中文摘要：

本文尝试以简单的对角线直观，连贯起数理逻辑史上的几个重大结果，一方面介绍其背后的动机、思想，另一方面强调对角线方法的意义。文章重思想，不重技术，或许可为从思想方面理解这些结果提供一条线索。

英文摘要：

By use of the diagonal method we try to present some significant results in the history of mathematical logic, emphasizing on the one hand the motivations and intuitive ideas behind these results, and, on the other, the important role played by the diagonal method in generating intuitions and ideas in mathematical logic. The technical details are mostly neglected, and the intuitive ideas highlighted. We hope this can serve as an introduction to these renowned results for the general reader.