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Bernhard Riemann's ideas concerning geometry of space had a profound effect on the development of modern theoretical physics. He clarified the notion of integral by defining what we now call the Riemann integral.
Riemann moved from Göttingen to Berlin in 1846 to study under Jacobi, Dirichlet and Eisenstein. In 1849 he returned to Göttingen and his Ph.D. thesis, supervised by Gauss, was submitted in 1851. In his report on the thesis Gauss described Riemann as having a gloriously fertile originality.
On Gauss's recommendation Riemann was appointed to a post in Göttingen. Riemann's paper Uber die Hypothesen welche der Geometrie zu Grunde liegen , written in 1854, became a classic of mathematics, and its results were incorporated into Albert Einstein's relativistic theory of gravitation. Gauss's chair at Göttingen was filled by Dirichlet in 1855 and, after his death, by Riemann. Even at this time he was suffering from tuberculosis and he spent his last years in Italy in an attempt to improve his health.
Riemann's ideas concerning geometry of space had a profound effect on the development of modern theoretical physics and provided the concepts and methods used later in relativity theory. He was an original thinker and a host of methods, theorems and concepts are named after him.
The Cauchy-Riemann equations (known before his time) and the concept of a Riemann surface appear in his doctoral thesis. He clarified the notion of integral by defining what we now call the Riemann integral. He is also famed for the still unsolved Riemann hypothesis.
References elsewhere in this archive:
Tell me about Riemann's part in investigating prime numbers
Tell me about his work on non-Euclidean geometry
Tell me about Riemann's work on topology
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