https://en.m.wikipedia.org/wiki/Bernhard_Riemann
Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Einstein's general theory of relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of Göttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary. In 1859, following Lejeune Dirichlet's death, he was promoted to head the mathematics department at Göttingen. He was also the first to suggest using dimensions higher than merely three or four in order to describe physical reality.[2] In 1862 he married Elise Koch and had a daughter.
http://www-history.mcs.st-andrews.ac.uk/Biographies/Riemann.html
To complete his Habilitation Riemann had to give a lecture. He prepared three lectures, two on electricity and one on geometry. 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.
https://www.thefamouspeople.com/profiles/bernhard-riemann-biography-440.php
https://en.m.wikipedia.org/wiki/Privatdozent
Privatdozent (for men) or Privatdozentin (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifications that denote an ability to teach (venia legendi) a designated subject at university level. In its current usage, the title indicates that the holder has permission to teach and examine independently without being a professor. The title is not necessarily connected to a salaried position, but may entail a nominal obligation to teach.
Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Einstein's general theory of relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of Göttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary. In 1859, following Lejeune Dirichlet's death, he was promoted to head the mathematics department at Göttingen. He was also the first to suggest using dimensions higher than merely three or four in order to describe physical reality.[2] In 1862 he married Elise Koch and had a daughter.
http://www-history.mcs.st-andrews.ac.uk/Biographies/Riemann.html
To complete his Habilitation Riemann had to give a lecture. He prepared three lectures, two on electricity and one on geometry. 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.
https://www.thefamouspeople.com/profiles/bernhard-riemann-biography-440.php
- In 1852, on the recommendation of Gauss, Riemann began his career as a Privatdozent at the University of Göttingen. Concurrently, he also worked for Weber without any pay. At the same time, he started preparing for his Habilitation, which would entitle him to obtain appointment as a lecturer.
- For his Habilitationsschrift (probationary essay), he chose the Fourier series on heat-flow, submitting it at the end of 1853. It was a masterpiece, which made great progress towards solving some of the foundational issues left unsolved by French mathematician Joseph Fourier in his work, ‘Théorie analytique de la chaleur’.
- He also submitted a list of three possible subjects for his Habilitationsvortrag (probationary lecture), out of which Gauss chose the third. It was titled ‘Über die Hypothesen, welche der Geometrie zu Grunde liegen’ (On the hypotheses that underline geometry).
- The lecture, given on June 10, 1854, not only introduced what today is known as n-dimensional Riemannian manifold, but also its curvature tensor and discussed the relation between mathematical space and actual space. However, the last was left as a theory for sixty years until it was proved by Einstein.
- Even after his habilitation was complete, Riemann continued to work as a privatdozent. The position did not entail any kind of salary; but he was able to collect fees from his students. His first course was on partial differential equations with applications to physics and he had very few students.
- In 1855, with the demise of Gauss, his chair went to Dirichlet. Dirichlet now tried to obtain the post of extraordinary professor for Riemann, but on being unsuccessful in his endeavor, he obtained another small job for him.
- Riemann, now earning a salary of 200 taler a year, concentrated on his work. His lectures during the period of 1855-1856 led to the publication of his ‘Theory of Abelian functions’ (1857). It is now considered to be one of the most notable works in mathematics.
https://en.m.wikipedia.org/wiki/Privatdozent
Privatdozent (for men) or Privatdozentin (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifications that denote an ability to teach (venia legendi) a designated subject at university level. In its current usage, the title indicates that the holder has permission to teach and examine independently without being a professor. The title is not necessarily connected to a salaried position, but may entail a nominal obligation to teach.
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