1826 On September 7th, Riemann (1826— 1866) was born in Hanover, Germany. His father is a priest. /kloc-At the age of 0/9, Riemann entered the University of G? ttingen to study theology according to his father's will. But he was soon infected by the strong mathematical atmosphere there, so that he gave up theology and studied mathematics instead. Riemann's intelligence and diligence were soon discovered by Gauss (1777-1855), so Riemann was fortunate to be a student of Gauss in his later years.

185 1 year 1 1 month, Riemann finished his doctoral thesis "The Basis of the Theory of Complex Variables". Gauss spoke highly of this paper, and wrote in his comments: "This is a very weighty and valuable article, which not only meets the requirements of doctoral thesis, but also far exceeds the requirements". As a result, Riemann not only got a doctorate, but also won the reputation of a first-class mathematician.

1854, Riemann published two papers, On the Possibility of Representing Functions with Trigonometric Series and Basic Assumptions of Geometry. In the latter paper, he extended the study of three-dimensional space to multi-dimensional space, introduced the concepts of manifold and manifold curvature, and thus developed a non-Euclidean geometry system, which laid a theoretical foundation for what was later called Riemannian geometry.

Riemann not only made outstanding contributions to function theory and differential geometry, but also made great achievements in the fields of number theory and partial differential equations. There are more than ten mathematical terms named after him, such as Riemannian geometry, Riemannian surface, Riemannian function, Riemannian integral, Riemannian conjecture and so on. So Riemann is a rare mathematical genius in the world.

However, Riemann also experienced many bumps and difficulties in his life. From 65438 to 0854, he became an extra lecturer at the University of G? ttingen, earning only by students' attendance fees. Because of his meager income, he often insists on working on an empty stomach. 1857 became an associate professor and was promoted to full professor two years later. However, due to the death of his brother, he has to bear the living expenses of his four sisters, so life has been very difficult. Riemann's weak body, coupled with the hardships of hard work and life, finally broke down from overwork and suffered from lung disease. Due to financial constraints, he failed to completely cure the disease, and later his condition deteriorated. Unfortunately, he died on July 20th, 866 at the age of 39.

Riemann made epoch-making contributions in many fields of mathematics all his life. His profound and unique thoughts have played an inestimable role in the development of mathematics and physics. It is really regrettable and sad that such a rare great mathematician died young. If he hadn't been defeated by illness because of the hardships of life, it can be expected that Riemann would have made more discoveries and innovations, and he would have left more spiritual wealth to our world.