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Mathematicians Encyclopedia Entry 1782376467

Bernhard Riemann was a German mathematician who made significant contributions to differential geometry, number theory, and mathematical analysis, leaving behind a lasting legacy in mathematics. ## Overview Bernhard Riemann was born on September 17, 1826, in Breselenz, Kingdom of Hanover (now part of Germany). His father, Friedrich Bernhard Riemann, was a Lutheran pastor, and his mother, Charlotte Ebell, was a homemaker. Riemann's early life was marked by a strong interest in mathematics, which was encouraged by his family. He entered the University of Göttingen in 1846, where he studied mathematics, physics, and philosophy under the tutelage of renowned mathematicians such as Carl Friedrich Gauss and Moritz Stern. Riemann's academic career was marked by rapid progress, and he earned his Ph.D. in mathematics at the age of 20. He then became a lecturer at the University of Göttingen, where he taught mathematics and physics. Riemann's research focused on differential geometry, number theory, and mathematical analysis, and he made groundbreaking contributions to these fields. ## History/Background Riemann's work on differential geometry led to the development of Riemannian geometry, which is a fundamental area of study in modern mathematics. He introduced the concept of curvature, which is a measure of how much a surface deviates from being flat. Riemann's work on curvature led to the development of the Riemann tensor, which is a fundamental object in differential geometry. Riemann's work on number theory led to the development of the Riemann Hypothesis, which is one of the most famous unsolved problems in mathematics. The Riemann Hypothesis deals with the distribution of prime numbers, and it has important implications for many areas of mathematics, including cryptography and coding theory. Riemann's work on mathematical analysis led to the development of the Riemann integral, which is a fundamental concept in calculus. He also made significant contributions to the study of complex analysis, including the development of the Riemann mapping theorem. ## Key Information * Riemann's most famous work is his paper "On the Number of Prime Numbers Less Than a Given Magnitude" (1859), which introduced the Riemann Hypothesis. * He was a pioneer in the development of differential geometry, and his work on curvature laid the foundation for modern geometry. * Riemann's work on mathematical analysis led to the development of the Riemann integral, which is a fundamental concept in calculus. * He was a prolific writer, and his papers and lectures were widely read and admired by his contemporaries. * Riemann was a member of the Prussian Academy of Sciences and the Royal Society of Sciences in Göttingen. ## Significance Riemann's contributions to mathematics have had a profound impact on many areas of study, including differential geometry, number theory, and mathematical analysis. His work on curvature and the Riemann tensor has led to significant advances in our understanding of space and time. The Riemann Hypothesis has important implications for many areas of mathematics, including cryptography and coding theory. Riemann's legacy extends beyond his mathematical contributions. He was a pioneer in the development of modern mathematics, and his work laid the foundation for many of the advances that followed. His emphasis on the importance of mathematical rigor and the need for a deep understanding of mathematical concepts has had a lasting impact on the development of mathematics. INFOBOX: - Name: Bernhard Riemann - Type: Mathematician - Date: September 17, 1826 - July 20, 1866 - Location: Breselenz, Kingdom of Hanover (now part of Germany) - Known For: Riemann Hypothesis, Riemannian geometry, Riemann integral TAGS: Differential geometry, Number theory, Mathematical analysis, Riemann Hypothesis, Riemannian geometry, Riemann integral, Complex analysis, Geometry.