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Mathematicians Encyclopedia Entry 1780050486

Bernhard Riemann was a German mathematician who made groundbreaking contributions to the fields of differential geometry, number theory, and mathematical physics, leaving a lasting impact on the development of modern mathematics. ## Overview Bernhard Riemann was born on September 17, 1826, in Breselenz, a small village in the Kingdom of Hanover (now part of Germany). He was the second of six children to a Lutheran pastor, Friedrich Bernhard Riemann, and his wife, Charlotte Ebell. Riemann's early life was marked by a deep love for mathematics, which was encouraged by his father. He studied mathematics at the University of Göttingen, where he was heavily influenced by the works of Carl Friedrich Gauss and other prominent mathematicians of the time. Riemann's academic career was marked by rapid progress and recognition. He earned his Ph.D. at the age of 20 and was appointed as a lecturer at the University of Göttingen at 24. He became a professor at the same institution at 33 and held this position until his untimely death at the age of 39. Despite his short career, Riemann's contributions to mathematics were profound and far-reaching. ## History/Background Riemann's work on differential geometry and number theory laid the foundation for many subsequent developments in mathematics. His most famous contribution is the **Riemann Hypothesis**, which deals with the distribution of prime numbers. In 1859, Riemann published a paper titled "On the Number of Prime Numbers Less Than a Given Magnitude," in which he introduced the concept of the **Riemann zeta function**. This function has since become a central object of study in number theory. Riemann's work on differential geometry, particularly his development of the **Riemann curvature tensor**, has had a lasting impact on the field. His ideas on the geometry of curved spaces have influenced the development of modern physics, particularly in the areas of general relativity and cosmology. ## Key Information * **Riemann Hypothesis**: A conjecture about the distribution of prime numbers, which remains one of the most famous unsolved problems in mathematics. * **Riemann zeta function**: A function that encodes information about the distribution of prime numbers. * **Riemann curvature tensor**: A mathematical object that describes the curvature of a manifold. * **Differential geometry**: A branch of mathematics that studies the properties of curves and surfaces. * **Number theory**: A branch of mathematics that deals with the properties of integers and other whole numbers. Riemann's contributions to mathematics have been recognized with numerous awards and honors. He was elected as a member of the Prussian Academy of Sciences in 1862 and was awarded the **Bolyai Prize** in 1865. ## Significance Riemann's work has had a profound impact on the development of modern mathematics and physics. His ideas on differential geometry and number theory have influenced many subsequent developments, including the development of general relativity and cosmology. The Riemann Hypothesis remains one of the most famous unsolved problems in mathematics, and its resolution is considered one of the most important challenges in mathematics today. INFOBOX: - Name: Bernhard Riemann - Type: Mathematician - Date: September 17, 1826 - July 20, 1866 - Location: Breselenz, Kingdom of Hanover (now Germany) - Known For: Riemann Hypothesis, Riemann zeta function, Riemann curvature tensor TAGS: **Riemann Hypothesis**, **Riemann zeta function**, **Riemann curvature tensor**, **Differential geometry**, **Number theory**, **Mathematical physics**, **General relativity**, **Cosmology**