BERNHARD RIEMANN Meaning and
Definition
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Bernhard Riemann was a German mathematician born on September 17, 1826, in Breselenz, Germany, and died on July 20, 1866, in Selasca, Italy. He is best known for his significant contributions to the field of mathematics, particularly in the areas of analysis, differential geometry, and number theory.
Riemann's most important and influential work was his 1854 habilitation dissertation, titled "On the Hypotheses Which Underlie Geometry." In this work, he developed what is now known as Riemannian geometry, which laid the foundation for the modern theory of manifolds and curved spaces. His ideas revolutionized the study of geometry by introducing the concept of non-Euclidean spaces, where the sum of angles in a triangle is not necessarily 180 degrees.
Additionally, Riemann made groundbreaking contributions to complex analysis, with his famous Riemann surface theory profoundly influencing the study of functions of a complex variable. He introduced the concept of Riemann surfaces to represent multi-valued functions, paving the way for new insights into the behavior of complex functions.
Moreover, Riemann's investigations into the distribution of prime numbers led to the formulation of the famous Riemann Hypothesis, which remains one of the most important unsolved problems in mathematics. This hypothesis conjectures that all non-trivial zeros of the Riemann zeta function lie on the critical line with a real part of 1/2.
Overall, Bernhard Riemann's contributions to mathematics and his groundbreaking explorations in diverse areas of the field make him one of the most influential mathematicians of the 19th century.
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Etymology of BERNHARD RIEMANN
The word "Bernhard Riemann" does not have a distinct etymology as it is a combination of a given name and a surname.
The given name "Bernhard" is of Germanic origin, derived from the Old High German "Bern(h)ard", which means "brave as a bear". It is composed of the elements "bern" (bear) and "hard" (brave, strong).
The surname "Riemann" originates from Germany and is of Germanic origin as well. It is derived from the Middle German word "riem(e)" meaning "thong" or "strap", which referred to someone who made or sold leather straps, belts, or harnesses. The suffix "-mann" in German means "man" or "person".
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