论数学真理是发现和发明的统一——以伽罗瓦群论为例

Mathematical Truth is the Unity of Discovery and Invention——With Galois Group Theory as an Example

十九世纪初,伽罗瓦在证明不存在一个五次方程的一般根式解法,建立了群论,用群论的深刻数学语言去描述基本对称概念使得代数学进入了一个新的时代。该文通过对伽罗瓦理论诞生前后的数学哲学思考,认为:纯粹数学是并非完全自由发明,数学对象的构造有其数学史和抽象结构上的根源,而数学问题是应对大自然的需要以及各种约定的最终衡量。在新概念的背景下,具体语境下,数学真理是发现与发明的统一。

In the early nineteenth century, by proving there is not a radical solution of the general equation , Galois established group theory with which profound mathematical language tcould describe the basic concept of symmetry made the algebra into a new era. The article besed on the birth of Galois theory thinking the Earlier, after philosophy of mathematics, that： pure mathematics is not entirely free invention, the construction of mathematical objects has their history of mathematics and Abstract structure of the source, and mathematical problem is to deal with the needs of nature and The ultimate measure of the various conventions. New concept in the context of the specific context, mathematical truth is discovered and the unity of invention.