阿贝尔已经发现了伽罗瓦的定理?
Had Abel Already Discovered Galois's Theorem?
杨保强1
作者信息
- 1. 延安大学数学与计算机科学学院,陕西延安 716000
- 折叠
摘要
数学家阿贝尔与伽罗瓦均处理了素数次不可约方程根式可解的问题,阿贝尔在伽罗瓦之前给出了一个判别定理.与伽罗瓦定理在表述上的相似性使得一些后世学者认为,阿贝尔已经得到了与伽罗瓦定理几乎一致的结果,且阿贝尔先于伽罗瓦而拥有这一定理.文章通过分析原始文本,追溯历史评论,指出阿贝尔的定理存在无法回避的问题,以至于它并不等同于伽罗瓦的定理,揭示阿贝尔并未先于伽罗瓦而已经发现了伽罗瓦的定理.同时,发掘伽罗瓦定理的原创性之所在以及阿贝尔结果的思想来源,以此案例说明数学史使我们正确看待过去数学的方式与意义.
Abstract
The mathematicians Abel and Galois both dealt with the problem that whether an irreducible equation of prime degree could be solvable by radicals.Abel gave a criterion theorem before Galois.Because of the similarity in expression with the Galois's theorem,some later scholars believed that Abel had already got results almost iden-tical to Galois's theorem,and Abel was in possession of this theorem before Galois.By analyzing the original texts and tracing the historical reviews,this paper points out that there are unavoidable problems in Abel's theorem,showing it is not equivalent to Galois's theorem,and reveals that Abel did not discover Galois'theorem ahead of Galois.At the same time,we explore the originality of the Galois's theorem and the thought source of Abel's re-sults,using this case to illustrate how the history of mathematics allows us to correctly view the methods and signifi-cance of past mathematics.
关键词
阿贝尔/伽罗瓦定理/素数次方程/根式可解/数学史Key words
Abel/Galois's theorem/equation of prime degree/solvable by radicals/history of mathematics引用本文复制引用
基金项目
延安大学博士科研启动项目(YDBK2022-64)
国家自然科学基金地区科学基金项目(12161086)
陕西高校青年杰出人才计划项目(QJ001)
出版年
2024
NETL
NSTL
万方数据