中文摘要：

随着欧洲核子中心发现希格斯粒子,粒子物理标准模型的最后一块拼图得到确实.粒子物理标准模型是建立在Yang-Mills理论的基础之上,它把粒子的行为和几何结构优美地连接起来.然而,没有人证明量子规范理论是建立在牢固的数学基础之上.本文介绍了建立量子规范理论数学基础面临的困难和挑战.

英文摘要：

After the discovery of the Higgs particle at LHC, the final ingredient in the particle physics standard model has been confirmed. The standard model has been established in the framework of Yang-Mills theory, which links elegantly the behavior of particles to geometry. However, no one has proved the mathematical soundness of quantum Yang-Mills theory. In this article, we introduce briefly the background of Yang-Mills theory, the difficulties and challenges in building the mathematical foundation of quantum Yang-Mills.