Bernhard Riemann Facts
Bernhard Riemann Facts

Interesting Bernhard Riemann Facts: 

Riemann was born in Germany to a poor Lutheran pastor; his mother died before he grew up. While he showed almost prodigious talent in math and calculation, his shyness kept him from speaking openly about his findings. 
Like so many other great mathematicians, Riemann attended school to become a pastor like his father but abandoned these studies to focus on math after demonstrating his skill in school. 
At the urging of his teacher, Carl Friedrich Gauss, considered by many to be the greatest mathematician who ever lived, Riemann gave up theology while at the University of Gottingen to focus on math. 
He transferred to the University of Berlin where he studied under Jacobi, Steiner, Lejeune Dirichlet, and Eisenstein. 
Riemann's contributions opened up research fields that combined analysis and geometry. These theories formed the basis of Riemannian and algebraic geometries, and complex manifold theory. 
Riemann's theory of surfaces was later elaborated upon by both Felix Klein and Adolf Hurwitz independently. This forms the foundation of topology, and is still a crucial component to understanding mathematical physics. 
He also made important advancements in real analysis and established both Riemann integral and Riemann sums, along with the later RiemannLiouville differintegral. 
His lone published work on the Riemann zeta function formed the basis for understanding prime number distribution, and the Riemann hypothesis investigates the properties of this same zeta function. 
Riemann's greatest contribution to spatial relations—a field which his teacher Carl Gauss was also influential in with his contributions to planetary motion—introduced a series of number coordinates at every point in space. These coordinates described how much curvature was present. 
Riemann discovered that in four dimensions, a series of ten numbers at each point is needed in order to describe the properties of a manifold. This is known as a Riemannian metric in his geometry. 
In 1853, Gauss asked Riemann to prepare a study on the foundations of geometry. It took months for Riemann to develop his theory of higher dimensions. 
He delivered his findings, called "Über die Hypothesen welche der Geometrie zu Grunde liegen" ("On the hypotheses which underlie geometry"). When this lecture was finally published two years after his death, the mathematical community received it with great praise and it is recognized as one of the most vital and influential contributions to geometry. 
This lecture is the foundation of the field known as Riemannian geometry. 
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