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Georg Friedrich Bernhard Rieman - Life
Milena Hering

Georg Friedrich Bernhard Riemann was born in Breselenz, Germany, on September 17th 1826. He was the second of 6 children of a Protestant minister and received his elementary education from his father, later assisted by a local teacher. At Easter in 1840 he moved to Hannover, where he stayed with his grandmother to visit the Lyceum. When his grandmother died two years later, he went to the Johanneum in Lueneburg. Because he was interested in mathematical matters beyond school, the director, Mr. Schmalfuss, encouraged him to do mathematics through lending him books about mathematics, which he would bring back a few days later to discuss them. Probably Euler and Legendres ``Théorie des Nombres" were among them.

In spring term 1846 he enrolled in the University of Göttingen, where he started studying theology and philology. But he always attended classes in mathematics, too, and finally his father gave him permission to do only mathematics. In this time, mathematical education in Göttingen was quite poor, even Gauss only taught elementary classes in applied mathematics and so Riemann moved to Berlin in spring 1847. There were Jacobi, Steiner and Dirichlet, who would have great influence on him.

In spring 1849 he returned to Göttingen, where the situation had changed due to the return of W.Weber. He took courses in physics, philosophy and education. In 1851 he wrote his thesis on complex function theory and Riemann surfaces and got his Ph.D. on December 16th.

The following two years he worked on his Habilitationsschrift about Fourier series. Of the three possible subjects for the Habilitationsvortrag, Gauss choose surprisingly the last: ``Über die Hypothesen, die der Geometrie zugrundeliegen", because he was curious how such a young man could handle a theme like that. A letter to his brother shows, that this had been the only theme, which he had not prepared properly and though he had handed in his thesis in December, the lecture took place only on June 10th 1854 and a quote of Dedekind describes the reaction of Gauss:

[Gauss sat at the lecture], which surpassed all his expectaions, in the greatest astonishment, and on the way back from the faculty meeting he spoke to Wilhelm Weber, with the greatest appreciation, and with an excitement rare for him, about the depth of the ideas presented by Riemann. [Werke, p.517, translated in Spivak, p.4A-3]
At this time Riemann worked as an assistant to H.Weber and held his first course as Privatdozent in partial differential equations with applications to physics. He was very shy and in his letters he reflects his difficulties to give a lecture. He was used to thinking in great steps and it was difficult for him to accomodate to the speed of his auditorium. In 1855/56 he taught his theory about abelian functions, where Dedekind, Bjerkness and Schering were his Auditorium.

Riemann could not be made an extraordinary professor and so he got a stipend of the government. The chair of Gauss went to Dirichlet, when Gauss died in 1855. In 1857 he became an extraordinary professor and finally in 1859 he became a full professor after the death of Dirichlet. When his brother died in 1857 he took care of his three sisters.

On 3rd June 1862 he married Elise Koch of Körchov, and they had a daughter. But in June 1862 he suffered a attack of pleuritis from which he never really recovered. He spent his last years in Italy and Goettingen. He found financial support to stay in Italy, where he visited Italian mathematicians, for example Betti, who he had met in Göttingen. In June 1866 he made his last trip to the Lago Maggiore, where he died fully conscious in 20st July and left a paper on natural philosophy unfinished.

He was member of the Gesellschaft der Wissenschaften, the Bavarian and Parisian Academy and the London Royal Academy. [Mathematische Werke, p 509-526]

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