巴黎综合理工学院早期的分析课与数学人才培养

The Teaching of Analysis and the Making of Mathematicians at the Ecole Polytechnique in Its Early Period

巴黎综合理工学院建立之初的目标是为国家培养管理人才和建设方面的工程师,但同时从这里走出了一批以教师为职业的数学家,构成了促进19世纪数学发展的重要力量。本文从该学院早期的分析课及人才培养两个方面进行探讨和分析,揭示促进19世纪法国数学研究的多种因素。这些因素既有认识论层面的,亦有制度层面的。拉格朗日作为该学院第一位分析课教师,在课程中提出了重要的数学分析理论,并努力将分析学严格化。他和蒙日的课程影响和鼓励了学院内年轻教师和学生开展数学研究。学院刊物也为数学研究和交流提供了平台。这些都推动了19世纪数学的发展和数学家群体的形成。明晰这一过程将使我们深入理解19世纪欧洲数学发展的特征和机制。

The Ecole Polytechnique was established to train engineers and administrators for serving the nation. As a result, it produced many mathematicians, who constituted a powerful force for the development of the discipline of mathematics in the 19^(th) Century. J. L. Lagrange(1736-1813), as the first professor of analysis at this school, presented significant theories of mathematical analysis and made efforts to bring rigor to this branch of mathematics in his teaching. Moreover, the course given by him and Gaspard Monge(1746-1818) influenced and encouraged both young teachers and students at this school to carry out mathematical research. The two journals created at the school provided a platform for them to publish their work, and hence stimulated the communication and transformation of mathematical knowledge. To clarify this history would help us to grasp the characteristics and the dynamic of the development of mathematics in Europe in the 19 th century. By analyzing the contents of the course that Lagrange taught at the Ecole Polytechnique and how mathematicians were produced there, this article aims to pinpoint Lagrange’s essential thought on analysis, and to clarify some factors for the development of mathematics, which are both epistemological as well as institutional.