Riemann's paper is regarded as one of the masterpieces in the history of mathematics in19th century. In fact, in order to determine the topic of the paper, Riemann submitted three topics to Gauss for him to choose from. Among them, the third topic is related to the geometric basis. Gauss has been thinking about this topic for six years. Riemann didn't have much preparation at that time, and he didn't want Gauss to choose it from the bottom of his heart, but Gauss only specified the third topic.
Riemann mentioned in his speech that his thoughts were influenced by two aspects: one was Gauss's study of curved surfaces, and the other was Herbart's philosophical thought. The full text is divided into three parts, the first part is the concept of dimensional manifold, the second part is the measurement relationship of dimensional manifold, and the third part is the application of space. Riemann's speech developed Gauss's research on differential geometry of surfaces and laid the foundation of Riemann geometry. His work was soon further developed by the heirs and became the mathematical basis of later general relativity.
Riemann didn't write many works in his life, but every paper by Ji Ping is a pioneering work in a certain field of mathematics. Some mathematicians commented: "Riemann is an imaginative genius, and his ideas have inspired mathematicians for a century even if they have not been proved." Riemann is one of the mathematicians who have the greatest influence on modern mathematics. Regrettably, this great mathematician died young at the peak of his creation, and he was less than 40 years old.