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1.数学是一种科学.一般说来,科学具有二种区别于文学、绘画、音乐、彫塑甚至建筑等文艺的根本性质.科学是累积而成的;科学本身就是一部科学史.也就是说,人们可以互不相关地阅读柏拉图、但丁、李太白、莎士比亚和迦梨陀娑等人的作品,而这些人谁也不曾显著地影响过谁。但是除了数学史上的一些专家们,又有谁读过阿基米德、牛顿和高斯的著作呢?诚然,每一个造诣颇深的数学学者必須在思想上一遍又一遍甚至整套地思考阿基米德、牛顿和高斯曾经发现的一些主要方法.虽然,在某种意义上说,他们的工作是陈旧的,但它已经进入人类知识总体,将继续生存下去.这正好说明了科学的累积性和数学包含自身历史的这一事实.
1. Mathematics is a science. In general, science has two fundamental characteristics that distinguish it from literature, painting, music, sculpture, and even architecture. Science is cumulative; science itself is a history of science. It is said that people can read the works of Plato, Dante, Li Taibai, Shakespeare, and Jia Li Tuojia without reference to each other, and none of these people have ever significantly influenced anyone. But in addition to some experts in the history of mathematics, who has read the works of Archimedes, Newton, and Gauss? It is true that every accomplished mathematician must think about Akimmi again and again or even in thought. Some of the main methods that Germany, Newton, and Gauss once discovered. Although, in a sense, their work is obsolete, it has entered the overall human knowledge and will continue to survive. This just illustrates the cumulative nature of science and The fact that mathematics contains its own history.