中国数学史的第一次研究是由李炎（1892- 1963）和钱宝聪（1892- 1974）领导的，其主要内容是发现中国过去的数学成就。从1970年代开始，吴文村等人将这一研究范式转变为恢复中国古代数学的{ \it how}。然而，这两种方法都关注同一个问题，即历史中的数学。第三种方法的主题应该是{ \it why} mathematics was done。将这一方法与前两种方法相结合，将使数学史研究范式由历史中的数学范式提升为数学史研究范式。
英文摘要：
The first approach to the history of mathematics in China led by Li Yan (1892--1963) and Qian Baocong (1892--1974) featured discovering {\it what} mathematics had been done in China's past. From the 1970s on, Wu Wen-tsun and others shifted this research paradigm to one of recovering {\it how} mathematics was done in ancient China. Both approaches, however, focus on the same problem, that is mathematics in history. The theme of the third approach is supposed to be {\it why} mathematics was done. Combining this approach with the former two, the research paradigm will be improved from one of mathematics in history to that of the history of mathematics.
In ancient times, China made great contributions to world civilization and in particular to mathematics. However, modern sciences including mathematics came to China rather too late. The first Chinese university was founded in 1895. The first mathematics department in China was formally opened at the university only in 1913. At the beginning of the twentieth century, some Chinese went to Europe, the United States of America and Japan for higher education in modern mathematics and returned to China as the pioneer generation. They created mathematics departments at the Chinese universities and s…
One of the variants for systematizing the activities of the historian of mathematics is proposed, as well as a scheme for organizing research and search work in the preparation of scientific articles and reports on the history of science.
Mathematical conquerors, Unguru polarity, and the task of history
我们比较几种方法的数学史最近提出的Blasjo，弗雷泽-施罗德，弗里德，和其他人。我们认为，从数学和历史的工具是必不可少的一个有意义的历史学科。在昂古鲁-韦伊关于几何代数概念的争论的延伸中，迈克尔·弗里德提出了一个反对安德烈·韦伊（Andre Weil）的“特权观察者”和皮埃尔·德·费马（Pierre de Fermat）的“数学征服者”的案例。“我们分析了弗里德关于昂古鲁所谓的历史学家和数学家历史之间的极性的版本。我们识别出了弗里德曼史学思想的一些公理，并提出了一个思想实验来衡量其相关性。Unguru和他的门徒Corry，Fried和Rowe将Freudenthal，van der Waerden和Weil描述为柏拉图主义者，但没有提供任何证据;我们提供相反的证据。我们分析了各种史学方法如何发挥自己的研究中的先驱数学分析，包括费马，莱布尼茨，欧拉和柯西。
Egyptologists and historians of mathematics around 1930 did an admirable job in showing that problem 14 of the newly discovered Moscow Papyrus from around 1850 BCE amounts to a general and exact calculation of the volume of a truncated pyramid (frustum). They were less successful in giving tentative explanations of what convinced the Egyptians of its correctness. In particular, they never looked into the possibility of dissecting three identical copies of the frustum and recomposing them into three boxes of differing sizes whose volumes can be easily calculated. This is surprising because the …
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics education which is struggling through a crisis of its own, socio-economic and political by its nature. The mathematical community faces Pandora's box of problems, which, surprisingly, are not usually discussed in any connected form. The present paper attempts to address this issue in a bit more joint and cohesive way.
We reconsider the classical equality 0.999. .. = 1 with the tool of circular words, that is: finite words whose last letter is assumed to be followed by the first one. Such circular words are naturally embedded with algebraic structures that enlight this problematic equality, allowing it to be considered in Q rather than in R. We comment early history of such structures, that involves English teachers and accountants of the first part of the xviii th century, who appear to be the firsts to assert the equality 0.999. .. = 1. Their level of understanding show links with Dubinsky et al.'s apos th…
