Bernhard Riemann

Georg Friedrich Bernhard Riemann (September 17th 1826 with Breselenz, Hanover - July 20th 1866 with Selasca, Italy) is a German Mathématicien . Influential on the theoretical level, it contributed an important share to the analyzes and with the differential Géométrie.

Biography

Born in Breselenz, a village in the kingdom of Hanover, in current Germany, Riemann is the second of six children. His/her father, Friedrich Bernhard Riemann, poor Pasteur Lutheran, fought in the Napoleonean Guerres. As of its more young age, Bernhard shows exceptional talents. Shy person, it is afraid to express himself and suffers from nervous breakdowns.

In 1840, Bernhard is established in Hanover to live in his/her grandmother. After its death in 1842, it goes to Lüneburg. In 1846, 19 years old, thanks to the money of its family, it started to study the Philosophie and the Théologie to become priest. In 1847, his/her father authorized it to study mathematics. He initially studied with Göttingen where he met Carl Friedrich Gauss, then with Berlin, where he had inter alia as professors Jacobi, Steiner and Dirichlet. He carried out his thesis with Göttingen under the direction of Gauss.

He gave his first courses in 1854. Promoted professor at the University of Göttingen in 1857, it took again the pulpit of Dirichlet. In 1862 it Marie with Elise Koch.

He dies of tuberculosis during its third voyage in Italy, at the 40 years age.

Work

In its thesis, presented in 1851, Riemann develops the theory functions of a variable complexes, in particular introducing the concept of the surfaces which bear its name, in particular the spheres of Riemann. It will look further into this theory in 1857, by developing the theory abelian functions.

At the time of its defense of enabling, in 1854, directed per Gauss, it gives a talk entitled On the assumptions subjacent with the geometry ( Uber die Hypothesen welche der Geometrie zu Grunde liegen ) which provides the foundations of the differential Géométrie. It introduced the good way of extending to N dimensions the results of Gauss itself on surfaces. This defense radically changed the design of the concept of geometry, in particular by opening the way with the not-Euclidean geometries and the theory of the General relativity.

One also owes him of important work on the integrals, continuing those of Cauchy, which gave inter alia what is called today the integral of Riemann.

In 1859, Riemann, which has just been appointed professor with Göttingen and the Academy of Science of Berlin, publishes an article " On the number of prime numbers lower than a given size ". It defines the function Zeta, by resuming work of Euler and by extending them to the Complex numbers, and uses this function with an aim in it of studying the distribution of the prime numbers. Famous the Hypothèse of Riemann on zero the noncommonplace ones of the function zeta formulated in this article still is not shown, and not belonged to the famous 23 problems of Hilbert.

See too

Surface of Riemann
Integral Sphere of Riemann
of Riemann
Assumption of Riemann
Assumption of Riemann generalized
Somme of Riemann
Theorem of representation of Riemann
Function zeta of Riemann
Concerning the number of prime numbers lower than a given size

External bonds

Analysis and Synthesis - There Scientific Method based one are Study by Bernhard Riemann From the Swedish Morphological Society
" Fragments on the gravitation and the lumière" of Bernhard Riemann in Review Fusion N°94
Work of Riemann digitized by the SCD of the University Louis Pasteur of Strasbourg

Sources

In the jungle of the prime numbers , John Derbyshire and Julien Randon-Furling, 2007