Georg Bernhard. BY: Drayanthony D. Akkard. Early life.
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His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars. His mother died before her children were grown. Riemann was the second of six children, shy, and suffered from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as fantastic calculation abilities, from an early age, but suffered from timidity and a fear of speaking in public.
In high school, Riemann studied the Bible intensively, but his mind often drifted back to mathematics. He even tried to prove mathematically the correctness of the Book of Genesis. His teachers were amazed by his genius and his ability to solve extremely complicated mathematical operations. He often outstripped his instructor's knowledge. In 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school).
Bernhard Riemann held his first lectures in 1854, which not only founded the field of Riemannian geometry but set the stage for Einstein's general 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.
1868. "On the hypotheses which lie at the foundation of geometry" in Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press: 652-61.
Riemann's idea was to introduce a collection of numbers at every point in space that would describe how much it was bent or curved. Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe the properties of a manifold, no matter how distorted it is. This is the famous metric tensor.