19世纪数学的三次变革及其影响  

The Three Transformations of Mathematics in the 19th Century and Their Influence

作　　者：张俊青[1] ZHANG Junqing(Department of Mathematics,Changzhi University,Changzhi 046011,China)

机构地区：[1]长治学院数学系,山西长治046011

出　　处：《广西民族大学学报(自然科学版)》2024年第4期8-15,共8页Journal of Guangxi Minzu University :Natural Science Edition

基　　金：山西省高等学校教学改革创新项目(J2021685)。

摘　　要：19世纪以前的数学在总体上是源于经验的,而在实践应用中解释自然的强大威力使其具有了客观性和唯一性的特质。19世纪出现的非欧几何使几何学摆脱了直观和经验的束缚;群论、四元数的创立和代数运算的公理化使代数学冲破了传统方程的藩篱;分析学应用边界的拓展和统一性的惯性思维促使其严格化、形式化和算术化,最终脱离了物理和几何背景。数学这三大领域发生的革命性变革,使其走上了由内部逻辑推动和人类理性主导的独立自由之路,从而使数学分裂为纯粹数学与应用数学。Mathematics before the 19th century was generally empirical,and the power of explaining nature in practical application gave it the qualities of objectivity and uniqueness.The emergence of Non-Euclidean geometry in the 19th century freed geometry from the constraints of intuition and experience;Group Theory,Quaternion and Axiomatization of algebraic operations enabled algebra to break through the barriers of traditional equations;The expansion of the boundaries of the application of analytics and the inertial thinking of unity promote its rigorization,formalization,and arithmetization,and finally break away from the physical and geometric background.The revolutionary changes in these three fields of Mathematics have made it embark on the road of independence and freedom driven by internal logic and dominated by human reason,Thus splitting mathematics into pure mathematics and applied mathematics.

关 键 词：数学革命 纯粹数学 数学本质 

分 类 号：N031[自然科学总论—科学技术哲学]