Georg Friedrich Bernhard Riemann was a revolutionary mathematician. He was born on September 17, 1826 in Breselenz, a village in Germany. His father, Friedrich Bernhard Riemann, who was a Lutheran minister, taught Riemann until he was ten. Then, Georg Friedrich Bernhard Riemann was taught by a teacher from a local school. Riemann had always displayed an interest in mathematics, especially when he studied at Lüneburg at the age of fourteen. His teacher gave him a textbook on a number theory by Legendre and six days later, Riemann had completed the 859 page book claiming to have mastered it. Once Riemann was nineteen, he attended the University of Göttingen in Germany. It was there that he began formulating ideas and theories that would drastically change the world of math forever.

In 1851, Riemann completed his doctoral thesis on the theory of complex functions at Göttingen for geometry. He combined the theory of complex functions, the theory of harmonic functions along with the potential theory and discovered that the existence of a wide class of complex functions satisfied only modest requirements. This proved that “complex functions could be expected to occur widely in math and that the theories of complex and harmonic functions were henceforth inseparable. Riemann also introduced the Laurent series expansion for functions having poles and branch points.” His mapping theorem stated that “any simply connected domain of the the complex plane having at least two boundary points can be conformally mapped onto the unit disk.” This lead to the idea of conformal mapping and simple connectivity. Riemann then decided to take Gauss’ geometric studies even further after Gauss asserted that one should ignore Euclidean space and treat eac...

... middle of paper ...

...on in a geodesic coordinate system such a metric is flat Euclidean, in the same way that a curved surface up to higher-order terms looks like its tangent plane. Beings living on the surface may discover the curvature of their world and compute it at any point as a consequence of observed deviations from Pythagoras’ theorem.”

Aside from developing is own hypotheses and studies, Georg Friedrich Bernhard Riemann was an inspiration to countless mathematicians as well. Riemann’s work with loci and algebraic functions was further studied by Charles- Emile Picard and Poincare. Both men were able to prove that a locus given by an equation f (x, y) = O can intersect itself at isolated points but along curves as well. Riemann also inspired the infamous Albert Eistein. Evidently, Eistein’s theory of general relativity was based off of Riemann’s ideas of Riemannian geometry.

In 1851, Riemann completed his doctoral thesis on the theory of complex functions at Göttingen for geometry. He combined the theory of complex functions, the theory of harmonic functions along with the potential theory and discovered that the existence of a wide class of complex functions satisfied only modest requirements. This proved that “complex functions could be expected to occur widely in math and that the theories of complex and harmonic functions were henceforth inseparable. Riemann also introduced the Laurent series expansion for functions having poles and branch points.” His mapping theorem stated that “any simply connected domain of the the complex plane having at least two boundary points can be conformally mapped onto the unit disk.” This lead to the idea of conformal mapping and simple connectivity. Riemann then decided to take Gauss’ geometric studies even further after Gauss asserted that one should ignore Euclidean space and treat eac...

... middle of paper ...

...on in a geodesic coordinate system such a metric is flat Euclidean, in the same way that a curved surface up to higher-order terms looks like its tangent plane. Beings living on the surface may discover the curvature of their world and compute it at any point as a consequence of observed deviations from Pythagoras’ theorem.”

Aside from developing is own hypotheses and studies, Georg Friedrich Bernhard Riemann was an inspiration to countless mathematicians as well. Riemann’s work with loci and algebraic functions was further studied by Charles- Emile Picard and Poincare. Both men were able to prove that a locus given by an equation f (x, y) = O can intersect itself at isolated points but along curves as well. Riemann also inspired the infamous Albert Eistein. Evidently, Eistein’s theory of general relativity was based off of Riemann’s ideas of Riemannian geometry.

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