庞加莱拓扑学思想动因探源  

Some Studies on the Motivations of Poincarés Topological Thought

作　　者：季理真[1] 王昌[2] JI Lizhen;WANG Chang(Department of Mathematics,University of Michigan,Ann Arbor 48105,USA;Institute for Advanced Studies in History of Science,Northwest University,Xi'an 710127,China)

机构地区：[1]美国密歇根大学数学系,安娜堡48105 [2]西北大学科学史高等研究院,西安710127

出　　处：《自然科学史研究》2023年第1期113-123,共11页Studies in The History of Natural Sciences

基　　金：国家自然科学基金资助项目“同伦论的历史研究”(项目编号:11501444)。

摘　　要：庞加莱被认为是“最后一位通才”,他对数学最为重要的贡献之一就是创建了代数拓扑学。本文基于原始文献和研究文献,结合著名数学家和数学史家的相关论著,不仅揭示了前人关于庞加莱拓扑学研究动机中所存在的一些缺陷,在更正这些错误的同时,更加全面系统地阐述了庞加莱拓扑学研究的动机,并进一步指明庞加莱猜想也是其拓扑学研究的一个潜在动因。同时,通过深入分析庞加莱对相关拓扑学结果的应用和庞加莱猜想在他整个拓扑学工作中的地位,从一个侧面反映了庞加莱数学研究领域的广泛性。Jules Henri Poincaré(1854-1912)is regarded as“the last universalist”.It is well known that one of his most significant contributions to mathematics is the creation of algebraic topology.Based on primary and secondary literature,combined with some relevant works written by famous mathematicians and historians of mathematics,this paper not only reveals and corrects some defects on the motivations of Poincarés topology in previous research,but also expounds the motivations of Poincarétopology research more comprehensively and systematically.It further points out that the PoincaréConjecture is also a potential motivation for his topology research.At the same time,in this paper,we analyze Poincarés application of relevant topological results and the status of PoincaréConjecture in his entire topological work,showing that it reflects the universality of Poincarés mathematical research field.

关 键 词：庞加莱 庞加莱猜想 拓扑学 近现代数学史 位置分析 

分 类 号：N09[自然科学总论—科学技术哲学]