双线性型理论的优先权及构建之争  

The Debate on the Priority and Organization of Theory of Bilinear Forms

作　　者：杨保强 曾仙赐 YANG Baoqiang;ZENG Xianci(School of Mathematics and Computer Science,Yan'an University,Yan'an 716000,China;Institute for History and Culture of Science and Technology,Guangxi Minzu University,Nanning 530006,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000 [2]广西民族大学科技史与科技文化研究院,广西南宁530006

出　　处：《广西民族大学学报(自然科学版)》2024年第4期1-7,15,共8页Journal of Guangxi Minzu University :Natural Science Edition

基　　金：延安大学博士科研启动项目(YDBK2022-64);国家自然科学基金地区项目(12161086);广西民族大学2022年引进人才科研启动项目(302061123)。

摘　　要：1873-1874年,数学家克罗内克和若尔当就双线性型理论发明的优先权以及构建问题展开了争论。该争论属于德国算术传统和法国代数实践两种不同文化特征的思想交锋,蕴含两位数学家关于普遍性的内在哲学的思考与诠释。双线性型理论如何构建的争论最终在第三者书写的数学中走向了综合和统一,若尔当最后也承认了克罗内克工作的优先性。争论虽然给若尔当本人带来了不利的影响,但对他的数学实践却有所裨益,也让我们对若尔当在数学史上的历史肖像产生新的理解。In 1873-1874,the mathematicians Kronecker and Jordan were quarrelling over the priority and organization of theory of bilinear forms.This argument belongs to the ideological confrontation between two different cultural characteristics of the German arithmetic tradition and the French algebraic practice,and it contains the two mathematicians'thoughts and interpretations on the intrinsic philosophy of generality.The debate over how bilinear theory was organized eventually led to a kind of synthesis and unity in mathematics written by a third party,and Jordan acknowledged Kronecker's priority afterwards.The controversy has brought unfavorable influence to Jordan himself,but it is beneficial to Jordan's mathematical practice,and also makes us have a new understanding of Jordan's historical portrait in the history of mathematics.

关 键 词：双线性型 若尔当 克罗内克 

分 类 号：N09[自然科学总论—科学技术哲学]