Riemann 1854 Habilitation Dissertation

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

Dirichlet loved to make things clear to himself in an intuitive substrate; along with this he would give acute, logical analyses of foundational questions and would avoid long computations as much as possible.

His manner suited Riemann, who adopted it and worked according to Dirichlet's methods.

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.

The work builds on Cauchy's foundations of the theory of complex variables built up over many years and also on Puiseux's ideas of branch points.

However, Riemann's thesis is a strikingly original piece of work which examined geometric properties of analytic functions, and the connectivity of surfaces.

Bernhard was the second of their six children, two boys and four girls.

Friedrich Riemann acted as teacher to his children and he taught Bernhard until he was ten years old.

He showed a particular interest in mathematics and the director of the Gymnasium allowed Bernhard to study mathematics texts from his own library.

On one occasion he lent Bernhard Legendre's book on the theory of numbers and Bernhard read the 900 page book in six days.

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