Riemann Dissertation

Riemann Dissertation-83
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.

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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.

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.

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 1851 he wrote his thesis on complex function theory and Riemann surfaces and got his Ph. 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.He was member of the Gesellschaft der Wissenschaften, the Bavarian and Parisian Academy and the London Royal Academy., Riemann was asked for three potential topics for his habilitation lecture, from which Gauss chose one.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.[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.To that end, consider, first, the place which mathematical discontinuities occupy in Riemann’s discovery, and then, the significance of Riemann’s emphasis on what he terms The origin of modern mathematics lies in what is commonly identified as a “Euclidean” notion of simple space-time.This idea of space-time pretends to represent the real universe, which it does not represent.

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