That statement plants Riemann, like his sponsor Karl Gauss before him, fully within the domain of physics, rather than the virtual reality which one associates with the influence of Bertrand Russell and the Bourbaki magazine.Although the principal part of my discoveries were not prompted by Riemann’s work, the approach adopted for solving the mathematical problems posed by those discoveries was prompted almost entirely by Riemann’s habilitation dissertation, leading to the designation of “La Rouche-Riemann Method.”To introduce Riemann’s posthumously published papers, I indicate the features of his dissertation which are most relevant to the problems of physical economy.
Riemann’s lecture was a truly groundbreaking piece of mathematics, laying the foundations of differential geometry, and in particular, describing how beings on a surface could measure its intrinsic curvature by observing deviations from the Pythagorean Theorem. Good.) I assume Gauss chose that lecture because he saw a hint of the profound insights it contained.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.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.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.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.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.