Chapters of Arithmetic and Nine Chapters of Calculations" was held in Xuzhou Normal University from 65438 to 0986, which was 40 to 50 in China. People agreed that this "seminar" solved the practical puzzles and difficulties in the research and teaching of Chinese mathematical history. During the "workshop", in addition to teaching courses and special reports, many "special discussions" were organized; In the "special discussion", you can speak freely, express your different views, debate and answer questions; Therefore, the "special discussion" has received unexpected results. After that, he also visited the historical sites and unearthed cultural relics exhibitions in Xuzhou area.
At first, there were 1 1 colleges and universities offering courses on the history of mathematics, and later it gradually expanded to more than 60 colleges and universities. However, this large-scale expansion makes the teaching material of the history of mathematics an urgent problem, so relevant personnel are organized to compile the teaching material. 1986 and 1987 published two university textbooks, A Brief History of Chinese Mathematics History and A Brief History of Foreign Mathematics History, respectively, which not only solved the problem of lack of mathematics history textbooks in some universities, but also provided amateur reading materials for some graduate students. These two textbooks have been adopted by most universities.
In order to unify the teaching requirements of the history of mathematics in colleges and universities, and unify the training scheme for graduate students in the history of mathematics, eight colleges and universities were convened in Beijing Normal University 1984, and jointly formulated the Teaching Outline of the History of Mathematics for Chinese and Foreign Students in Colleges and Universities (Draft) and the Training Scheme for Graduate Students in the History of Mathematics (Draft), which were reported to the State Education Commission for the record.
In the training of graduate students, not only graduate students exchange visits with relevant personnel of "mutual aid group" schools, but also invite relevant personnel of "mutual aid group" schools to give lectures, which promotes the connection between schools in postgraduate training; As for the advanced students from Munich University in Germany, Tokai University in Japan and Tohoku University in Japan who came to Beijing Normal University for further study, they also received the support of the relevant personnel of the "mutual aid group" school.
In order to dig deep into China's classical mathematical masterpieces, a series of studies on the history of Chinese mathematics was made, and two academic monographs were published in 1982 and 1987 respectively, namely, Nine Chapters of Arithmetic and Liu Hui and Qin and Nine Chapters of Shu. After the publication of these two books, they aroused strong repercussions at home and abroad and were highly praised by many experts at home and abroad. They think that the study of the history of Chinese mathematics is not a problem that can be studied in depth. On the contrary, they think that the research prospect of the history of Chinese mathematics is very broad and promising. Therefore, many scholars at home and abroad are engaged in the study of the history of Chinese mathematics. Because these two monographs are very special, some academic papers in other fields are not convenient to be included, so at almost the same time, the Essays on the History of Chinese Mathematics (I), Essays on the History of Chinese Mathematics (II) and Essays on the History of Chinese Mathematics (III) were published successively. Therefore, it provides an academic garden for scholars and readers.
In order to carry forward China's excellent ancient science and technology culture, with the approval of the State Education Commission, the National Natural Science Foundation and other five units funded it twice. The "740th Anniversary of Qin Jiuzhang and Nine Chapters Arithmetic" and Liu Hui's academic thought seminar were held in Beijing Normal University at 1987 and 1965438 respectively. Academic seminars on such topics are rare in the world, so they have attracted the attention of international academic circles. Before the meeting, they received congratulatory messages from many international academic celebrities, and after the meeting, they received conference papers. Scholars attending the meeting include 10 ethnic groups, with more than 50 and 60 people respectively. These two international conferences on special topics have had a great influence in international academic circles.
In order to deeply study China's classical mathematics, it was originally planned to publish books such as Essays on the History of Chinese Mathematics (IV), Research on Liu Hui, History of Chinese Mathematics, Mathematics of Southern and Northern Dynasties, Mathematics of Sui and Tang Dynasties, etc. Among them, Essays on the History of Chinese Mathematics (IV) has been published for a long time, but it has not been published for technical reasons. The History of Chinese Mathematics is stepping up its writing; It is a national key book during the Eighth Five-Year Plan period and has a long way to go. All the authors are confident to finish this task. The study of Liu Hui is the inheritance and development of Arithmetic in Nine Wars and Liu Hui. After six years of preparation and overcoming many difficulties, I finally met the readers. For various reasons, there are still many unsatisfactory places. Please forgive me, criticize and correct me. The publication of Liu Hui Research can not be separated from the great help and support of Taiwan Province Jiuzhang Publishing House, Shaanxi People's Education Publishing House, Mr. Sun Wenxian and Mr. Yang Yi. Here, I would like to express my heartfelt thanks. I was going to have a comprehensive and in-depth discussion on Liu Hui's achievements. However, due to the late publication, late distribution and time-consuming proofreading, I would like to extend my deep apologies to readers.
Today, the "mutual aid group" is no longer suitable for the needs of the current situation, and it has been replaced by the "talent group". We seek truth from facts, keep moving forward and strive for new achievements.
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I hope it helps you.