从Fredholm到Banach的算子理论发展，是泛函分析学科建立的一个决定性阶段，也得到数学史学者的广泛关注和研究。但目前已有研究成果更侧重陈述事实，缺乏对事实背后所隐藏数学思想方法的深入挖掘。本项目将以积分方程的求解为主线，研究Fredholm、Hilbert、Riesz、Banach等数学家的相关工作，在解读原始文献基础上，重构各个数学家的算子理论思想路线图，深入探讨他们之间数学思想方法的传承、发展与突破。力图通过全面有新意的解读，勾勒出一条内在思想逻辑清晰的算子理论思想脉络图。进而从算子角度进一步了解泛函分析的发展进程，探讨算子理论对整个分析学发展的影响。

The development of the operator theory from Fredholm to Banach is a decisive stage in the establishment of functional analysis, which has drawn extensive attention and research from scholars in mathematical history. However, at present, many researchers have placed more emphasis on historical facts, and their works are lack of in-depth explorations of the mathematical ideas behind the facts. In this project, we will take the solving of integral equations as the main line, investigate the related works of Fredholm, Hilbert, Riesz, Banach and other mathematicians, reconstruct the idea maps of operator theory of each mathematician on the basis of interpreting the original documents, probe the inheritance, development and breakthrough of mathematical ideas among them in depth. With a comprehensive interpretation from new view, we try to outline a clear logical thinking diagram of the history of operator theory. Furthermore, this project will promote the understanding of the development of functional analysis from the perspective of operators, and explore the influence of operator theory on the development of analytics.