十九世纪晚期统一几何学的两种途径  

Two Ways of Unifying Geometry in the Late 19^(th) Century

作　　者：张俊青[1] 

机构地区：[1]长治学院数学系,山西长治046000

出　　处：《中央民族大学学报（自然科学版）》2016年第1期22-26,共5页Journal of Minzu University of China(Natural Sciences Edition)

基　　金：山西省高等学校教学改革项目(No.J2012106)

摘　　要：十九世纪几何学呈现出分支林立、支离破碎的局面,由此,用统一的观点解释几何学便成为数学家的重要任务.克莱因以变换群的思想统一几何学,希尔伯特提出了另一条对现代数学影响深远的途径——公理化方法,这两种思路已经远远超出几何学的范围而成为现代数学统一化趋势的重要推手.然而,这种统一化、标准化的数学思维和数学"生产方式"只是基础主义者一厢情愿的幻想.In the 19th century, the geometry showed branch of various and reduced to fragments. Thus, it become an important task of mathematicians using unified view to explain them. Klein uni- fied geometry by the thought of the transformation group, Hilbert put forward another way to unify geometry, that was axiomatic method. The two ways had gone far beyond the scope of the geometry to become an important impetus which unified the modern mathematics. However, it is just the wish- ful thinking of Modernist to unify and standardize mathematical thinking and mathematical produc-tion.

关 键 词：几何学的统一 变换群 公理化方法 

分 类 号：N09[自然科学总论—科学技术哲学]