一个数学定理是怎样被误读的?

How Was a Mathematical Theorem Misunderstood?

一般五次方程根式不可解的证明是近代数学史的一个里程碑事件,在这个定理的证明中,鲁菲尼-柯西定理占据着核心地位,因此,在众多数学史著作中,常常会引述鲁菲尼-柯西定理。但是,由于柯西原文的描述容易引起误解,导致后世数学史家对鲁菲尼-柯西定理给出了三种意思相左的释读,以至于谬种流传,在数学史著作中造成了混乱。通过追根溯源,梳理了对这个重要定理产生误读的历史脉络。这一个案研究,反映了一些近现代数学史研究存在的一些不良现象:缺乏对原始文献的文本分析,望文生义,以至以讹传讹。

The proof of the impossibility of solving algebraically the general quintic equation is a milestone in the history of modern mathematics.The Ruffini-Cauchy theorem plays a core role in this proof.Therefore,the Ruffini-Cauchy theorem is usually quoted in many works on the history of mathematics.However,since the original description of Cauchy causes misunderstandings easily,later historians of mathematics made three contradictory interpretations of the Ruffini-Cauchy theorem,which led to the spread of fallacies and the confusion of the interpretation of the Ruffini-Cauchy theorem in the works of the history of mathematics.This treatise sorts out the historical context of the misunderstanding of this important theorem by tracing the source.Meanwhile,this case reflects some harmful phenomena in the study of the history of modern mathematics,including the lack of textual analysis of the original literature,the interpretation without real understanding and even the circulation of erroneous reports.