从Gauss到Riemann的微分几何学发展，是微分几何学史上极为重大的变革，也是国内外数学史界研究的热点。关于这段历史虽然已有大量研究成果，但大都仅关注Gauss与Riemann两位数学家的微分几何工作，直接从Gauss跨跃到Riemann。本项目将从Gauss到Riemann的微分几何学史的关注点部分地分配给Gauss与Riemann之间的Minding、Jacobi、Liouville、Bonnet等数学家的相关工作。在解读原始文献的基础上，重构相应数学家个体的微分几何学工作的思想脉络，探讨有关Gauss与Riemann工作本身的若干历史问题，研究这段时期数学家们对Gauss微分几何工作的接受与发展过程，全面考察Riemann微分几何工作的背景和思想来源。对这段历史进行全面而有新意的解读，力图呈现从Gauss到Riemann的微分几何学发展的整体图景。

The development of differential geometry from Gauss to Riemann is a crucial transformation in the history of differential geometry, which is also a hot topic in the field of history of mathematics. There are massive achievements on this topic published in the past, but many of them only focus on Gauss and Riemann with a discontinuous history. Our research move part of the emphasis to relevant work of Minding, Jacobi, Liouville and Bonnet between Gauss and Riemann. By reinterpreting the original literature, the thinking process behind these literature are reconstructed. Then, some historical issues concerning Gauss’ and Riemann’s work, the reception process of Gauss’ differential geometry work, and the background and sources of Riemann’s geometric ideas are investigated. In recent years’ study, our research method and aim get clear gradually, with some historical issues and some concrete historical problems extracted. After the investigation of these historical issues and problems, a new landscape of development of differential geometry from Gauss and Riemann will be in front of us.