中文摘要：

运用文献分析研究和数学史比较研究方法，分析了高斯哥本哈根获奖论文产生的历史背景及其对内蕴微分几何学的贡献．结果表明，高斯完成于1822年12月的获奖论文，不仅解决了哥本哈根科学院的征奖问题，更重要的是它奠定了其内蕴微分几何学研究的基本思想和方法．

英文摘要：

Based on the source investigation and the comparative approach of history of mathernatics,a historical background of Gauss＇ competition essay and its contribution to intrinsic differential geometry are discussed. The paper indicates that the essay,which was accomplished by Gauss in the December of 1822, not only solved the competition question presented by Copenhagen Academy of Sciences on the one hand, but also established the essential idea and methods of his intrinsic differential geometry.