第一次数学危机及其意义探析  

On the First Mathematical Crisis and its Significance

作　　者：张今杰[1] 陈华[1] 

机构地区：[1]湘潭大学毛泽东思想研究中心,湖南湘潭411105

出　　处：《宁波大学学报（人文科学版）》2011年第6期7-12,共6页Journal of Ningbo University：Liberal Arts Edition

基　　金：国家社科基金项目(11BKS081);湖南省教育厅优秀青年项目(09B107)

摘　　要：2的出现动摇了毕达哥拉斯的"数本论"的信念根基,导致了数学史上第一次危机。第一次数学危机的本质在于悖论及其内含的无限性概念。第一次数学危机带来了希腊数学界的极大混乱,但危机的解决带来了数学公理化体系和逻辑学的发展。The discovery of 2 shook the very foundation of Pythagoras’ theory of ＂All Things are Numbers＂ thus leading to the first mathematical crisis in the history of mathematics.The essence of the first mathematical crisis lies in its paradox and the concepts of ＂infinity＂.It brought great chaos to Greece mathematical community;The solution of the crisis,however,has brought a mathematical axiom system and an opportunity of logic development.

关 键 词：悖论 无理数 数学危机 “万物皆数” 公理化体系 

分 类 号：O144.2[理学—数学]