Following the example of German mathematicians, Bernhard Riemann made important contributions to mathematical analysis and differential geometry, some of which paved the way for the development of general relativity. His name appears in Riemannian zeta function, Riemannian integral, Riemannian lemma, Riemannian manifold, Riemannian mapping theorem, Riemannian-Hilbert problem, Riemannian thinking loop matrix and Riemannian surface. For the first time, he gave a speech entitled "On Hypothesis as the Basis of Geometry" and founded Riemann Geometry, which provided a mathematical basis for Einstein's general theory of relativity. 1857 was promoted to an adjunct professor at the University of G? ttingen, 1859 became a full professor after Dirichlet's death.

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Riemann (1826 ~ 1866), George Friedrich Ferdinand Prinz von Preu?en bernhard.

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German mathematician and physicist. 1826 was born in BreSlentz, Hanover on September 7th, and 1866 died in Senasca, Italy on July 20th. 1846 He entered the University of G? ttingen to study theology and philosophy, and then transferred to mathematics. During his college years, he went to Berlin University to study and was influenced by jacoby and Dirichlet. 1849 back to Gedingen. 185 1 year received a doctorate. 1854 became a lecturer at the University of G? ttingen, 1859 succeeded Dirichlet as a professor. 185 1 year proves the necessary and sufficient condition for the differentiability of complex variable function (i.e. cauchy-riemann equations). With the help of Dirichlet principle, Riemann mapping theorem is expounded, which becomes the basis of functional geometry theory. 1853 defines Riemann integral and studies the convergence criteria of trigonometric series. 1854, Gauss carried forward his research on differential geometry of surfaces, understood the essence of space by using the concept of manifold, established the concept of Riemannian space by using the positive definite quadratic form determined by the square of differential arc length, and incorporated Euclidean geometry and non-Euclidean geometry into his system. The research paper on Abel function published in 1857 leads to the concept of Riemannian surface, which brings the theory of Abel integral and Abel function to a new turning point and makes a systematic study. Among them, Riemannian surfaces are deeply studied from the perspectives of topology, analysis and algebraic geometry. A series of concepts that have far-reaching influence on the development of algebraic topology are founded, and Riemann-Roche theorem supplemented by G Roche is expounded.

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In the paper on the distribution of prime numbers published in 1858, Riemann zeta function is studied, and the integral expression of zeta function and its functional equation are given. His famous Riemann conjecture is still unsolved. In addition, he also made great contributions to partial differential equations and their applications in physics. Even for physics itself, such as heat, electromagnetic non-over-distance action and shock wave theory. Riemann's work directly influenced the development of mathematics in the second half of19th century. Many outstanding mathematicians have re-demonstrated the theorem asserted by Riemann, and many branches of mathematics have made brilliant achievements under the influence of Riemann's thought. Riemann first put forward a new idea and method of studying number theory with complex variable function theory, especially zeta function, which initiated a new period of analytic number theory and had a far-reaching influence on the development of simple complex variable function theory.

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1826, he was born in Breselenz, a small town in the kingdom of Hanover (now Germany). His father, Friedrich Bernhard Riemann, was a local Lutheran priest. He ranks second among six children. 1840, Riemann moved to Hanover to live with his grandmother and entered middle school. After his grandmother died in 1842, he moved to Johnny's, Lueneburg. 1846, according to his father's wishes, Riemann entered the University of G? ttingen to study philosophy and theology. During this period, he went to some math lectures, including the most Riemannian by Gauss.

Lecture on least square method. With his father's permission, he changed to mathematics. /kloc-in the spring of 0/847, Riemann transferred to Berlin University and joined jacoby, Dirichlet and Steiner. Two years later, he returned to G? ttingen. 1854, he delivered his first speech entitled "On Hypothesis as the Basis of Geometry", which initiated Riemann geometry and provided a mathematical basis for Einstein's general theory of relativity. 1857 was promoted to an adjunct professor at the University of G? ttingen, 1859 became a full professor after Dirichlet's death. From 65438 to 0862, he married Elis Koch. 1866, he died of tuberculosis in Silaska on his third trip to Italy.

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He made great contributions to mathematical analysis, differential geometry and differential equations. He introduced the theory of trigonometric series, thus pointing out the direction of integral theory, laying the foundation of modern analytic number theory and putting forward a series of problems; He first introduced the concept of Riemannian surface, which had a great influence on modern topology. In algebraic function theory, such as Riemann-Nocci theorem is also very important. In differential geometry, Riemann geometry is established after Gaussian. His name appears in Riemann zeta function, Riemann integral, Riemann lemma, Riemann manifold, Riemann mapping theorem, Riemann-Hilbert problem, Cauchy-Riemann equations and Riemann loop matrix.