流形概念的历史演变

The Historical Evolution of Manifold

流形是现代数学的重要研究对象。流形概念的起源可追溯到高斯的内蕴几何思想,黎曼继承并发展了高斯的想法,并给出了流形的描述性定义。随着集合论和拓扑学的发展,希尔伯特用公理化方案改良了黎曼对流形的定义,最终外尔给出了流形的严格数学定义。对流形概念演变过程的研究可以更好地理解空间观念的变革历史。

The concept of manifold is an important object of modem mathematics. It originated from intrinsic geometry of Gauss and was developed by Riemann. Hilbert modified Riemann＇s definition of manifold by the axiomatic approach and Weyl gave the final mathematical definition of manifold. The historical exploration on the origin of manifold not only helps us to understand the evolution of space , but also provides a significant perspective to reveal the links between mathematics and physics.