Riemann 1854 Habilitation Dissertation

Riemann 1854 Habilitation Dissertation-69
In the spring of 1846 Riemann enrolled at the University of Göttingen.

In the spring of 1846 Riemann enrolled at the University of Göttingen.

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At this time a teacher from a local school named Schulz assisted in Bernhard's education.

In 1840 Bernhard entered directly into the third class at the Lyceum in Hannover.

Gauss had to choose one of the three for Riemann to deliver and, against Riemann's expectations, Gauss chose the lecture on geometry.

Riemann's lecture Über die Hypothesen welche der Geometrie zu Grunde liegen , delivered on 10 June 1854, became a classic of mathematics. In the first part he posed the problem of how to define an n-dimensional space and ended up giving a definition of what today we call a Riemannian space.

While at the Lyceum he lived with his grandmother but, in 1842, his grandmother died and Bernhard moved to the Johanneum in Lüneburg.

Bernhard seems to have been a good, but not outstanding, pupil who worked hard at the classical subjects such as Hebrew and theology.Also Listing had been appointed as a professor of physics in Göttingen in 1849.Through Weber and Listing, Riemann gained a strong background in theoretical physics and, from Listing, important ideas in which were to influence his ground breaking research.He spent thirty months working on his Habilitation dissertation which was on the representability of functions by trigonometric series.He gave the conditions of a function to have an integral, what we now call the condition of Riemann integrability.In the second part of the dissertation he examined the problem which he described in these words:- To complete his Habilitation Riemann had to give a lecture.He prepared three lectures, two on electricity and one on geometry.Riemann's thesis, one of the most remarkable pieces of original work to appear in a doctoral thesis, was examined on 16 December 1851.In his report on the thesis Gauss described Riemann as having:- , the degree which would allow him to become a lecturer.This was granted, however, and Riemann then took courses in mathematics from Moritz Stern and Gauss.It may be thought that Riemann was in just the right place to study mathematics at Göttingen, but at this time the University of Göttingen was a rather poor place for mathematics.

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