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. He is a quiet, morbid and shy person who likes to be alone all his life. His colleague Dai Dejin is one of the few people who know him. According to Dai Dejin, in addition to Riemann's poor physical condition, he is still
Riemann Atlas (3 sheets)
Hypochondriac patient
1840, Riemann moved to Hanover to live with his grandmother and entered middle school.
1842, after his grandmother died, he moved to the Johannes Museum in Lueneburg.
From 65438 to 0846, Riemann entered the University of G? ttingen to study philosophy and theology. During this period, he went to some math lectures, including Gauss's lecture on least square method. With his father's permission, he changed to mathematics. I went to Berlin University for two years during my college years and was influenced by C.G.J Jacobi and P.G.L Dirichlet.
/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.
185 1 year received a doctorate from the University of Berlin.
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.
Riemann integral is defined in 1853, and the convergence criterion of trigonometric series is studied.
1854, carried forward Gauss's research on differential geometry of surfaces, used the concept of manifold to understand the essence of space, and established the concept of Riemannian space by using the positive definite quadratic understanding measure determined by the square of the length of differential arc, and incorporated Euclidean geometry and non-Euclidean geometry into his system.
1854 became a lecturer at the University of G? ttingen.
1857, he gave a speech entitled "On Hypothesis as the Basis of Geometry" for the first time, founded Riemann Geometry, and made contributions to Einstein.
Liman tomb
Tan's general theory of relativity provides a mathematical basis.
1857 published a research paper on Abel function, which led to the concept of Riemannian surface, brought the theory of Abel integral and Abel function to a new turning point, and made 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. 1857 was promoted to be an supernumerary professor at the University of G? ttingen. 1859, he succeeded Dirichlet as a professor. And published a paper on the number of prime numbers less than a given value, and put forward the Riemann hypothesis.
From 65438 to 0862, he married Elis Koch.
1866 On July 20th, he died of tuberculosis in Silasca on his third trip to Italy.
Main contribution
1859 On the distribution of prime numbers, on the number of prime numbers less than a given value, this paper studies the Riemann zeta function, gives the integral expression of zeta function and the functional equation it satisfies, and points out that the distribution of prime numbers has a deep relationship with Riemann zeta function. The core of this correlation is the integral expression of J(x).
1854, Riemann gave a speech entitled "On Hypothesis as the Basis of Geometry" at the University of G? ttingen where Riemann Geometry was founded. Riemann regards the surface itself as an independent geometric entity, not just a geometric entity in Euclidean space. 19 15 years, a Einstein established a new theory of gravity-general relativity by using Riemann geometry and tensor analysis tools.
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. He is one of the most original mathematicians in the history of mathematics in the world. Riemann's works are few, but extremely profound, full of creation and imagination of concepts.
His name appears in Riemannian Zeta function, Riemannian integral, Riemannian lemma, Riemannian manifold, Riemannian space, Riemannian mapping theorem, Riemannian-Hilbert problem, Cauchy-Riemannian equations and Riemannian loop matrix.
Personality assessment
Sir Eddington once said, "Geometricians like Riemann can almost foresee more important features of the real world."
Gauss said: "Riemann ... has a creative, active, real mathematician's mind and outstanding creativity."
Bell, a historian of modern mathematics, said: "As a mathematician, Riemann's greatness lies in the strong universality and infinite scope of his methods and new ideas revealed to pure mathematics and applied mathematics."
German mathematician Klein said: "Riemann has extraordinary intuitive ability, and his understanding genius is better than all other algebraic scientists."