克莱因论古代数学及其代数化进程

Klein on Ancient Mathematics and Its Algebraization Process

各种原因导致雅各布·克莱因(Jacob Klein)的数学思想史研究被同时代人所忽视,但该研究的重要价值今天愈发显现。克莱因试图通过对数学“实际历史”的意向性分析来激活古代沉淀的数学经验,他将现象学方法与范例研究巧妙地结合起来,从两种“意向性转换”的视角描述了韦达、笛卡尔、斯台文、沃利斯等数学家所推动的代数化进程,把韦达基于比例理论的“类的运算(logistice speciosa)”思想与笛卡尔的“符号抽象”概念归结为近世代数的实质。他详细描述了符号化数学的概念史并为其发展提供了思想史证明,为我们理解代数和现代性的本质提供了一个新的视角。他的研究凸显了古希腊数学的原创性、独特性和内在要素的完备性,不同于以往辉格史的研究和世界主义的理想化科学图景。

Jacob Klein’s work on the history of mathematical thought has been neglected by his contemporaries for various reasons,but its value is increasingly apparent today.He attempted to activate ancient sedimentary mathematical experience through an intentional analysis of the“actual history”of mathematics.He ingeniously combined phenomenological methods with Case studies and described the process of algebraization promoted by mathematicians such as Vieta,Descartes,Stevin,and Wallis from the perspectives of two types of“intentional conversion”.He reduced Vieta’s idea of logistice speciosa,which based on the theory of proportionality,and Descartes’concept of“symbolic abstraction”to the essence of algebra.He characterized in detail the conceptual history of symbolic mathematics and provided a historical proof of thought for its development,which provided a new perspective for us to understand the essence of algebra and modernity.Unlike previous Whig history studies or the idealized scientific picture of cosmopolitanism,Klein’s study highlights the originality,specificity and completeness of the intrinsic elements of ancient Greek mathematics.